Manual of Biostatistics JP Baride, AP Kulkarni, RD Muzumdar
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Biostatistics: (1) It is the science and art of collection, compilation, presentation, analysis and interpretation of numerical data concerned with biological events which are affected by the multiple factors. (2). It is the science which applies the theory of probability to the making of estimates and inferences about the characteristics of population.
First definition explains the steps (collection, compilation, presentation, etc.) through which data goes during the statistical process. By saying that it deals with the “Biological events”, it has differentiated itself from pure statistics which does not deal with these events. The second definition has outlined the applications of biostatistics.
Population (Universe) and Sample: In biostatistics the term “population” is us ed to denote the “units” under study. Thus, if we want to study all the individuals in a city, all individuals will form a population. On the contrary, if we want to study air pollution in all cities in a district, then all cities will form the population. The term population incudes all persons, events and objects under study. If the objective is to assess the quality of tablets of a batch, then all tablets from that batch form the population. Sample is the portion of the population selected by a process called “Sampling”. Instead of studying the entire population only sample is studied. If sampling process is correct and scientific, then one can make reasonable estimates about the population. Population is defined (described) in terms of size, structure, time-frame, geography, and nature.
In terms of size, the population can be finite or infinite. When the units in population are countable, the population is finite. (e.g. students in a class, individuals in a country). When the units in the population are not easily countable (e.g. world population) or can be created by infinite permutations/ combinations (e.g. throws of a dice) the population is said to be infinite.
In terms composition, the population can be homogenous or heterogenous. When there is practically very little variation in the characteristics of the units in the population then it is homogenous population. (e.g. size of the tablets in a bottle). When there is wide variation in the characteristic under study, the population is heterogenous. 2It may be noted that the population may be homogenous for one characteristic and heterogenous for other.
Population needs to be defined in terms of time. Thus, when we speak of population of a city or country, we must specify the time we are referring (i.e., population of 1991 or 2001).
When we speak of the population of a town or a state, we are actually defining the geographic limits of the population.
In terms of nature, the population can be static or dynamic. When the units in the population change very frequently, thereby affecting the parameter, the population is said to be dynamic. (e.g. patients in a hospital). When the population units do not change frequently, then it is called static population. It may be noted that the population can be static for one characteristic and dynamic for the other.
Parameter and Statistic: Parameter is a constant that describes the population, while statistic is a constant that describes the sample. In a college (population) there are 40% girls. This describes population, hence is a parameter. If in a sample of 200 students from this college, we find that there are 90 (45%) girls, then 45% will be statistic as it describes sample. For a given characteristic of the population there will be only one parameter. However, there can be as many statistic as are the number of samples. If the statistic is based on scientific sampling, we can have reasonable estimate of parameter.
Attribute and Variate: When we study population, we may be interested in its different aspects. Together these are called characteristics and are of two major types. Attribute is a characteristic based on which the population can be divided into categories or classes. A unit in the population can belong to one of these categories/classes. Sex, caste, religion, severity-grade of a disease are some of the examples of attribute. When there are only two categories in the data, it is dichotomous data. Variate is a characteristic which has a scale of measurement (e.g. height, weight, Hb%, income, I.Q. etc). A continuous variate is the one which theoretically can assume any value from zero to infinity. The measurement can thus, exist in fractions or decimals (e.g. height, weight). A discrete variate is the one which even theoretically cannot be measured in fraction or decimal (e.g. size of a family, RBC/WBC count).
Inference: Inference is a process of drawing conclusion based on the data and some statistical applications. Usually, the inference is about the parameter based on the statistic. The inference can be about magnitude, difference or association. Usually, the inference is about the parameter (mostly unknown) based on statistic. We define the population, examine it and find the prevalence of a disease in the sample. This is statistic. Based on this we make an estimate about the prevalence of the disease in population (Parameter). When after a study we conclude that “boys are taller than girls” we are actually drawing inference on the difference. Similarly, when we conclude that “tall person is also likely to be heavy” we are in fact declaring our inference on the association between height and weight.
Forecasting: Forecasting is a method of making prediction about one characteristic in a unit in population based on some other characteristic or characteristics. Making prediction about birth-weight of newborn based on some maternal measurements like abdominal girth is an example of forecasting. Forecasting involves examining the units in population for the characteristics under study and finding if any pattern exists in their relationship.
The word “Statistics” conveys different meanings to different persons. Some common viewpoints are described below.
  1. Statistics as a numerical data: Here, statistics tells us the facts that it deals with figures, counts, and measurements. It is thus affected by the collection process and personal bias.
  2. Statistics as a tool: A car mechanic uses specific tool for specific procedure. Similarly, a statistician uses specific procedure for specific objective. Statistics provides us with the tools for data collection, presentation, analysis, and interpretation.
  3. Statistics as a science: Any branch of knowledge cannot become science unless it has a firm foundation of principles, laws, tests, and theories. Based on these, the discipline can make firm predictions. Due to the existence of laws and theory of probability, principle of normal distribution, tests of significance etc, statistics has earned a status of science. In fact, due to this very reason, it finds wide applications in varied disciplines like agriculture, weather forecasting, politics, and health.
Data can be classified in following ways:
  1. Based on characteristic,
  2. Based on source,
  3. Based on field, and
  4. Based on contents.
  1. Based on characteristics: The data can be of following sub-types.
    Qualitative: Relates to attribute
    Quantitative discrete: Relates to discrete variate
    Quantitative continuous: Relates to continuous variate.
  2. Based on Source: If the data is derived from the direct measurements/observations on the population units, it is primary data. (e.g. observations based on the actual measurement of height, weight, Hb% etc of individuals by the investigator/ or his team). When the data is not derived from the primary source, but is derived from sources like records it is secondary data.
  3. Based on field: In computer database management software, data is arranged in tabular form. The columns are called fields and rows are records. Each field can hold record of its type which needs to be described at the time of creation of database. The common types of fields are character type, numeric type, date type, and logical type.
    Character type: e.g. name, address
    Numeric type: e.g. age, height, weight, blood sugar level, systolic/diastolic BP, serial number etc.
    Date type: e.g. date of birth, date of admission, date of discharge etc. The date can be expressed in British format (dd/mm/yyyy), American format (mm/dd/yyyy), or ANSI format (yyyy/mm/dd) format.
    Logical type: This refers to dichotomous data, e.g. sex (male/ female), result of drug trial (cured/not cured), residence (urban/ rural) etc.
  4. Based on contents: Depending on the contents, the data can be classified into four types as below:
    1. Nominal data: It is another name for qualitative data. Here, the data is presented as frequency distribution of some characteristics like sex, religion etc. The groups 5do not have any logical order. There is no implication of order or ratio of the adjacent categories. When there are only two possible categories, the data is named dichotomous (e.g. smokers/non-smokers, male/female).
    2. Ordinal data: Here, the data is presented according to rank or order. There is thus, a logical order. (e.g. frequency distribution of students according to the rank in an examination.) Here, there is no implication of class-interval. In the example quoted, the difference in the marks obtained by first/ second and second/ third student may not be equal. The groups are thus, not equidistant for marks. Since, it relates to rank, true zero does not exist.
    3. Interval data: In this type, the data is placed in meaningful intervals and order. For example, frequency distribution of patients according to temperature groups like below 37°C, and above 37°C. Here, the groups are meaningful because, the difference in the temperature of 37°C and 36°C, and 38°C and 37°C is equal, i.e. 1°C. However, there is no implication of ratio in the sense that 30°C is not twice as hot as 15°C.
    4. Ratio data: In this type, the data is presented in frequency distribution in logical order and meaningful groups. In addition, a meaningful ratio exists. For example, frequency distribution of pulse rate, height, weight etc. Thus, pulse rate of 120 is twice as fast as that of 60. Similarly, a person with weight 80-kg is twice as heavy as the one with weight of 40 kg. Further, in this data type, a true zero exists. For example, pulse rate of zero means no pulse at all.
The differences in these four data types are summarized below:
Nominal Data
Ordinal Data
Interval Data
Ratio Data
  • Logical Order
  • Meaningful Group-interval
  • Meaningful Ratio
  • True Zero
In any statistical exercise, the identification of the type of data is essential for following reasons.
  1. It helps further analysis,
  2. It helps selection of data presentation method, and
  3. It helps selection of test of significance.
Following methods are commonly used for data collection:
  1. Measurement: In this method the required information is collected by actual measurement in the object, element or person. The measurement and actual enumeration generates primary data.
  2. Questionnaire: In this method a standardized and pretested questionnaire is sent and the respondents are expected to give the information by answering it. The success of this method depends on the quality of questionnaire, the enthusiasm of the respondents and the ability of the respondents to give accurate and complete information. By this method the information about large number of attributes and variates can be collected in a short-time.
  3. Interview: This method can be used as a supplement to the questionnaire or can be used independently. Here the information is collected by face to face dialogue with the respondents. The success of this method depends on the rapport established between the interviewer and the respondent, ability of the interviewer to extract the required information from the respondent and the readiness of the respondent to part with the information.
  4. Records: Sometimes the information required can be available in various records like census, survey records, hospital records, service records etc. The utility of the information depends on its uniformity, completeness, standardization, accuracy and the reasons for which the information was recorded.
Problems in Data Collection
  1. Variation: The term biological variation is used for variation that is seen in the measurements/counts in the same individual even if measurement/enumeration method is standardized and even if the person taking measurement/ making counts is same. Blood pressure of an individual can show variation even if it is taken by identical method, applying identical criteria and even if it is measured by the same person. The term sampling variation is used for variation seen in the statistic of two samples 7drawn from same statistical population. (Even if there are 40 % girls in a college, two samples of identical size drawn from this population may vary from this parameter and may show difference between them).
  2. Mistakes and errors: These are of three types.
    1. Instrumental error /technical error: These are introduced as a result of faulty and unstandardized instruments, improper calibration, substandard chemicals etc.
    2. Systematic error: This is an error introduced due to a peculiar fault in the machine or technique. This gives rise to same error again. For example, if the ‘zero’ of the weighing machine is not adjusted properly, it will give rise to a systematic error. In Chinese method of measuring the age, a person born anytime in a calendar year is considered as one year old. If the age is counted by this method, it will give rise to a systematic error when compared to our method of measuring the age of the person.
    3. Random error: Random error is introduced by changes in the conditions in which the observations are made or measurements are taken. For example, a person may stand in different positions at two different times, when his height is being taken. A person may tell his age differently when asked on two different occasions. In such cases even if the instrument/method is good an error can occur. The error due to this phenomenon will not be constant or systematic.
    Errors and mistakes can be prevented/minimized by
    1. Using standard, calibrated instruments.
    2. Using standardized, pretested questionnaire.
    3. Using trained, skilled persons.
    4. Using multiple observations and averaging them.
    5. Using correct recording procedures.
    6. Applying standard and widely accepted statistical manipulations (Calculations).
  3. Bias: Bias is a systematic error which is introduced in the study due to various reasons. Bias results in tendency to produce results that differ in systematic manner from the true values.
Three major types of bias have been described below:.
  1. Selection bias: When the persons selected for the study systematically differ from those not selected, selection bias occurs. This type of bias occurs when the entry in the study is not random but is left to the persons concerned. Selection of volunteers and exclusion of those not volunteering, exclusion of those absent due to sickness introduce selection bias.
  2. Measurement bias: This is also called as classification bias. This results when the criteria used for measurement/ diagnosis of the disease and exposure are not standardized or if they are inaccurate, imprecise and ambiguous. Use of faulty and un-calibrated instruments, substandard chemicals, faulty questionnaire, untrained/inexperienced staff etc. result in measurement bias.
  3. Confounding bias: In epidemiological study we assess the association between an exposure factor and an outcome. It is possible that, both of these may be associated with a third factor. This is called confounding factor. To be eligible to be labelled as confounder, the factor should fulfill following criteria:
    • It should be a risk factor for outcome under study.
    • It should be associated with the cause under study in the population from which cases are drawn.
    • It should not be a cause of outcome.
Under this situation, the association between the factor under study and the outcome could be due to the confounding effect and the bias so introduced is called as confounding bias. Restriction of the study to limited number of variables, matching, stratified analysis, and multivariate analysis are some of the techniques that can deal with the problem of confounding bias.
Precautions in Data Collection
  1. Standardization: One of the objectives of data collection is to compare with similar studies. However, the comparison is difficult and at times impossible if the data collection methods differ. Using standard and universally accepted methods and techniques reduces these problems to a great extent. Use of standard, pretested questionnaire, use of universally accepted methods and techniques, use of standard definitions for categorization (classification) are some of the techniques used in this context.
  2. Training: Training of the persons involved in data collection ensures uniformity, accuracy, and completeness of the data collection. The training is required for various measurements, use of questionnaire and in interview methods.
  3. Pretesting.: Even if standard methods/techniques are used and trained persons are employed, data collection needs pretesting especially if interview/ questionnaire is used. Pretesting is a sort of mock trial of the exercise of data collection, but on a smaller scale. Preferably, it should not include the population in actual study. Pretesting avoids ambiguities, inaccuracies and uncertainties. It can also be used as a training exercise for the personnel involved.
  4. Storage: If the time duration between data collection and analysis is expected to be long some sort of durable storage device for collected data must be used. Registers, cards, folders, punch cards etc were used in the pre-computer era. Storage of data in computer has added advantage of retrieval, ease in data presentation and analysis. Care should be taken to protect the data from insects, rats and environmental changes.
Compilation of data involves following important steps:
  1. Data Editing: Data editing is correction for incompleteness, inaccuracies, illegal entries, and inconsistencies in data. Some examples are given below.
    • Non-recording of weights of few students.
    • Recording of period of gestation in weeks for some and in months for the remaining women.
    • Recording age as on 1st January for some and as on the date of interview for some persons.
    • An eighteen year old mother with 4 children.
    • Puerperal sepsis as a cause of death in male.
    • Entry of a fifty year old woman in a study designed for women 15 to 44 years only.
    Use of standard/ pretested formats, inclusion of detailed instructions with data entry schedule, training of persons involved, supervision, sample checking, checks introduced in data schedules, computerization of data entry are some of the data editing techniques.
  2. Data Reduction: Data reduction is the reduction of voluminous raw data in manageable amount for the purpose of presentation and analysis. In epidemiological studies we are interested in person, place and time distribution. Obviously, this requires grouping of raw data in various person, place and time units. Tabulation is the most common method of data reduction. If the objectives of study are clear and preset, dummy tables are created in the study protocol itself. Conversion of raw data into tables and graphs with the help of various computer application software like MS-Excel, Lotus, SPSS, EPI-Info is also possible. Data reduction involves a compromise between loss of details and compactness achieved.
Frequency distribution is the summary of the number of times different values of a variable occur. Data in Table 1A is an example of frequency distribution of marks (out of 100) obtained by students in an examination.
Table 1A   Frequency distribution of marks
Cumulative %
50 or below
When presented without any data reduction, it is called simple frequency distribution. When presented with data reduction (example: column 1 and 2 in Table 1A) it is called grouped frequency distribution. When presented as proportion or percentage of groups (example column 1 and 3 of Table 1A), it is called relative frequency 11distribution. When presented as data in column 1 and 4, it is called cumulative frequency distribution. Graphical presentation of cumulative frequency of grouped data is called ogive (see Figure below).
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Objectives of Data Presentation:
  1. To arouse the interest of the readers.
  2. Data reduction without compromising details.
  3. To enable readers to have quick grasp and impression to draw meaningful impressions.
  4. To facilitate further analysis.
  5. To facilitate communication.
Methods of Data Presentation:
  1. Informal: Text and semitabular
  2. Formal : Tables, graphs, centering constants and measures of variation.
    (These are described in detail elsewhere in this book).
Tabular presentation is most common method of data reduction and involves presentation of raw data in columns and rows.
Precautions in Tabular Presentation
  1. Table should have a title describing “what”, “where”, and “when”. Title should be clear, concise and self explanatory.
  2. Columns and rows should have appropriate sub-titles.
  3. The group-intervals in columns and rows should not be too narrow nor too wide to defeat the purpose of data reduction. Same is true about the number of groups (columns and rows) made. The group-intervals should be mutually exclusive and there should be no overlapping.
  4. Units of measurement (like years for age, kg for weight, cm for height) should be mentioned.
  5. Full details of deliberate exclusions if any should be given.
  6. Short-forms/ symbols used if any should be explained in footnote.
  7. No place in the body of tables (cells) should be left blank.
  8. Source of data, if imported, should be mentioned.
Types of Tables
  1. Reference table or master table: This table shows all variables that can be cross classified. In fact, it contains all the result of data reduction.
  2. Correlation table (Table 1): This shows the two quantitative variables cross classified in many classes. It is used to calculate correlation coefficient (r).
  3. Association table (Table 2): This table shows association between two qualitative variables. It is also required for calculating sensitivity and specificity of screening test.
  4. Two by two table: This table just shows frequency distribution of two variables or two classes (Table 3).
  5. Text table: It is descriptive table. It does not contain any numerical data (Table 4).
Table 1   Height in cms and weight in kg of 440 college students
Table 2   Association between Tuberculin and Lepromin Test
Tuberculin Test
Lepromin Test
Table 3   Sex distribution of students in two colleges
Table 4   Some information about the authors of this book
This is a visual presentation of data. It makes data interesting and makes its understanding easy even for illiterate persons. A meaningful impression can be attained even before one starts analyzing the data in depth.
Precautions in graphical presentation:
  1. Each graph should have a self explanatory title like a table.
  2. Horizontal axis (X-axis) is absicca, while the vertical axis (Y-axis) is ordinate. The scales for both the axis should start from zero. The scales should be so selected that there is optimal utilization of paper. The scale should be indicated, with unit of measurement, at an appropriate place in the presentation.
  3. If there is a break in continuity, it should be shown with a broken line.
  4. Key (legend) should be self explanatory.
Types of graphs: Although, there are many types of graphs, description of all of them is beyond the scope of this book. Following graphs are described.
Bar diagram
Pie diagram
Line diagram
Arithlog paper
Epidemic curve
Bar diagram (Bar chart): This type of graph is indicated for qualitative and quantitative discrete data. Variables are depicted as bars of equal breadth. Length of the bar is proportional to the frequency of variable. As a rule the distance between bars is kept equal to or less than the breadth of the bars. The frequency may be shown on Y-axis (vertical bars) or on X-axis (horizontal bars.) In simple bar chart a single variable is depicted (Fig. 1).
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Fig. 1: Admission capacity of medical colleges
A multiple bar chart (MBC) exhibits more than one variable. However, it is customary to limit the variables to four (Fig. 2). Unlike MBC, in proportional bar chart, instead of absolute frequency, proportion (or percentage) of variables is depicted (Fig. 3).
Pie diagram (Pie chart): This type of presentation is indicated for qualitative and quantitative discrete type of data. The frequency of a variable is compared as a segment of a circle. If the frequency of a variable is A in total of N, then the segment allocation to it in a circle is = A × 360/N. In this way allocation for all variables is calculated and represented in a circle (Fig. 4).
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Fig. 2: Sexwise strength in different faculties
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Fig. 3: Proportional bar chart: Proportional distribution of boys and girls in different faculties
Histogram: Histogram is method of choice for quantitative continuous data. It is an area diagram consisting of series of adjacent blocks (rectangles). Entire area covered by the rectangle represents the entire frequency and the area covered by the individual block represents the frequency of the variable represented by that block. Histogram can deal with the data with unequal class-intervals also. X-axis represents class-interval and Y-axis represents frequency per unit of class interval. Frequency polygon is a linear representation of histogram. The centres of top of each rectangle are joined by a line. Due to difficulty in understanding histogram/ frequency polygon are not very popular methods.
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Fig. 4: Distribution of beds in a hospital
Line diagram: Line diagram is used to represent change in frequency of a characteristic over a period of time (Fig. 5). This can uncover trend if any. Presuming the change is likely to continue, one can predict (forecast) the frequency of the characteristic at anytime outside the range of observation. This is called extrapolation. Estimating the frequency of the characteristic at anytime within the range of observation is called interpolation. When the frequency at one of the extreme period (time), usually beginning, is presumed to be one (or 100) and frequencies of other periods is computed proportionately and line diagram is drawn it is called proportionate line diagram. It is used to compare proportionate change in two variables over a period of time.
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Fig. 5: Crude death rate (CDR) and crude birth rate (CBR): India 1941-1999
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Fig. 6: Relative decline crude death rate (CRD) and crude birth rate (CBR): India 1941-1999
(e.g. crude birth rate and crude death rate: Fig. 6). Note that compared to Fig. 5.) It is relatively easier in Fig. 6 to appreciate that the rate of decline is faster for CDR as compared to CBR. However, the frequency assigned to variables in Fig. 6 is relative to that in the base year i.e. 1941 to 1951.
Scatter Diagram: This graphical presentation is used to show relationship if any between two quantitative variables. It is customary to depict independent variable on X-axis and dependant variable on Y-axis. The general direction (trend) of the dots on graph indicates whether there is any positive or negative correlation in the two variables. Following data is used for Fig. 7.
Crude Death Rate
Life Expectancy (Yrs)
It is clear from Fig. 7 that the relationship between CDR and LE is negative type, i.e. as the CDR decreases the LE increases.
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Fig. 7: Scatter diagram: Crude death rate and life expectancy
Pictogram: This method is indicated for qualitative or quantitative discrete data. Frequency of a characteristic is displayed alongside a picture which has some resemblance to the characteristic depicted.
Spot map: Spot map is used to show occurrences of events with reference to geographic locations. It is very useful tool for showing “Place distribution” in epidemiological studies. Fig. 8 shows one such spot map of an outbreak of typhoid. The figures in parenthesis indicate population and those outside indicate the number of cases. It is clear from this map that there is some problem in the south-east section of the village that needs investigation.
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Fig. 8: Spot map: Typhoid cases in a village
Epidemic curve: Epidemic curve is used to show the occurrence of events with passage of time. It is used to present “Time distribution” in epidemiological studies. It is seen from Fig. 9 that maximum cases occurred in fourth week starting 1st December, 1996. The origin of outbreak should therefore, be traced to a period 2 to 3 weeks (= incubation period of typhoid) before this week.
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Fig. 9: Weekly distribution of typhoid cases in an outbreak
(Sigma) Means summation of
Standard deviation of sample
(mu), Standard deviation of population
π or Π
(pi) Universal constant, result of 22 ÷ 7
Numeric value of a variable in sample/ population
Arithmatic mean of variable in sample
Arithmatic mean of variable in population
Size of sample
Size of population
Proportion of an attribute in sample
Proportion of an attribute in population
Less than
More than
Not equal to
Alpha, used to denote Type-I Error
Beta, used to denote Type-II Error
Used as an alternative to sign of multiplication (x).
Centering constants are also termed as “Measures of central tendency”. Three types of centering constants are used: Mean, Median, and Mode.
Mean: When one speaks of mean (or average), he is usually referring to arithmatic mean. Mathematically, it is the summation of all observations and dividing it by the total number of observations.
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For population mean:
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For grouped data, in which each group also contains large number of observations, the center point of each group is decided first. (m1 for group 1, m2 for group 2, m3 for group 3 and so on. It is the arithmatic mean of the minimum and maximum value in the class/ group interval.). These centre points are then multiplied by the number of observations in the respective group. (m1*n1, m2*n2, m3*n3 and so on.) All these are then added and divided by the total number of observations, i.e. N
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Other means that are also used in statistics are: Geometric mean and harmonic mean. Arithmatic mean is affected by all the observations as each contributes to its calculation. However, the effect of extreme values is more as compared to those values that are nearer to the mean.
Median: Median is the middle observation if the series is arranged in ascending or descending order. If n is an even number, then the arithmatic mean of the middle two observations is taken as the median. Unlike mean, median is not affected to a great degree by extreme values. It is a useful expression for skewed measurements like age structure of population.
Mode: It is the most frequently occurring observation. If there are two observations that occur most frequently, the series is said to have “Bimodal distribution.” Mode is not used much in biostatistics.
These are also called measures of dispersion. Centering constants are representative values of the series. They do not express the range of normalness. Centering constants together with measures of variation help understanding of the data better than the centering constants alone. Following measures of variation are commonly used: Range, inter-quartile range, percentiles, average deviation, standard deviation, variance, and coefficient of variation.
Range: It is the statement of minimum and maximum value. It just describes the spread of the observation, but does not quantify the variation.
Interquartile Range: The series of observation is divided into two halves and median is located. If n is an even number, then medians for both halves are located presuming each half to be an independent series. If n is an odd number, median of the series participates in locating the median of both upper and lower halves. Lower median and upper median is the interquartile range and it contains middle 50% observations. It is a better indicator of variation than the range.
Percentile: Median divides the series into two equal halves. If the series is divided into 10 equal halves each part will be called “decile”. Similarly, if the series is divided into 100 equal parts each part will be called “percentile”. Here, median would be 50th percentile. Nine hundredth observation in a series of 1000 observations will be 90th percentile. The percentiles are commonly used in nutritional studies and I.Q. studies.
Average Deviation: It is the arithmetic mean of the difference of each observation from mean of the series. Here, both negative and positive differences are treated as positive. Mathematically, it is calculated as below.
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Standard Deviation (S.D.): It is “the square root of the average of the squared deviations of the measurements from their mean”. The steps involved in calculation of S.D. are:
  1. Calculate arithmetic mean (m or M)
  2. Calculate difference of each measurement with mean (x – m) or (x – M)
  3. Calculate squares of each of the differences. (x – m)2 or (x – M)2
  4. Add all squared differences. Σ(x – m)2 or Σ (x – M)2
  5. Divide the summation by n − 1 or N
  6. Calculate square root. So that
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Example 1: Hb of 10 women in gm% is shown below. Calculate S.D. 10.0, 9.8, 9.0, 9.2, 9.3, 8.3, 7.0, 11.0, 7.8, 10.0
(x – m)
(x – m)2
n = 10
m = 91.4/10
 = 9.14
Using eqn-5:-
s = √{(12.504)/(10−1)}
= √1.3893
= 1.17 gm %
Totals: 91.4
Uses of Standard Deviation:
  1. It is the most commonly used measure of variation.
  2. Its calculation is a preliminary step in calculation of variance and coefficient of variation.
  3. Its calculation is a preliminary step in tests of significance.
  4. It is used to decide whether a given observation is common or uncommon. Measurements beyond the range of ± 2 S.D. are considered as uncommon or rare. Rare measurements are also likely to be abnormal.
Variance: Variance is the square of S.D. In Example 1 shown above, variance will be = 1.3893. Since it is square of S.D., it has no unit of measurement. It is used in advanced statistics.
Coefficient of Variation (CV): It is the ratio of S.D. and mean expressed as percentage.
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CV is useful in comparing variation in two characteristics with different units of measurement like height and weight, Hb% and E.S.R. etc.
In statistics various types of distribution are described. Some of these are binomial, poisson, skewed, and normal (Gaussian) distribution. The normal distribution is the most commonly used among these. It was described by De Moirre and Gauss independently in the year 1733. It is a symmetrical distribution and fundamental to many tests of significance. “Normal” is the name given to the distribution. So, one should not expect to know about “Abnormal curve”, because none exists at least in statistics !
Characteristics (Properties) of Normal Curve
  1. It is bilaterally symmetrical, bell shaped curve.
  2. The frequency of measurements goes on mounting (increasing) from one side, reaches peak, plateau and then goes on declining exactly as they have mounted.
  3. The highest point in the frequency distribution represents mean, median and mode.
  4. An ordinate dropped on X-axis from the top of the curve divides the area into exactly two equal halves. Traditionally, the left half represents measurements less than mean.
  5. Mean median and mode are identical.
Standard Normal Curve: The look of frequency distribution of a variable which has normal distribution will depend on its S.D. If S.D. is large, it will have a broad base, while if S.D. is small (in magnitude) it will be narrow at base. This poses difficulty in universalization of normal distribution, which is solved by a procedure called “standardization of normal curve.”
Example – 2:- Let us consider two variables Hb% and height. Say, in 1000 students the mean and S.D. are as below.
Unit of Measurement
Mean (m)
If we draw frequency distributions for these variables, measurements 12.0 gm% and 12.5 gm% of Hb will be 1 and 2 S.D. more respectively than that of its mean (i.e. 11.5 gm%). Similarly, measurement 154 cm. and 156 cm. will be 1 S.D. and 2 S.D. more than its mean i.e. 152 cm. It is seen that although the units of measurements are different, measurements Hb =12 gm % and height = 154 cm are brought to same plain because they are 1 S.D. more than their respective means. Same is true for measurements Hb =12.5 gm% and height = 156 cm, as they are 2 S.D. more than their respective means. This has been possible because instead of using the respective units of measurement (gm % and cm.), in this example, we have used S.D. as the unit of measurement to place a specific measurement with reference to its mean. This procedure wherein we use the unit of S.D. to place any measurement with reference to mean is called “standardization of normal curve”. The curve or frequency distribution diagram that emerges through this procedure is called “standard normal curve”. This “unit of standard deviation” is named as “relative deviate”. R.D. for a given measurement in a sample or population can be calculated with the help of equations 6 and 7 respectively.
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Properties of Standard Normal Curve: In addition to the properties of normal curve mentioned above, standard normal curve has following properties:
  1. Mean, median and mode are identical and are presumed to be zero.
  2. Area under curve is presumed to be 1.
  3. Theoretically, the curve does not touch baseline, as it is based on infinite number of observations.
  4. The area under the curve can be transferred into what is known as ‘relative deviate scale’. Tables with this scale are prepared by the statisticians and one such table is reproduced in appendix A.
The graphical concept of standard normal curve is shown in Fig. 10.
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Fig. 10: Graphical concept of normal curve
Relative Deviate: (R.D. or z): R.D. is the estimate of a given measurement in units of S.D. Its calculation for an observation in a sample or population is done with the help of equation numbers 6 and 7 respectively. In example 2, the z value for Hb% = 11.7 will be = (11.7 − 11.5)/0.5 = 0.4. Similarly, z value for height will be = (149 − 152)/2 = −1.5. The area under normal curve for common z values is as below.
  • Mean ± 1 z = 68%
  • Mean ± 2 z = 95%
  • Mean ± 3 z = 99%
(These are also called 68%, 95%, and 99% “confidence limits or confidence intervals.”)
Uses of the Concept of Normal Curve
  1. To give an estimate of the number of units in a given range of measurement: If we are given mean and S.D., then with the help of the concept of normal curve, we can give an estimate of number of units in any given range of measurements.
    Example 3: (Fig. 11): From the data in example 2, find out the number of individuals in the range of height of 152 cm and 154 cm. Here, we calculate z for x = 154 cm with the help of equation 6
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    The area under curve for z = 1 is 0.3413 (Appendix-A, column 2, line 12). This means the area to be estimated is = 0.3413. Since, the total area is 1.0, the number of patients in the range will be 34.13 % or approximately 341 (out of 1000).
    Example 4: (Fig. 11): From the information in example 2 and 3, how many persons will have height above 154 cm.? Here also we have to find z for x= 154. This has already been done in example 3. Standard normal curve is a symmetrical entity. So, area under curve on either sides of mean = 0.5. So, 0.5 − 0.3413 = 0.1587 is the area to be estimated. Thus, about 159 individuals will have height 152 cm or more.
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    Fig. 11: Graphical presentation of example 3 and 4
    Example 5: (Fig. 12): Here, we have to find areas for x = 154 cm (Area A in Fig. 12) and for x = 151 cm (Area B in Fig. 12). Area A is already calculated in example 3 and is 0.3413. For area B, z for x = 151 is calculated with the help of equation 6 and is 0.5. Area for z = 0.5 is 0.1915 (Appendix-A, column 2, line 7). Total area A + B = 0.3413 + 0.1915 = 0.5328. Thus, about 533 individuals will have height in the range of 151 cm to 154 cm. (It may be noted that we calculate areas A and B separately, find the areas and add them. Addition of z values and finding area for summation of z values is a common mistake). By the logic applied in example 4, area for height less than 151 cm will be 0.50 − 0.1915 = 0.3085.
  2. To decide common/uncommon measurements: By convention any value beyond the range of 95 % confidence limits is considered as uncommon or rare.
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    Fig. 12: Example 5
    Thus, to the extent of the example 2, height above 156 cm and below 148 cm will be considered as uncommon or rare as these are beyond 95 % confidence limits.
When two samples of same size are drawn from a population, their means (m1 and m2) show variation with reference to each other and with reference to the population mean (M). This variation shown by the samples is known as sampling variation. This is dependent on two factors: i) variation in the universe as quantified by the S.D. (μ) of the population, and ii) the sample size (n). More the variation in universe more will be the variation in samples. Lesser the sample size more will be the variation. Interestingly, the means of the samples (m1, m2, m3 etc) show normal distribution around population mean (M). This is analogous to individual measurements (x1, x2, x3 etc.) showing normal distribution around sample mean (m). Thus, the confidence limits (or Confidence-Interval C.I.) for sample means would be as shown below.
  • 68% C.I. = M ± 1 μ
  • 98% C.I. = M ± 2 μ
  • 99 % C.I. = M ± 3 μ
However, population mean (M) and S.D.(μ) are rarely known. In order to circumvent the problem, statisticians have devised tool called 28standard error of mean (for quantitative characteristic) and standard error of proportion (for attributes). The presumptions in both the tools is that the statistic mean of the sample (m) and S.D.(s) of the sample are the best estimates of their respective parameters, i.e. the mean of the population (M) and S.D. (μ) of the population.
S.E.M. is calculated for quantitative characteristic with the help of following equation:
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Thus, estimates of M would be as under.
  • 68 % C.I. = m ± 1 (S.E.M.)
  • 95 % C.I. = m ± 2 (S.E.M.)
  • 99 % C.I. = m ± 3 (S.E.M.)
Applications of S.E.M.
  1. Estimation of Mean of the population: As said above, most of the times the mean of the population is unknown. With S.E.M. we can make a reasonable estimate of the population mean with the help of a representative sample drawn from the population. Most commonly accepted estimate is that of 95 % C.I. indicated above. If m is the mean of the sample, and s is the S.D. and SEM is the standard error of mean, then m ± 2 (SEM) will be a reasonable estimate of M (mean of the population).
    Example 6: If mean birth weight of a sample of 100 newborns was 2.5 kg with S.D. 1.1 kg give an estimate of the birth weight of newborns in the population.
    Here m = 2.5, s = 1.1, and n = 100.
    So that S.E.M. (using equation − 8)
    = 1.1 ÷ √100
    = 0.11
    Thus, estimate of 95% C.I. will be 2.5 ± 2(0.11) i.e. 2.28 to 2.72.
  2. Statement about sample: With S.E.M. one can judge whether a given sample is likely to belong to a population with known parameter.
Example 7: Mean birth weight of Indian baby is 2.8 kg. In a sample of 200 newborns of mothers with history of tobacco consumption during pregnancy, the mean birth weight was 2.5 kg with S.D. 1.2 kg. Comment.
Here M = 2.8 kg, m = 2.5 kg, s = 1.2 kg, and n =200
∴ S.E.M. = (1.2 ÷ √200) = 0.0848
The 95 % C.I. for population would be:
2.5 ± 2 (0.0848) = 2.33, 2.67
The population parameter (2.8 kg) is well beyond this range. Hence, the sample is less likely to belong to population with mean birth weight 2.8 kg (Note that here the word ‘population’ is used in statistical sense). In essence it means that the newborns of mothers with history of tobacco consumption will have lower birth weight (in the range of 2.33 kg to 2.67 kg) and this will be lower than the national average.
SEM is a measure for quantitative characteristic. SEP is a measure for qualitative characteristic. Like means of samples, the proportion of an attribute (p1, p2, p3 etc) in repeated samples of same size (n) show variation within themselves and with reference to population parameter (P). This is due to sampling variation. Like means of samples, the proportions of an attribute in samples of fixed size show normal distribution around the parameter. The tool analogous to SEM for attribute is SEP
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Here p is the proportion of persons with an attribute and n is the sample size. (1-p is the proportion of the persons without the attribute in question). With SEP the confidence limits for the parameter (P) would be:
  • 68% C.I. = p ± 1 (SEP)
  • 95% C.I. = p ± 2 (SEP)
  • 99% C.I. = p ± 3 (SEP)
Application of SEP
  1. Estimation of parameter: As said above, the proportion of an attribute in a sample, i.e. p (the statistic) can be used to have an 30estimate of the proportion of the attribute in population, i.e. P (the parameter). Estimate of 95% C.I. is usually accepted.
    Example 8: In a randomly drawn sample of 250 individuals aged 35 years and above in a city, 5 individuals were found to be diabetic. Give an estimate of the number of diabetics if the total population of individuals 35 years and above is 10,000.
    Here p = 0.05, n = 250; Using Equation 9
    S.E.P. = √{ 0.05 (1 − 0.05)/250} = 0.013
    95% C.I. = 0.05 ± 2(0.013) = 0.024 to 0.076
    The number of diabetics works out to 240 to 760 in those aged 35 years and above in the city.
  2. Making statement about the sample: With the help of S.E.P., we can draw an inference on the possibility of a sample drawn from a population with known parameter.
Example 9: Sex ratio of a city is 933. In an outbreak of the total 410 cases 208 were females. Comment.
Sex ratio is the number of females per 1000 males. From this, the proportion of females (P) in the city works out as below:
P = 933 × 1000/1933 = 0.4826
Proportion of females in sample (p) is
= 208/410
= 0.5073
S.E.P. = √{0.0.5073 (1 − 0.5073)/410}
= 0.0246
Based on this, the 95% C.I. would be:
= 0.5073 ± 2(0.0246) = 0.4481 to 0.5665
It is seen that parameter (P = 0.4826) is included in this range. Thus, we can say that the sample could very well be from a population in which proportion of females is = 0.4826 (or 48.26%). There is no reason to believe that females have been disproportionately more affected by the disease. We could have said this if the population parameter (P) would have been outside the C.I.
The concept of probability is very important in statistics. Probability is possibility of occurrence of any event or a permutation/combination of events. For example, probability of drawing an ace from a pack of 52 cards is 4 out of 52. This is because there are 4 aces in a pack of 52 cards. Similarly, probability of show of “one” in one throw 31of a six sided dice is 1 in 6. In a throw of coin, probability of “Head” is 1 in 2 as the coin has 2 sides only. By application of statistics we can estimate the probability of “aces” in subsequent draws from a pack of 52 cards, or probability of throw of “2” in successive throws of a dice, or probability of “Head” in two successive throws of coin. Probability of various permutations and combinations can be worked out. In biostatistics, especially in various tests of significance, we are interested in “Probability (P) of the observed difference in two samples due to chance (i.e. due to sampling variation.” Here the probability scale has a range of 0 to 1. By P = 0, we mean that there is absolutely no chance that the observed difference could be due to sampling variation. By P =1, we mean that we are absolutely certain that the observed difference in two samples is due to sampling variation. However, such extreme results are rare. In a given case P is in between 0 and 1. If P = 0.4, we mean that the chances that the given difference is due to sampling variation are 4 in 10. Obviously, the counterpart of the statement is that the chances that the observed difference is not due to sampling variation are 1 − 0.4 = 0.6, i.e. 6 in 10. The essence of any test of significance in biostatistics is to find out P value and draw the inference. It is customary to accept the difference to be due to chance (i.e. sampling variation) if P is 0.05 or more. The observed difference in the samples under this condition is said to be “Statistically not significant”. If P value is less than 0.05, the observed difference is considered as not due to sampling variation, but due to some difference in the samples themselves. The observed difference, under these circumstances, is said to be “Statistically significant”.
Like probability, null hypothesis is another important concept in statistics. In any test of significance, we start with the hypothesis that “the observed difference in the samples under study is due to sampling variation” and proceed to prove/disprove this hypothesis. As said above, essence of any test of significance is to calculate probability. It is customary to accept the null hypothesis if probability value is 0.05 or more. With every null hypothesis there is an alternate hypothesis. Usually, the alternate hypothesis is “that the observed difference in the samples is not due to the sampling variation, but is due to the difference in the samples”. In fact, this 32itself is the objective of the study. If alternate hypothesis is accepted, the null hypothesis is automatically rejected. However, if the null hypothesis is accepted, two possibilities exist.
  1. That the alternate hypothesis is rejected, and
  2. That the sample size may be inadequate to detect the difference.
The tests of significance can broadly be classified into two major categories. Parametric and non-parametric tests.
Parametric tests: A typical parametric test is performed with following assumptions.
  1. Dependent variable is continuous type, i.e. measured in interval or ratio scale.
  2. Underlying population from which the sample data are drawn has normal distribution. For testing this assumption one can apply Kolmogorov-Smirnov static (with or without Lilliefor's correction)
  3. When differences or measures of association are being tested, the variances of samples do not differ significantly. To test this hypothesis one can use Levene's test.
Parametric tests can be applied to test difference or correlation. The commonly used parametric tests are:
  1. For testing the difference:
    1. t-Test (Paired and unpaired)
    2. Analysis of variance (ANOVA): One way ANOVA, simple factorial ANOVA, general factorial ANOVA, repeated measures ANOVA
    3. Test of significance of difference between two means.
  2. For testing the correlation: Pearson's product moment correlation coefficient.
Non-parametric tests: A typical non-parametric test does not start with the assumptions made for the parametric test. However, if the assumptions made under parametric test are correct, it is necessary to use parametric test. This is because, use of non-parametric test will decrease the power of the test. Following non-parametric tests are commonly used.
  1. For ordinal and non-parametric data to test difference
    1. Man-Whitney's test
    2. Wilcoxan's matched pair test
    3. Sign test
    4. Mc-Nemar's test
    5. Kruskal Wallis's test
    6. Friedman's test
    7. Kendall's test
  2. For category- type data to test difference
    1. Chi- square (χ2) test.
    2. Fischer's exact test
    3. Cochrane's Q-test
  3. For ordinal/non-parametric data to test correlation
    1. Spearman's rank correlation
    2. Kendall's
  4. For nominal type data
    1. Phi-coefficient.
    2. Cramer's V
In all the tests it is presumed that samples have been drawn randomly and are representative of the population from which they are drawn. It is also expected that precautions mentioned earlier in data collection in order to avoid errors and bias are taken.
Test of Significance of Difference Between two Means
Indications: The test is indicated when the data is quantitative and difference between means of two samples is to be tested. Size of both samples should be above 30.
  • Null hypothesis: The difference in the means of two samples is due to chance (i.e. due to sampling variation).
  • Alternate hypothesis: The difference in the means of two samples is not due to sampling variation, but is due to the factor under study.
Statistics required:
  • Arithmetic means of two samples: m1 and m2
  • Standard deviation of two samples: s1 and s2
  • Size of the two samples: n1 and n2
Example 10: The mean height of 100 medical students in a city was 155 cm with S.D. 5.0 cm. The mean height of 150 engineering students was 157 cm with S.D. 6.2 cm. Comment.
Steps: The example justifies use of the test under description.
  1. Statement of Hypothesis:
    Null hypothesis: There is no difference in the heights of the two groups of students. The observed difference is due to sampling variation.
    Alternate hypothesis: The observed difference in the heights of the two groups is not due to sampling variation, but is due to some difference in the two groups.
  2. Calculation of Standard Error of Difference Between Two Means (SEDM)
    m1 = 155 s1 = 5.0 n1= 100
    m2 = 157 s2 = 6.2 n2 = 150
    Calculate S.E.M. for two samples (Equation-8)
    S.E.M.1 = s1/√n1 = 5.0/√100 = 0.50
    S.E.M.2 = s2/√n2= 6.2/√150 = 0.51
    Calculate SEDM:
    SEDM = √{(SEM1)2 + (SEM2)2} ---Equation 10
    = 0.71
    Calculate z
    z = |m1 – m2|/SEDM ----------- Equation 11
    = |155 − 157|/0.71 = 2.81
    Find area under normal curve (A) for z
    Refer to appendix-A (Area for z = 2.81 is 0.4975)
    A = 0.4975
    Calculate probability (two tailed)
    P = 2 (0.5 – A) ------- Equation-12
    = 2 (0.5 − 0.4975) = 0.0025
    If P is 0.05 or more:
    • null hypothesis accepted,
    • alternate hypothesis is rejected,
    • difference in two means is statistically not significant
    If P is less than 0.05:
    • null hypothesis rejected,
    • alternate hypothesis is accepted,
    • difference in two means is statistically significant.
In our example, since probability (P) is less than 0.05, null hypothesis is rejected, alternate hypothesis is accepted, and 35difference in the two means is statistically significant. It means that to the extent of this example, engineering students are taller than the medicos. A further probe into this may reveal the reasons. May be, there are significantly more females among medicos.
Test of significance of difference between two proportions
Indications: This test is indicated when difference between proportion of an attribute in two samples is to be tested.
Null hypothesis: The difference in the proportion of attribute in two samples is due to chance (i.e. due to sampling variation.)
Alternate hypothesis: The difference in the proportion of the attribute in two samples is not due to sampling variation, but is due to the factor under study.
Statistics required:
  • Proportion of the attribute (p1 and p2)
  • Size of the two samples: n1 and n2
  • Number of units with attribute in sample 1 & 2
  • m1 and m2
Example 11: Findings of a clinical trial of a new drug in a disease are given below. Interpret.
Not cured
Steps: The example justifies use of the test under description.
  1. Statement of Hypothesis
    Null hypothesis: There is no difference in the proportion of the attribute (proportion of patients cured) in the two groups of patients. The observed difference is due to sampling variation.
    Alternate hypothesis: The observed difference in the proportion of patients cured in the two groups is not due to sampling variation, but is due to the difference in the efficacy of the drugs.
  2. Calculation of Standard Error of Difference Between Two Proportions (SEDP)
    p1 = 0.85, p2 = 0.90
    n1 = 100, n2 = 200
    m1 = 85, m2 = 180
Step 1: Calculate combined proportion (p) of the units with the attribute.
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Step 2: Calculation of SEP for two samples.
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(N.B.: Note that p1 and p2 are not used for calculation of SEP1 and SEP 2. Instead the statistic derived by addition of m1 and m2 is used.)
Step 3: Calculation of SEDP.
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Step 4: Calculate z:
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Step 5: Find area under normal curve (A) for z. Refer to appendix-A (Area for z= 1.28 is 0.3997)
Step 6: Calculate probability (two tailed), using equation 12
= 2 (0.5 − 0.0.3997) = 0.2006
Step 6: Interpret:
If P is 0.05 or more:
  • null hypothesis accepted,
  • alternate hypothesis is rejected,
  • difference in two means is statistically not significant
If P is less than 0.05:
  • null hypothesis is rejected,
  • alternate hypothesis is accepted,
  • difference in two means is statistically significant.
In our example, since probability (P) is more than 0.05, null hypothesis is accepted, alternate hypothesis is rejected, and difference in the two means is statistically not significant. It means that the apparent difference in the cure rate of the two drugs is due to sampling variation and there is nothing to choose between the two drugs on the basis of cure rate. Other factors like cost, toxicity, route of administration etc come into play in deciding the choice of the drug.
Unpaired t-Test
Indication: The test is an alternative to the test of significance of difference between two means when sample size is small. (less than 30).
Null hypothesis: The difference in the means of two samples is due to chance (i.e. due to sampling variation).
Alternate hypothesis: The difference in the means of two samples is not due to sampling variation, but is due to the factor under study.
Statistics required: For this test, the raw data is required. Required calculations are made from this.
Example 12: The Hb% of 10 pulmonary TB patients (x1) and 12 comparable controls (x2) is given below.
TB Patients: 9.0, 8.6, 7.5, 8.0, 7.3, 8.0, 7.0, 9.0, 8.0, 8.6 (n1=10, m1 = 8.1, s1=0.696)
Controls: 9.5, 9.0, 7.7, 8.8, 8.0, 9.0, 8.1, 9.2, 8.5, 8.6, 9.0, 10.0 (n2 =12, m2 = 8.78, s2= 0.652)
Steps: The example justifies the application of Unpaired “t” test.
Step 1: Statement of Hypothesis:
Null hypothesis: There is no difference in the Hb% of the two groups of persons. The observed difference is due to sampling variation.
Alternate hypothesis: The observed difference in the Hb % of the two groups is not due to sampling variation, but is due to TB in first group.
Step 2: Calculation of pooled S.D. (PSD)
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(See Tables 6 and 7 for calculations)
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Table 6   Calculations Example: 12 (TB Patients) Mean (m1) = 8.1
Table 7   Calculations for Example:12: (Controls) Mean (m2) = 8.78
x2 − m2
(x2 − m2)2
If standard deviations s1 and s2 are known,
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(This is almost similar to PSD calculated previously. The minor difference is due to approximations and “rounding-off”.)
Step 3: Calculation of t:
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Step 4: Calculation of Degrees of freedom: (d.f.)
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Step 5: Finding Probability: (See Appendix B): The probability for calculated t for 20 D.F. is in between 0.02 and 0.05. The P value calculated directly by using software MS-Excel is = 0.029
Step 6: Interpret: It is same as for other tests of significance. In our example, P is less than 0.05. So, null hypothesis is rejected, alternate hypothesis is accepted and difference between two means is statistically significant. In other words it indicates that Hb% is affected and is significantly low in TB patients as compared to controls.
Paired t-Test
Indications: Paired t-test is indicated when we have pairs of quantitative measurements and statistical significance of the differences in these pairs is to be determined and the number of pairs is 30 or less. (if the pairs are more than 30, test of significance of two means is used. Such occasions come in “before-after studies” and “twin studies”.
Hypothesis: (Similar to that in unpaired t-test).
Statistics required: Like unpaired t-test, this test also requires raw data.
Example 13: Antihypertensive effect of a drug was tested on 15 individuals. The recordings of diastolic blood pressure in mm of Hg are shown in Table 8.
Interpret: Steps: The data in example 13 justifies application of paired t-test.
Step 1: Statement of hypothesis
Null hypothesis: There is no difference in the diastolic B.P. before and after the drug treatment. The observed difference is due to sampling variation.
Alternate hypothesis: The observed difference in B.P. before and after drug treatment is due to the drug.
Step 2: Calculate mean difference in the pairs. This is done in table 8 and is shown at the bottom of the column against row titled mean (= 13.6). This means that there has been an average fall of 13.6 mm of Hg in diastolic B.P. after the drug treatment.
Table 8   Diastolic mm of Hg in 15 patients, before and after drug treatment
Before Trt. (x1)
After Trt (x2)
Difference (d) = x1 x2
d-md (md= mean of d)
Step 3: Calculate pooled standard deviation (PSD)
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Step 4: Calculate standard error of PSD (SE-PSD)
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Step 5: Calculate t:
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Step 6: Calculate degrees of freedom (DF)
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Step 6: Find out probability: (Refer to Appendix – B): Probability for calculated value of t, for 14 DF is less than 0.001 (The P value as calculated directly by using computer software MS-Excel is 0.00024)
Step 7: Interpret: The P value is less than 0.05. Hence, null hypothesis is rejected, alternate hypothesis is accepted, and the difference in before- after values is considered statistically significant.
Chi-Square Test
Chi-square is a test of significance. It is an alternative to the test of significance of difference between two proportions. It tests the difference between two groups with reference to a particular observation. The difference can be between two independent variables. There may be an association between variables like immunization status and risk of disease or drug administration and chance of getting cured. This may be the difference “just observed” or it may be “real difference-association” between two variables. The observed difference may be a “real” difference or difference “purely by chance”. This means one is measuring the level of association between two variables. In case the observed difference is likely to be the difference by chance then one can say that there existed no real difference between the groups. This much difference is naturally expected difference and the difference is not statistically significant difference. It can be other way round too. This difference may not be expected 42but unusual, unexpected difference and in that case one can conclude that the difference is statistically significant. The level to conclude “significant or not significant” depends on level of normally expected chance difference which may be 5% or 1%. This can be accepted or rejected by stating the “null hypothesis” and then rejecting or accepting it.
Null hypothesis is the first step in application of test of significance. We initially assume that in fact there is no difference between the samples drawn from the universe. The difference is zero or null. This then is not true, it is our assumption. It is our hypothesis. Our assumption that the difference is zero means we form our null hypothesis. By this we further state that the difference observed is chance occurrence and therefore it should not be given importance. However, to say that with confidence we apply test of significance, to prove or disprove our hypothesis, that there is no real difference between two samples and both belong to same universe. If the test shows that they do belong to two different universes, the observed difference is statistically significant, then it will mean that there exist some important factors which are responsible for causing this observed difference. They need further attention, scrutiny or modification. However, the difference is not because of chance then the null hypothesis is rejected and if the null hypothesis is true then it is accepted. However, the acceptance or rejection of null hypothesis should be considered valid only when sufficient size existed in either of the groups.
Chi-square test can be applied to qualitative categorical data of large sample size; more than thirty. Application of Chi-square test gives a Chi-square value which in turn is then compared with values given in readymade Chi-square tables after finding out the degrees of freedom.
Chickenpox vaccine protects against chickenpox. 155 primary school children were observed for development of chickenpox, 86 in vaccinated group and 69 in unvaccinated group. The resulting morbidity after exposure to chickenpox was as follows:
Chickenpox vaccination and disease
Not vaccinated
Not attacked
The data shows that vaccination plays an important role in protecting against chickenpox. Those vaccinated have lesser attack rate than those not vaccinated. But does it mean significant difference? We formulate the “null hypothesis”, that there exists no difference in attack rate in vaccinated and unvaccinated individuals and the observed differential protection is just a chance occurrence.
The application of the Chi-square test to this data goes through following steps of calculation of Chi-square value by formula.
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Where E is expected value, O is observed value. To find out E, expected frequency in each cell multiply row total (RT) by column total (CT) and divide by its grand total (GT), i.e.
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Then for every cell deduct expected frequency from the actual observed frequency, i.e. (O-E). Then square the differences between O – E and divide by expected frequency, i.e.
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Add together similar results from every cell, i.e.
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which will give the Chi-square value.
Next step will be finding out the degrees of freedom, i.e. d.f. It will be number of rows minus one multiplied by number of columns. minus one, i.e.
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The next step will be referring to the Chi-square table for finding out probability “p” for a given d.f. and Chi-square value. (See Appendix) The significance of Chi-square value depends upon accepted level, whether 5% or 1% (0.05 or 0.01). The p if is more than 0.05 or 0.01 then the observed difference is statistically not significant and then null hypothesis is accepted. The p value if is less than 0.05 or 0.01 then the observed difference is statistically significant and the null hypothesis is rejected, thereby indicating that the difference observed is related to something else than the mere chance.
For a two by two table, the O – E method is called as “two sample Chi-square” test. In case more than two groups are to be compared the test is called as “K sample Chi-square” test. (Overall comparison of rates or proportions for more than two groups). In two sample Chi-square or K sample Chi-square there exist only two possible results, either eyes or no; either success or failure, either positive or negative. The third test “Common distribution chi-square” test using the same method of O-E, compares more than two categories. The Chi-square test can be used as “test of goodness of fit”. A theoretical distribution like blood group, appearance of diabetes in off springs if either or both of them parents are diabetic is known distribution. Now after observation of population distribution with reference to blood group and history of diabetic parents one can explain how much is the similarity between the observation made and the theoretical distribution. How good is the fit. The Chi-square can be used as a “test of association”, the association between two variables and the samples. There exists a definite association between lepromin and tuberculin reaction. This can be confirmed by Chi-square. The Chi-square therefore is said to be a “versatile test”.
Chi-square when used as test of association warrants “Yates correction” if the expected frequency is less than five in any cell. It means the difference between expected and observed frequency should be brought to zero by addition or substraction of 0.5 before it is squared.
For two by two table a quicker method of Chi-square calculation is
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Not Seen
Example 14:
In a clinical trial of enteric fever 50 persons out of 100 were cured with chloramphenicol and 70 persons out of comparable 100 persons were cured with septran. Comment on efficacy of either of the drugs.
Not Cured
50 (a)
50 (b)
100 (e)
70 (c)
30 (d)
100 (f)
120 (g)
80 (h)
200 (k)
  1. χ2 with Yates Correction
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  2. χ2= ∑{(O – E)2/E} without Yates Correction
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With Yates correction it will be
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p will be between 0.005 and 0.01 (see Appendix B).
The possibility of getting such a difference in cure rate due to therapies, purely by chance is 1:100 to 5:1000. The possibility of chance occurrence thus is very low (far below 0.05). Hence cure is due to the drugs used in two therapies. Since more persons have 46been cured with septran than with chloramphenicol, septran appears to be superior to chloramphenicol, as far as cure of patient is concerned.
Correlation measures linear association (or relationship) between two quantitative variables. The statistic that is calculated is called correlation coefficient (r) and it has a possible range of −1.0 to +1.0. Positive sign indicates positive correlation. Here, if one variable increases other also increases (as in height and weight). Negative sign indicates negative correlation. Here, as one variable increases, other one decreases. The magnitude of correlation indicates degree of correlation. Higher the value of r, higher is the correlation. An r value of 0.0 indicates no correlation at all. An r value of 1.0 indicates perfect correlation. For calculating r we must have n pairs of measurements of x and y. Traditionally, y is a dependent variable, and × is an independent variable. Thus, in measurement of correlation between height and weight, height will be x and weight will be y. Having obtained n pairs of observations of x and y, correlation coefficient (r) is calculated by using the following equation:
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Example 15: Table-AA shows height and weight of 10 individuals. Using equation given above
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Regression coefficient: It is denoted by b. It is also called “slope”. The slope is the vertical distance divided by the horizontal distance between any two points on the regression line, which is the rate of change along the regression line. It is calculated by I following equation:
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Regression coefficient is useful to give an estimate of y for known value of x using equation: y = a + bx
Here, a is theoretical value of y if x = 0. (It is also called Y-Intercept). It is derived by following equation:
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Having known these values y (wt) for any known value of x (height) can be estimated (predicted) with the help of equation
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For example, for height = 155cm. wt will be
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Similarly for height = 176 cm. expected wt will be
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Table AA   Height and weight of 10 individuals
Wt (kg)
Σ xy
(In fact well-known Broca's index is developed on same lines. For Broca's index b = 1.0, and a = −100)
Regression Line: Calculate y for two extreme values of x (say x1 and x2), using equation y = a + bx, we get estimates of corresponding values of y (say y1 and y2). In our example, x1=150 cm and x2 =179 cm. Estimates of y1 and y2 are 51.70 kg and 75.64 kg respectively. We now get two points.
  1. x1= 150 cm, y1=51.70 kg
  2. x2= 179 cm, y2=75.64 kg.
Plot these points on the graph and join these points with a straight line. What we get is a regression line. We can then obtain estimates of y for any known value of x with the help of regression line.
Precautions in Interpretation of Correlation
  1. Existence of correlation is not a proof of cause and effect relationship.
  2. Like any statistic, r is subject to sampling variation. There are statistical tests to test the hypothesis r = 0 and r =1. These are beyond the scope of this book and can be found in any textbook on Statistics.
  3. Estimating y for any value within the range of observations is called interpolation. For our example given above, range of x is 150 to 179 cm. We can estimate wt for any height beyond this range, it is called extrapolation. Extrapolation may not be valid as the relationship of x and y may not be the same as is seen within the observed range.
  1. Data presentation: Statistical methods and techniques like centering constants, measures of variation and various methods of data presentation (like, tables and graphs) help in understanding of the complex data.
  2. Making estimates: In the preceding sections we have seen how the statistics helps us in making estimates about parameter with the help of measurements/counts of scientifically drawn sample. This saves time and resources.
  3. Making forecast: Statistician tries to find out trend in data presented in time scale. Based on this reliable forecasts can 49be made. This helps in anticipating the future needs and thus facilitates planning.
  4. Planning clinical trial: Statistics helps us in planning a clinical trial in a scientific way. The procedures like sampling, blinding and analytical techniques like stratification, multivariate analysis and tests of significance ensure that results are valid.
  5. Sorting reliable from unreliable: Literature is full of studies on various aspects of health related problems. Confusing and at times contradictory results are seen in different studies. A trained statistician can scrutinize these studies and sort out reliable studies from unreliable ones. This helps us in drawing scientifically correct inference.
  6. Uses to clinical medicine:
    1. Common/uncommon, Normal/abnormal: In life-sciences we are always faced with the problems of deciding the limits of “what is normal range” for a variable. This is due to biological variation. However, statistics has given us a tool of “confidence limits” that helps us to decide “common” and “rare”. This is the first step in deciding “normal” and “abnormal.”
    2. Correlation and association: Many times two or more conditions coexist. Statistics helps us in deciding whether this coexistence is a chance occurrence or a significant association. This helps in “syndrome identification”. Identification of an association between risk factor and a disease helps in diagnosis and prevention. Correlation is the relation between two quantitative variables. If any pattern is observed in the relationship between two quantitative variables, one can make a reasonable estimate of one variable with the measurement of the other. Broca's index is one such example of making estimate of weight if height is known. If for estimation, the variable requires costly and time-consuming tests, then measurement of cheaper and quicker tests becomes handy.
  7. Uses to community medicine: Statistics with the help of various tools and techniques, helps us in assessing the status of health, finding out the causes of differences observed (in various person/place/time units), evaluating health services/interventions, help in selection of best alternative, and in forecasting future needs.
Statistics has applications (uses) in all branches of sciences. However, its deliberate or unintentional misuse can lead to fallacies. Such fallacies lead to erroneous conclusions or same data being interpreted differently by different persons. Fallacies can creep up at different stages through which data goes like data collection, compilation, analysis, and interpretation. Some common fallacies are described below.
  1. Fallacies at data collection: Fallacies at data collection are the mistakes and errors that occur at data collection. Use of uncalibrated/ poor quality instruments, deployment of inexperienced/ unskilled/ untrained persons to take measurements, use of poorly designed/ un-pretested questionnaire containing ambiguous questions etc are some common reasons for the fallacies at this stage. At the start of clinical trial one has to define criteria for diagnosis of disease under study. If these criteria are subjective, those who are not eligible to enter in the study get entry and those who are not eligible are left out. This results in what is called as “Selection bias.” In analytical studies (like, case control study and cohort study), one has to define criteria for exposure factor under study and that for the outcome factor under study. Similarly, criteria to grade the severity of exposure and outcome are also required to be defined in some epidemiological studies. If these criteria are poorly defined and/ or are subjective, an exposed person may be classified as “unexposed” and vice versa. Similar errors can occur in deciding whether outcome has occurred in a given person or not. This results in “Classification bias”. In case control study, outcome and exposure occurs before study has started. Investigator's attempt is to obtain information about “exposure” and “outcome” by retrospective enquiry. It is common observation that exposure is remembered more vividly if the outcome has occurred as compared to if the outcome has not occurred. This introduces “Differential misclassification bias”. In retrospective enquiry for estimating birth rate, one has to recall whether birth has occurred and if so it had occurred in the period of interest (say 1st January 2001 to 31st December 2001). Events that occur at borderline of the period of interest (e.g. on 31st December, 2000 and 1st January, 2002) are likely to be included even if they should not be. Similarly, events on 1st January, 2001 are likely to be excluded selectively as they may be placed wrongly in the calendar year 2000. 51Inability to remember an event related to exposure (e.g. inability to correctly answer the question “Did you eat salad in the dinner on such and such date?”) or inability to place exposure correctly with reference to time (e.g. Inability to answer question “At what age did you start smoking?”) leads to “Recall bias.” In occupational medicine, one of the objectives is to show relation between occupational environment (exposure factor) and an occupational disease (outcome factor). Mostly, this is done by selecting studying the employees who are “currently” employed in the occupation. However, it is possible that “currently” employed persons in that occupation are working there as they have not suffered from the outcome under study. Conversely, those who are not currently working there may have left this job as they have experienced the outcome or may have died due to it or may be absent due to it. The bias so introduced is “Healthy worker effect.” Ambiguities in questionnaire in data introduce misclassification bias. Answer to question “How old are you” will differ depending on what reference point is selected for calculation of age and what is the level of accuracy expected.
  2. Fallacies at data compilation: Data compilation involves arranging data in some sort of sequence, order or groups. It also involves data editing and data reduction. Problem comes if the groups are not mutually exclusive. For example, look at the groups made for height of college students in the data given below.
    Height (cm)
    170 and above
    Here, a student with height 155 cm can be put either in first or second group depending on the whims of the compiler. This is highly undesirable as it can introduce misclassification bias. The last group is left open as far as range is considered. It will be impossible to calculate mean height from the grouped data given above.
    If data editing is not done properly, illegal entries remain to introduce selection bias. Inconsistencies like, a male person operated for hysterectomy, a four year child with weight of 50 kg, a primi with history of previous caesarean etc remain to introduce variety of bias.
  3. Fallacies at data presentation: In graphical presentation, it is customary to start scale at zero for both x and Y axis. However, in bar chart if the axis does not start from zero, an erroneous conclusion about comparison of two variables may be reached as is seen from Figures 13A and B. In time related graphics like, change in crude birth rate, same data may show a “dramatic decline” (as in Fig. 15) or “not so dramatic decline” (as Fig. 14) depending on the scale chosen.
  4. Fallacies at data analysis and inference: Drawing inference from compiled and analysed data is sometimes very subjective. It is like telling whether a glass is half full or half empty. Some common fallacies at this level are explained below.
  1. Fallacies with averages: Arithmetic mean is affected by extreme values. Care should be taken while interpreting or comparing averages based on small numbers. Adding averages of two series and computing pooled arithmetic mean is a common mistake. It mean's height of boys in a college is 160 cm and that of girls is 150 cm, the mean of all students in the college may not be equal to 160+ 150/2, i.e 155 cm. This is because the numbers on which the averages of the two groups are based may not be equal. This will be clear from the following data.
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    Fig. 13: Number of boys and girls in a college
    Mean Ht (cm)
    One can have different series with same mean, median, mode, and range as the following series with mean = median = mode = 5, and range= 1,9 show.
    1. 1,1,1,5,5,5,9,9,9
    2. 1,4,4,5,5,5,6,6,9
    3. 1,2,3,5,5,5,7,8,9
  2. Fallacies with proportions: Like arithmetic averages, one should not add proportions to derive combined proportions. For example, in the data given below, the combined proportion (%) of in girls in College-1 (p1) and in College-2 (p2) is not equal to the arithmetic mean {(p1 + p2)/2}.
    Number (p1)
    Number (100 – p1)
    300 (30.0%)
    700 (70.0%)
    200 (40.0%)
    300 (60.0%)
    500 (33.3%)
    1000 (66.7%)
    Proportion may be used as an indicator for showing change in a variable over a period of time. It must be remembered here that it (proportion) is derived as a product of numerator and denominator. Thus, any change in it can be due to change in one or both of them. For example, look at the following statement. Proportional mortality rate (PMR) of TB in Hospital-X was 20% and 10% for the years 2000 and 2001. It is concluded that this is due to new intervention measures adopted in 2001. The fallacy behind the argument is evident from the data given below which shows that the information about PMRs for the two years is correct. However, the deaths due to tuberculosis have remained same and the decrease in PMR is due to increase in the deaths due to “other causes.”
    Deaths (TB)
    Deaths (Other)
    PMR (TB)
  3. Fallacies in correlation and association: Showing relation in two quantitative variables is correlation and showing relation between two qualitative variables is association. Proof of a strong correlation/ association (either positive or negative) is not a proof of causality. For example, one can show a positive correlation between sales of colour T.V. sets in Maharashtra and number of girls admitted in Engineering colleges in the state for period 1985 to 2000. However, we will not accept the causal relationship between the two. Similarly, any attempt to extrapolate a regression beyond the range of observation should be viewed with caution. This is because, the relation between the two variables as is seen in the observed range of the two variables may not be same beyond the observed range.
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    Fig. 14: Birth rate: 1941-2001
    Another problem in establishing the association between two variables (exposure factor and outcome factor) is the existence of a third party called “confounding variable.” To be eligible to be called as a confounder, the variable must satisfy following conditions.
    1. It must be a risk factor for outcome even in those who are not exposed to the exposure factor being studied.
    2. It must be associated with exposure factor in the population from which cases (outcome) are derived.
    3. It must not be a step in the causal chain of the outcome.
    Confounding is the bias that the investigator hopes to avoid and should avoid. Many times there is a confusion in the three major types of bias (i.e in selection bias, classification bias, and confounding bias.)
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    Fig. 15: Birth rate: 1941-2001
    One rule of thumb is that if the bias can be measured and controlled by data analysis techniques like stratified analysis and multivariate analysis, it is confounding bias. Age is potential confounder in many studies and its confounding effect should always be assessed.
  4. Comparing mangoes with apples: While drawing an inference on the association between exposure factor (in analytical study) or intervention (in experimental study) on one side and outcome factor on other side, one must remember that outcome is dependent on factors other than exposure factor under study (in analytical study) and intervention (in experimental study). If the two groups being compared are not comparable, at least for the factors affecting the outcome, then in effect we are comparing apples with mangoes. Age, sex and socioeconomic status are the factors which affect the outcome in many diseases. Examine the following data:
    Patients Treated
    Cured (%)
    It appears that drug-B has better cure rate than drug-A. However, examine the detailed analysis given below.
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    Fig. 16: Classification of cancers by two hospitals
    It is clear from the detailed analysis, that sexwise cure rate is same for the two drugs. Cure rate is less by 10% for females in both groups. The proportion of females is 50% for drug A and only 20% for drug-B and this appears to be the real reason for the overall difference in the cure rate.
    Another example of comparing mangoes is comparison of mortality due to a disease in two hospitals A and B. It will be seen that for all severity grades from I through III, hospital-B includes more severe cases as compared to hospital-A. This is due to difference in the gradation scheme accepted by the two hospitals. As such, the gradewise mortality is bound to be more in hospital-B than in hospital-A, in spite of the same quality care (Fig. 16).
  5. Non-consideration of period of exposure: In some preventive trials, one of the groups is given intervention under study and control group is given placebo. If the persons in intervention group enter the study at different points of time, then their “period of exposure” should be counted from the date of entry in the study. Consider following example. In 12000 children vaccinated for a disease, 507 (i.e. 4.22%) suffered in first year of study. In 12000 unvaccinated children, 936 (i.e. 7.8%) suffered in the same period. Apparently, it seems that vaccination gives some protection. However, the study protocol indicates that 1000 children were enrolled and vaccinated on the first of every month for 12 months. Then, the period of exposure for unvaccinated children would be 12000 × 12 = 144,000 person-months. However, the period of exposure for the first batch enrolled on first of first month of study will be 1000 × 12= 12000 person-months. 57The period of exposure for subsequent entrants will be 1000 × 11, 1000 × 10, 1000 × 9 … 1000 × 1. So that the total period of exposure for the vaccinated children after vaccination will be 78000 person-months. The incidence for both groups thus works out to be 0.65 per 100 person-months.
  6. Generalization: Can we generalize observations made on a sample? This depends on the validity (lack of systemic error) in the observations. Validity has two components. Internal validity and external validity. Internal validity is the applicability of the inferences drawn on the sample to the population from which the sample is drawn. External validity is application of the inferences drawn on the sample to the units outside the population. External validity implies universalization (or generalization) of the inferences. Based on a sample of students from medical colleges and engineering colleges in Maharashtra, one draws inference that girls are more likely to join medicine as compared to engineering in Maharashtra. This is internal validation. If one draws inference that this is the situation in the entire country, then it is generalization of the inference. Factors that detract from the internal validity are selection bias (viz. self selection, healthy worker effect etc.), classification bias, and confounding bias. If such biases exist in the sample and attempt is made to draw inference for population, then it would be a statistical fallacy. Internal validity is prerequisite for external validity. Generalization requires judgement on the features in the observation that can be generalized.
To compute is to ‘calculate, to reckon, to count, to estimate, to rate’. One who computes is a computer and computer is a machine that computes. However, the modern computers do much more than mere computing. A computer has a Central Processing Unit (CPU) that does the complex computational tasks. In addition it has memory that can store the information and make it available anytime in future. Various input devices like key-board, mouse, light pens, graphic pads, scanners etc help in putting data in the computers. The output devices are the ones in which the processed data appears/is stored. These include monitor (Visual display unit), printers, floppies and compact discs. In order to communicate with the computer, one needs operation systems (OS) that act as interface between the 58computer and the user. Popular OS are DOS, Windows, Unix, and Linux. Computer languages help us to communicate with the computer. Much progress has been made in this direction with the help of languages like BASIC, COBOL, PASCAL, C, C++, Visual-BASIC, ORACLE, Visual C++, JAVA, HTML and DHTML etc. Computer softwares are the programmes designed for specific tasks or a group of tasks. The softwares act as an interface between OS and the user. The softwares/applications designed to serve the variety of needs like document preparation (MS-Word, Word Perfect), Desk Top Publications (Page Maker), data base management (Fox Pro, MS-Access, EPI-Info), Computer assisted drafting (CAD softwares), statistical operations (SPSS, MS-Excel, Lotus), etc are now available. Efficiency of the computer depends on three factors processor, storage capacity of hard disk and RAM. The efficiency of processor is measured in MHz/GHz (Mega- Hertz/Gega- Hertz.). Currently available Pentium-IV processors for Personal Computers are of 1.5 GHz. The hard disks with storage capacity of 40 GB (Gega-byetes) are now available. The RAM (Random Access Memory) currently in market can be upto 256 MB (Mega-byetes). With concept of networking of the computers, it is possible for computers to communicate with each other and this has opened new field like electronic mail (e-mail), chats, and internet. All these developments have proved to be tremendously helpful to medical profession. Following are the some of the areas in which computer can be and has been of immense help.
  1. Case records: Doctors have to keep records of their patients for variety of purposes, like case management, birth -death registration, income -tax and for the purpose of Consumer Protection Act. Computer applications designed for the specific needs of the doctors are now available. These help in data entry, editing, and retrieval. Preparation of various reports with the recorded data is also possible.
  2. Prescribing: The number of drugs is increasing and various proprietary names have added to the complexity. Drug database applications help doctors to choose the drugs with appropriate dose with reference to patient variables like, age and weight.
  3. Differential diagnosis: Some programmes when operated in diagnostic mode, require inputs in the form of patient information. The programme then comes up with probable 59diagnosis. The risk estimates of various conditions like MI can be obtained.
  4. Image-storing: ECGs, X-rays, MRIs, CT scans, ultrasound images can be stored in computer and can be made available anytime in future for comparison. These images can be transferred from one computer to other for the purpose of research, service, education etc.
  5. Diagnostic instruments and equipments: There is a virtual explosion of instruments and equipments which are computerized. These have increased the utility and efficiency of the procedure.
  6. Material management: Use of database software and applications has made the task of management of drugs and consumable a lot easier and efficient. One can keep track of the moving items easily and accurately. Records of various firms supplying various items, rates of various items (with their specifications) etc. can now be stored in computer. This also helps in accounting procedures.
  7. Personnel management: Time-tables and schedules which were prepared manually can now be prepared with the help of computer.
  8. Epidemiological studies: Computer is an useful asset for epidemiological study of any kind right from planning to inference. Determination of sample size, preparation of questionnaire, data entry, data validation, data editing, tabulation, graphic presentation, application of tests of significance are some of the tasks that can be done with the help of computers.
  9. Education: Interactive textbooks, 3-D animation, annotations, glossary, cross references are some of the strengths of computer as an educational tool/media. Abstract ideas can be presented in understandable form with computer. Computer based tests can help in objective assessment of the knowledge of the students. Simulation exercises help in assessing the skills.
  10. Literature search: Search for references through library is a tedious and time consuming task. Computerized databases for medical literature is now available. MEDLINE is one such popular database. Abstracts of articles published in various indexed journals (about 3700 in number) since 1966 60are in MEDLINE data base. It can be accessed through website or In addition, some of the journals have their own websites that can be accessed free or at subscription. Topicwise or authorwise search is possible.
Sampling is the process by which some units of a population or universe are selected for the study and by subjecting to statistical computation, conclusions are drawn about the population from which these units are drawn, as it is difficult to study each and every individual of the population.
The ‘universe’ refers to the statistical universe consisting of delineated and identified mass of population from which sample is taken.
Sampling technique consisting of different methodologies aims for the objective in such a way that every member of the population or universe has got equal chance to appear in the sample. If the individual components of the population are already numbered serially, say from 1 to 100, then the required sample can be readily drawn with the aid of a table of ‘random sampling numbers’.
In sampling “sampling error” is inevitable. It is the chance difference between sample statistic and that of the universe, parameter of universe. Increase in sample size or presorting to amore appropriate sampling method can minimize it.
Decide a “sampling frame” which is the universe. The total data like houses in a village from which sample is to be drawn.
Decide “sampling unit”, which is the item, observation from the sample frame like individual house in a village.
Advantage of sampling is that it is economical method from point, e.g. view of resource consumption, results are available earlier after sampling. The data can be studied more accurately and errors can be estimated, determined before hand. However, the sample is never devoid of sampling error. In case the incidence of condition is low, large sample is required to be studied. Sometimes it may not be ethically, scientifically correct and one will have to study entire universe.
Some non-statistical considerations are of importance in sampling. Purpose of sampling, availability of time for study and availability of various resources have a great influence on determining sample size and sampling method.
Sampling must be completely unbiased if the facts determined from them are to be applied to the universe from which they are drawn; hence it has to be random. Then the sample will represent the entire universe in true sense with reference to the mean and SD of the universe.
Sampling is required because:
  1. It is difficult to study the universe.
  2. Study of sample saves the time.
  3. Study of sample is economical in all senses.
  4. Supervision during the study is better.
  5. Results are received earlier and application of those is timely.
Sampling Methods
  1. Random Sampling: Every observation has equal chance to enter into the sample. Decide the sampling unit. Serially number the universe/ population and prepare the list. Determine the sample size desired depending upon the acceptable sampling error. Use the “random number table” or by method of ‘shuffling the cards’ the sample can be drawn or a computer can be used.
  2. Systematic/Serial Sampling: Number the items in the universe. Pick up randomly any number from ‘0’ to ‘9’. Take every ‘nth’ number like 6th/ 9th till you draw the desired sample. However, there is a chance that the system in universe if corresponds to this procedure then the bias may enter. For example, every nth house may be a corner house or a shop
  3. Stratified Sampling: Used when sub-groups are present in the universe. Within the strata maximum homogeneity and between the strata maximum heterogeneity is essential. Do proportionate sampling from each strata. The small sub-groups of universe can be handled by this method.
  4. Multistage Sampling: Useful when sampling is to be done from a huge universe, e.g. the entire nation, taking samples from states, districts, tehasils, villages, towns etc.
  5. Multiphase Sampling: A desired character of sample is examined and a sub-sample is drawn from this sample for further information, e.g. in nutritional studies first carrying out clinical assessment and then in sub-sample laboratory tests.
  6. Cluster Sampling: Cluster is the primary sampling unit. Maximum heterogeneity within the cluster and maximum homogeneity between the cluster is essential. It is cheap, listing of item 62is avoided, and is convenient to operate. Have larger number of small size clusters.
    In general the steps are as follows: i) Define the universe. ii) Define the sampling unit to be included. iii) Put these in alphabetic manner in a list. iv) Determine sampling interval i.e. total cumulative population ÷ 30 v) Choose a beginners point by using random number table or selecting a digit from a currency note, that gives first unit to start in point number iii. vi) Select subsequent clusters by formula random number + sampling interval. vii) First sub-unit in a cluster to start work too is decided by random numbering.
  7. Purposive Sampling/Nonrandom/Selective: Selected by choice for in-depth evaluation/study or for obvious reason as forthcoming cooperation of people. As is not very representative of universe, generalization from it cannot be made.
  8. Interpenetrating Sampling: Taking a sub-sample of main sample for in-depth study with reference to scarce resource.
  9. Overlapping Sampling: Overlapping time frames.
Some Important Definitions
  1. Alpha (α): Significance level of a test. It is probability of rejecting a true null hypothesis. Also called “Type-I Error”.
  2. Beta (β): The probability of failing to reject the null hypothesis when it is false. It is also called “Type-II Error”.
  3. Confidence level: The probability that an estimate of a population parameter is within certain specified limits of the true value. It is commonly denoted by 1- α.
  4. Power of a test: It is the probability of correctly rejecting a false null hypothesis. It is denoted by 1-β.
  5. Precision: It is measure of how close are the estimates to each other. It may be expressed in absolute terms or relative points.
  6. One sided test: In hypothesis testing, when the difference being tested is directionally specified beforehand it is one sided test. For example, when X1 < X2 (and not X1 > X2) is being tested against null hypothesis X1 = X2.
  7. Two sided test: In hypothesis testing, when the difference being tested for significance is not directinally specified beforehand. (For example, when test takes no account whether X1 > X2 or X1 < X2).
  8. z 1-α/2, z 1-α, z 1-β: Represent the number of standard errors from the mean. z 1-α/2 and z1-α are the functions of the confidence level, while z 1-β is the function of the power of the test. Commonly used z values are given below.
    95 % Confidence, Two sided test: z 1-α/2 = 1.96
    95 % Confidence, One sided test: z 1-α = 1.65
    90 % Precision: z 1-β = 1.28
    80 % Precision: z 1-β = 0.84
  9. Study units: The individual units of the population whose chararacteristics are to be measured.
Determinants of sample size: In general, sample size depends on following factors:
  1. Level of precision expected. (absolute/ or relative)
  2. Level of confidence, and
  3. Whether it is one sided or two sided test.
Some common situations for determining sample size: Although, sample size determination is required in any epidemiological study, some common situations are discussed below. Interested readers should refer to “Sample size determination in health studies: A practical manual: By: Lwanga; S.K. and Lemnshow; S.: W.H.O.(1991)”
  1. Sample size for estimating population proportion: This is a very common situation. For example, a medical officer of health wants to know the proportion of persons affected due to a disease. Here, one should have some idea of the anticipated population proportion which is obtained either through pilot study, from records or experience. The estimate can be obtained with absolute or relative precision.
    1. Estimate with absolute precision: Example: A medical officer wants to estimate the prevalence of enteric fever in an epidemic. He wants the estimate within 5 percent points of the true value with 95% confidence. He is certain that the true prevalence cannot exceed 10% of the population. Here, following needed indicators are given:
      Anticipated population proportion (P)
      = 10%
      Confidence level
      = 95%
      Absolute precision (5-15%) (d)
      = 5 percent points.
      Two sided estimate so
      The sample size n is calculated with following equation:
      zoom view
      [If a reasonable estimate of P is not available, safest one is 0.5 (50%). Sample size with other indicators remaining same is maximum. For our example it is 384]
    2. Estimate with relative precision: Example: In above example, if we want an estimate within the range of 5% of the true estimate then it would be considered as “estimate with relative precision.” Here the estimate is required within the range of 9.5 % and 10.5% (i.e. +/- 5% of 10%). Here, we use following equation:
      zoom view
      Here, r indicates relative precision. For our example r = 0.05
      zoom view
    3. Hypothesis testing for population proportion: Example: Cure rate with a drug is widely reported as 80%. A new treatment is claimed to offer same cure rate. How may patients must be treated to test the hypothesis that the cure rate with new treatment is 90% against an alternate hypothesis that it is NOT 70% at 5% level of significance (i.e. 95% confidence)? Investigator wants to have 90% power of detecting a difference between cure rates of 70 to 90% (i.e. 10 percent points).
      Test cure rate (P1)
      = 80%
      Anticipated cure rate
      = 70 to 90%
      Level of significance
      = 5%
      z = Z1-α/2
      = 1.96
      Power of test
      = 90%
      b =Z1-β
      = 1.28
      Alternate hypothesis (two sided)
      Cure rate
      # 80%
      For Pa = 0.7
      zoom view
      Similarly, for Pa = 0.9, n = 136. So, one should take sample size of 188.
      For one sided hypothesis, i.e. Pa > 80%. Here, for 90% power of one sided test, z = 1.65 and b = 1.28 sample size works out to be 109.
  2. Sample size for detection of difference in proportion in two samples: In a pilot study of 50 persons engaged in tea gardens, 20, i.e. 40% had hookworm infection. In a control group of 50 persons, 10 (i.e. 20%) had the worms. If we wish to take up a larger study, and want to estimate risk-difference within 5 percent points of true value with 95% confidence, what should be the minimum sample size in each group?
    Anticipated population proportion (P1,P2)
    = 40%, 20%
    Confidence level
    = 5%
    Absolute precision (d) (5 percent points)
    = 5 %
    z (two sided)
    = 1.96
    Null hypothesis: P1 – P2
    = 0
    Alternate Hypothesis:(Two sided)
    P1 # P2
    Sample size (n) is calculated by using following equation:
    zoom view
    zoom view
    In our example:
    zoom view
    zoom view
  3. Sample size in a clinical trial: It is believed that cure rate with drug-A is 70%, while that with drug-B is 80%. How large should be the sample size in each group if an investigator wants to detect, with a power of 90%, whether the second drug has cure rate that is significantly higher than the first at 5% level of significance?
    • P1 = 70% (i.e. 0.70)
    • P2 = 80% (i.e. 0.80)
    • P = (P1+ P2)/2 = 0.75
    • z = Z 1-α = 1.65 (Test is one sided)
    • b = Z 1-β = 1.28
    • Null hypothesis: P1 = P2
    • Alternate Hypothesis: P2 > P1
    zoom view
    If a two sided test is to be applied, z will be = 1.96. Other calculations remain same and n = 391.
  4. Sample size in case-control study. Hypothesis test for odds ratio: The notation for typical case-control study is as below.
    No disease
    Here: Odds ratio = ad/bc
Example: Efficacy of measles vaccine in preventing broncho-pneumonia in children 1 to 4 years is to be tested by a case-control study. Available information indicates that vaccination coverage in the population is 80%. So that, only 20% of controls are likely to be unvaccinated. The investigators wish to have 80% chance of detecting an odds ratio significantly different from 1(Z 1 – β = 0.84) at 5% level of significance. If an odds ratio of 2 would be considered significant difference between the two groups, how large a sample should be included in each group?
  • Test value of odds ratio = 1.0
  • Anticipated P1 of “exposure” given “disease” = ?
  • Anticipated P2 of “exposure” given “no disease” = 20%
  • Anticipated odds ratio (ORa) = 2.0
  • Level of significance = 5%
  • Power of test = 80% Alternate Hypothesis OR # 1.0
For calculation of P1 use following equation can be used.
zoom view
[If ORa <1.0, the values of P1 and 1/ ORa may be used].
In our example, P1 works out to 0.33 for OR=2.0
The sample size (n) is calculated by following equation:
zoom view
Collection, compilation, analysis, and presentation of numerical data related to or derived from records of vital events.
Vital Event
Birth, death, marriage, divorce, adoption, legitimating, recognition, annulment and legal separation.
Fertility Measurement
Birth Rate
Number of live births in an area in an year x 1000/ mid-year population of the area in the years.
It does not take into consideration still births and abortions. Entire population in denominator is not a child bearing population.
General Fertility Rate
Number of live births x 1000 / number of women in child bearing age. Points to the capacity of current female population in reproductive age group to increase the population of the area.
Age Specific Fertility Rate
Number of live births at a specific age of mother x 1000 /number of women in that specific age. From 15 to 44 years, total six group of equal size are assumed. Useful to direct couple protection method at a specific age groups and economise on resources.
Total Fertility Rate
It is calculated by summation of the age specific fertility rates and expressed per woman. It gives the number of children likely to be borne by a woman.
Gross Reproduction Rate
Total fertility rate x number of female births ÷ total number of births. This gives average number of girls likely to be borne to a woman if she is exposed to existing fertility rate and she completes her reproductive spars of thirty years. This gives future perspective of population growth.
Net Reproduction Rate
At each age of woman current fertility and mortality rates are applied and an estimate is given as to how many girls will be borne at each age and from this an estimate is made how many female children a woman will be bear in total reproduction spans to replace herself. If it as one then the population size will be more or less constant.
Child Woman Ratio
Number of 0 to 4 year age children x 1000/ number of women in child bearing age. Useful in places where birth registration is poor.
General Marriage Rate
Number of marriages x 100/ number of unmarried persons in reproductive age group in the population.
Crude Death Rate
Total number of deaths in a population in an year x 1000/ ÷ midyear population in an year.
Infant Mortality Rate
Number of deaths below one year of age ÷ total number of live births x 1000.
Maternal Mortality Rate
Number of maternal deaths during pregnancy, childbirth and within 42 days of delivery x 1000/ total number of live births.
Cause of Specific Death Rate
Deaths due to a specific cause x 1000/ midyear population.
Period Specific Death Rate
Deaths due to a specific cause in a specific period x 1000 / population in that specific period.
Case Fatality Rate
Number of deaths due to a specific disease x 100 / number of patients of that specific disease.
Age Specific Death Rate
e.g. = Deaths at the age group of 21 to 25 years x 1000 / population in the age group of 21 to 25 years.
Perinatal Mortality Rate
Number of foetal deaths from 28th week of gestation to infant deaths within first seven days of life x 1000 / number of live births.
Neonatal Mortality Rate
Deaths of infants under 28 days x 1000 / number of live births.
Post Neonatal Mortality Rate
Infant deaths after 28 days but below 1 year of age x 1000 / number of live births.
Proportional Mortality Rate
e.g. = Number of deaths due to CAD in a specific period x 100 /(number of deaths due to all causes in the same period).
Standardised Mortality Ratio
e.g. = Observed deaths in a particular occupation ÷ expected number of deaths in total occupation at mortality rate in general population.
  1. Net migration = In migration – Out migration
  2. Migration rate = Number of migrants x 1000 / Total population
  3. Efficiency of migration = In migration – Out migration /In migration+ Out migration.
MORBIDITY STATISTICS: (Not Vital Statistics)
  1. Incidence rate (Spells): New spells of disease in a specific period x 1000/ ÷ average number of susceptible exposed
  2. Incidence rate (Persons): Number of persons who start disease in specific period x 1000 / Average number of persons at risk for the disease
  3. Point prevalence rate: Number of new and old cases of a disease in a period x 1000/ estimated population in that period
  4. Period prevalence rate: Number of old and new cases in specific period x 1000 / Estimated mid period population
  5. Prevalence = Incidence x average duration.
  6. Secondary attack rate: Total number of diseased from among the susceptibles exposed x 100 / total number of susceptibles exposed
A hospital generates lots of data and statistical informations generated from hospital data is hopsital statistics. According to World Health Organization, hospital statistics provides data for:
  1. Preparing hospital budget.
  2. Distribution of resources to various departments.
  3. Computation of cost-benefit and unit costs of various services.
  4. Financing agencies.
  5. Future projections and planning.
  6. Assessment of utilization of services.
  7. Evaluation of various services and their improvement.
The imprtant indicators used are described briefly below.
  1. Total beds (Bed compliment): It is the total number of beds normally available for the use of patients.
  2. Average daily patients (Census) : It is the average daily number of inpatients receiving care, excluding newborns, in a defined 71period. It is calculated by adding up the daily number of patients and dividing it by the number of days. Usually it is calculated for a week or a month.
  3. Patients-day: The number of patients at 1200 (midnight) is enumerated. A patients-day is period for which an inpatient avails service between census-hour (i.e. 1200 midnight) on two consecutive days. Here the date of discharge is excluded.
  4. Bed occupancy: It is calculated by:
    Patients day x 100 / Total beds.
    This gives bed occupacy for a day. For any period bed occupancy is the ratio of actual patients-days tof maximum possible patient days between the period under question. Maximum possible patients-days will be Total beds x Number of days in the period under question. Bed occupancy calculated for different wards and departments indicates utilization of beds.
  5. Average length of stay: This is the average patients-days of service rendered by the hospital. When calculated for different service departments, it may indicate where there is scope for improvement.
  6. Turnover interval: It is the average number of days a bed remains vacant. Large turnover intervals indicate inefficient use and scope for improvement.
  7. Death rate: Gross death rate for the hospital is = Total number of deaths in a given period/(Total discharges + Total deaths). It can be calculated separately for patients given anaesthesia, patients undergoing operation, women availing delivery service, etc.
Definition, Approaches and Keywords
Research is systematic process aimed at acquiring new knowledge through verifiable examination of data and empirical testing of hypothesis. Research in faculty of medicine is directed to improvement in health care. However, the research in medicine is constrained by ethical considerations which may not come into research in some scientific discipline like chemistry. Research in medicine is also required to give consideration to priorities. Thus, research on new drugs for TB, search for vaccine against AIDS and malaria, development of strategies for elimination of polio get priority.
Approaches to research: Selection of approach to research will depend on the existing level of knowledge. Exploratory approach is indicated when there is no or minimal knowledge about the pathogenesis of a disease, its risk factors and interventions. Here, no hypothesis is generated. Hence, hypothesis formation itself may be the objective. In analytical approach, there is some or conflicting knowledge about the pathogenesis, risk factors etc. Hypothesis generated in this regard through exploratory studies needs confirmation. However, there is no manipulation by the investigator. Same is true about the exploratory studies. So, exploratory and analytical studies are essentially observational studies. In experimental approach, we are a step ahead of the analytical studies. There is an active attempt on the part of the investigator to manipulate the conditions to confirm a hypothesis generated through an experiment.
Various methods of epidemiological studies are enumerated below.
  1. Exploratory studies:
    1. Cross sectional studies
    2. Prospective studies
  2. Analytical studies
    1. Case-control studies
    2. Cohort studies
  3. Experimental studies
    1. Randomized Controlled Trials
      1. Clinical trial
      2. Field trial
      3. Community trial
    2. Non-randomized trials
      1. Trials without control
      2. Natural experiments
      3. Before-after trials
The methods described above are quantitative methods of research. If sampling methods are scientific, the results of these studies can be applied to the population from which the sample is drawn. This is called internal validity. If it can be shown that the sample represents populations other than the one from which it was drawn, then the observations on the sample can be applied to the other population as well. This is called external validity. However, the major concerns of these studies are the sampling methods and 73sample size. The qualitative research methods, on the other hand do not provide quantitative indicators, but help in understanding some complex phenomenon. These methods were widely used in behavioral sciences like sociology. Their use in medicine in general and public health in particular is relatively new development. Behavioral problems like sickness behavior, health behavior and treatment behavior can be studied with qualitative methods, some of which are enumerated below.
  1. Case studies
  2. Focus group discussion
  3. Projective methods
  4. Delphi technique
  5. Nominal group method
Some keywords in research methodology:
  1. Goal is the ultimate desired end result (impact) of a program or activity. It is not bound by time. (Impact is a change in health status as indicated by changes in mortality, morbidity, fertility, disability etc. Goal is thus related to impact. Thus, we can have a goal of reduction of Infant Mortality Rate to below 60 per 1000 live births. Many times goals are not precise. “Health For All” is an example.
  2. Objective is the planned or intended end result (Output or Effect) of a program or activity. It is bounded by time. Usually it is a step in attainment of goal. Thus, we can have an objective of 85% coverage of immunization and 100% deliveries by trained staff. Output includes products and services provided by the program like, number of sterilizations performed, immunizations given etc. Effect is the change in knowledge, attitude and practices (skills) as a result of an intervention.
  3. Target is an indicator with magnitude. It is also bound by time and is quantifiable and measurable.
  4. Variable is characteristic that is to be measured. It can be a variate or attribute. (These have already been in explained under “Definitions and Common Terms”) These could be Independent (e.g. inputs), Dependent (e.g. output, effect, Impact), Confounding (Intervening), or Background (age, sex, occupation, income, religion, caste etc.).
  5. Hypothesis is a tentative prediction or explanation. This could relate to association between two attributes (like, smoking and 74cancer) or correlation between two variates (like, height and weight). The hypothesis can then be stated some thing like this:
    “Smoking causes lung cancer”.
    “Weight has a positive correlation with height”.
    With, experience and knowledge the hypothesis can be refined as the one given below.
    “Smoking X number of cigarettes for Y years causes pulmonary carcinoma”.
  6. Population (already explained in previous sections).
  7. Sample (already explained in previous sections).
  8. Protocol is the plan or blue print of the research project. It describes the goals/ objectives, variables, hypothesis, instruments (material and methods) etc. related to the research.
  9. Pilot is the research conducted on smaller scale in a short time. The objective could be:
    1. Gaining experience in the methodology
    2. Training of the personnel
    3. Determining sample size
  10. Study instruments include data collection instruments (observation, interview, questionnaires, schedules, or projective techniques) and additional instruments like, personnel and equipments. Observation, questionnaire and interview, all can be “Structured” or “Unstructured”. Questions can be “Open ended” or “Close ended”.
Research Protocol
Designing a research protocol involves following steps. These steps are not necessarily in sequence, but there can be a considerable overlap.
  1. Research topic and problem
  2. Search for related work
  3. Statement of objectives
  4. Selection of study variables
  5. Statement of hypothesis
  6. Research strategy
  7. Selection of study instruments (Material and Methods)
  8. Dummy tables
  9. Write-up
  1. Research topic and research problem: Selected research topic should be some concern and in the end should further our knowledge. In general it should
    1. Provide additional information on some specific health problem,
    2. Evaluate a health care program or its component,
    3. Compare two or more health interventions, and
    4. Give estimates about future.
    The research problem needs to be stated in clear terms. This helps in the further steps. The protocol should also state the relevance the problem and its field of application.
  2. Search for related work: Before starting the research, it is necessary to search for related work done anywhere at any other time in the past. This is required for following reasons.
    1. Investigator becomes familiar with the topic. This improves his/her understanding.
    2. It is useful in defining the study variables.
    3. It helps in formulation of hypothesis.
    The search can be done by following methods.
    1. Discussion with experts.
    2. Finding published work in journals and then finding cross references.
    3. Use of cumulative medical index.
    4. Internet (Websites like, provide abstracts)
  3. Objectives: Statement of objectives gives a clear direction to the research project. In general objectives are associated with specific research question. If we want to know about the efficacy of new drug against a disease, the objective would be “to find the efficacy of the drug against the disease”. If we want to ascertain whether exposure to certain chemical increases the risk of certain disease, then the objective would be “to determine whether exposure to the chemical is associated with increase in the risk of the disease”.
  4. Study variables: various types of study variables have already been described. The that would be used in the study will have to be mentioned clearly in the research protocol. This clarifies what is measured and how. The study variables are usually standardized and have method of calculation and unit of measurement.
  5. Hypothesis: The concept of hypothesis and techniques in its formulation are alraedy described. It translates the problem into 76precise, unambiguous predictions. In the examples quoted under “objective” the hypothesis can be as below.
    1. “Newer drug has higher cure rate and lower rate of toxicity than the established drug”.
    2. “Exposure to the chemical for 10 years or more increases the risk of the disease.”
  6. Research strategy: A research strategy is nothing but the approach selected among the various options like exploratory, analytical and experimental. The choice would depend on the level of existing knowledge and the research problem. In few instances it may be guided by the resources available. It also includes description of settings under which the study will be conducted, e.g. hospital or community. It also includes defining the population, place and time of the study. Usually some sampling technique will have to be resorted to. Sampling should address to sample size, method and sampling error. Reasech instrument will decide whether controls will be required or not.
  7. Study instruments: Description of study instruments involves detailed description of data collection method, e.g. questionnaire, interview, measurement etc. It should also clarify whether pretesting, pilot studes were done or not. Study instruments should also specify the data analysis and inference techniques (statistical methods) proposed to be used.
  8. Dummy tables: Dummy tables are empty tables without any data proposed to be used for data analysis. It clarifies the data reduction that will be done. To some extent, dummy tables also give an idea about the statistical techniques to be used.
  9. Writeup: The writeup is the detailed report of the protocol. Generally the financing agencies expect the protocol to be in particular format. It should be adhered to. A good writeup is always accompanied by executive summary.
Reporting of the research work: An investigator would like to publish the research work in some journal. Each journal has its own format for the literature it publishes. In general following heads should be covered.
Summary, introduction, objectives, material and methods, observations and discussion, conclusions and recommendations, references.
Ethical Considerations in Medical Research
As said above, the research in the field of medicine, unlike in basic sciences, is bound by the ethical considerations. It is expected that each institution should have an ethical committee. It should discuss the ethical issues related to any research conducted, supported or financed by it. Fortunately The Indian Council of Medical Research has come up with “Ethical Guidelines For Biomedical Research on Human Subjects” in the year 2000. Interested readers can obtain the dtetails of the guidelines from that institution. It consists of 11 guiding principles that are enlisted below.
  1. The principle of essentiality.
  2. The principle of voluntaryness and informed consent.
  3. The principle of non-exploitation.
  4. The principle of privacy and confidentiality.
  5. The principle of precaution and risk minimization.
  6. The principle of professional competence.
  7. The principle of accountability and transparency.
  8. The principle of maximization of public interest and distribution.
  9. The principle of public domain.
  10. The principle of totality and responsibility.
  11. The principle of compliance.
The Drug Controller General of India has given following guidelines for a good clinical trial.
  1. Title describing the trial.
  2. Unique identifying code for the trial.
  3. Name, qualifications, address and phone/fax numbers of the investigators.
  4. Study site: Address, and phone number/fax number.
  5. Sponsor's address, phone number/fax number.
  6. Statement of confidentiality and bonafide disclosure.
  7. Introduction giving background and justification for trial.
  8. Objectives (questions for which answers are seeked).
  9. Study design.
  10. Study subjects with details.
  11. Drug to be studied with its details.
  12. Observations to be made (study variables).
  13. Data recording methods.
  14. Statistical methods to be used.
  15. Administrative details like, ethical committee report, regulatory approval, informed consent, risk coverage, etc.