Health and DiseaseCHAPTER 1

Systems of medicine have been in practice since antiquity, but typically they achieved little. In absence of knowledge of anatomy, physiology and pathology, the practice of medicine carved its niche as a mystic specialty that a few shamans and priests were capable of. This kind of medicine was learnt from experiences, kept minor ailments under check, and was generally accepted by people. Nothing fancy was expected from the doc, just a few herbs, a little bloodletting, and there you go. The idea of hygiene and community sense, once reaching its pinnacle in Roman and Indian civilization, achieved an all time low in the middle ages. No wonder plagues swept across Europe that time.

The father of scientific medicine was (probably) Paracelsus, who publicly burnt the works of Galen and went out to preach that medicine was governed by the same principles of the natural philosophy, the same rules that rotated the planets in their courses. Andreas Vesalius raised anatomy to a science, and so did Ambroise Pare for surgery. Thomas Sydenham established the clinical methods, William Harvey pioneered the circulatory system – and Antoni van Leeuwenhoek came up with his microscope. The change had set in.

Unforeseen to the harbingers of the industrial revolution, the after effects were already beginning to take a toll on the mean life expectancy of England’s laboring class. The cholera epidemic in London of 1832 led Erwin Chadwick to investigate the health of the inhabitants of a large town in England. His report stated, albeit revolutionary for his time, that filth is man’s greatest enemy, and the style of documentation is still a lesson.

Following the ‘Great Sanitary Awakening’ in England (inspired by the works of Erwin Chadwick), the first Public Health Act was passed in 1848. It emphasized mostly on sanitation and community hygiene, and was implemented from 1880–1920. These 40 years were aimed at control of physical environment (sanitation). The points stressed upon were improvement of sanitation, water supply and sewage disposal. The modern concepts of septic tanks and protected urinals and air-conditioned meat vendors was born in this era.

This period focussed on the quality of life (i.e. improving the host factor in the epidemiologic triangle). The stress was upon nutrition, education and general well-being of the community. It was this phase that mental disorders came into limelight. In total, the phase was aimed at improving the herd immunity (the resistance of a community to a disease).

As the communicable diseases were conquered (at least, in the developed world), the noncommunicable diseases began to steal the show. Research in the later half of twentieth century emphasized on social and behavioral aspect of diseases. Much ado was placed over the social harmful factors (smoking, sedentary lifestyle, malnutrition, alcohol, etc).

In spite of medical advances

Preventive medicine is the art and science of

Social medicine is a natural successor to social anatomy (demography), social physiology (well-being of the community) and social pathology (dowry, early marriage, malnutrition, prostitution, etc.).

It is the study of :

This is the utopian definition of health, “complete physical, mental and social well-being” is neither practical nor feasible. According to this definition, health is no static entity, but it resembles a pendulum oscillating between positive health and death.

Health is a condition or quality of humans expressing adequate functioning in a given condition – genetic or environmental.5

It is the +ve end of the health pendulum (Fig. 1.1)—A perfect functioning of humans in terms of biological, social and psychic components.

Over the ages, what people have thought of ‘health’ has undergone several changes.

Self care (as you know – the best care) is all those practices which keep the individual healthy (hygiene, sleep, good food, no smoking/drinking, active life). 6It is unaided by professionals and unchallenged by health insurance companies. Every individual takes care of himself/herself determined by the degree of his/her enlightenment.

NO. “Physical, mental and social well being” cannot be achieved by any individual simply by himself, whatever his socioeconomic status is. No system of internal medicine (centered around a single patient) can provide total health. The poor, being the ones with the cash flow, are less dependent on individual health care and more on state health services. But the rich too, can NOT simply buy health, and have to depend upon community health sometime or the other. For example, nosocomial infections are a problem of super specialty hospitals that predominantly affect the rich. These highly resistant organisms have evolved over decades of rueful antimicrobial practices, and such practices can never be stopped until the state comes up with a definitive ‘antimicrobial policy’ which will be based on regular sampling of organisms from environment, testing their resistance patterns and recommendation of a select set of antimicrobials for each category of organisms, beginning with the one with the narrowest spectrum. This is only one of several instances of how community health affects the rich people and super specialty ‘five star’ hospitals.

There are three levels of community activity in health care

The paradigm of socialized medicine is that the state is responsible for health of its citizens, not merely doctors and hospitals. Indian constitution recognises the responsibility of the state for the health of its citizens. Also, National Health Policy 1983 indicates commitment to health for all.

Programs have been taken in international level concerning health. This is necessary because, especially communicable diseases are a threat to the whole human population. The UN, Technical Cooperation in Developing Countries (TCDC), Association of South East Asian Nations (ASEAN) and South Asian Association for Regional Cooperation (SAARC) are important mechanisms for international cooperation.

Health is a combined property of man and his environment. These are all the factors, ultimately, who determine the health of the individual.

It is not where community medicine can interfere much. Genes will continue to produce ailments and we can at most go for genetic screening and counseling of high-risk parents.

Internal environment. The cause of majority of noncommunicable disease like ischemic heart diseases, diabetes, etc.

External environment. Most communicable diseases/“environmental” diseases are due to the external environment. The external environment can be divided into physical, biological and psychosocial components—each of which affects health.

It is ‘the way people live’. It includes culture, behavior, and personal habits (smoking, etc.). Lifestyle develops from a combined influence of peers, parents, siblings, teachers and media (television, internet).

Health requires a healthy lifestyle. The 1960–1980s saw the social engineering phase of public health – when lifestyle was the most stressed upon factor.

Economic status. It determines the purchasing power, standard of living, quality of life and disease pattern. The per capita GNP is usually the important factor if the wealth is distributed evenly (which eventually is a far dream in most of the countries in the world). Ironically – poverty and affluence can both be curses over health.

Education. Particularly, education of women is important, as the mother is in charge of the household. The world map of poverty, unemployment, communicable diseases closely coincides with that of illiteracy. Studies indicate that education, upto an extent, can compensate for the degradation of other determinants of health like economy and health facilities.

Occupation. Unemployment leads to high morbidity and mortality, psychic and social disorders (like eveteasing). Again, working in a physically/mentally 8hostile environment (acid factory/dye industry/grumpy boss/hostile colleagues) will affect the health of the individual.

Politicians decide health policies, choice of technology, resource allocation and manpower policy. Often the main obstacles to implementing a health service are not the technology but a forthcoming change in government. The percentage of GDP spent on health (should be 5% according to WHO) is a quantitative indicator of the government’s dedication to the health of its public.

Food and agriculture, education, industry, communications especially, via electronic means, social welfare, rural development indirectly affect the health. This is no medical zone. Doctors can’t create employment, distribute free manure and seeds to farmers, cook mid-day meals or anything like that. They are called only after children are poisoned by a mid-day meal for damage control.

It is the service given to individual or community for prevention of disease, promotion of health and therapy. Any organization which is primarily involved in health care comes under health system.

A health indicator should be

Anthropometry. Usually done in preschool (<5 years) children usually to see nutritional status. 46% of children in India are underweight, one of the highest rates in the world and nearly the same as subSaharan Africa.³

These indicate the quality (how good the health care facility is), quantity (how many of hospitals, doctors and health care workers are there) and distribution (how evenly the facilities are spread across the country) of health services.

The incidence of homicides, suicides, crime, juvenile delinquency, drug abuse, domestic violence, accidents, smoking and alcoholism indicate the health status of the society as a whole.

Proportion of GDP spent on health and primary care. Indicates how dedicated the state is to providing ‘health for all’ for its citizens. India spent a healthy 6% of GDP towards healthcare in the mid 1990s, but the amount has declined since and by 2007, has declined to 2% only,⁸ which translates to only Rs 37/month/Indian on health care.⁹

Per capita ¹¹ income. India boasts of some of the richest men in the world, but on an average, an Indian man earns $1070 per year only (ranked 143nd in the world), and 75.6% of the population live on less than $2 per day (purchasing power parity), which is equivalent to 20 rupees per day in nominal terms.¹² Poverty forces poor people to work unhealthy professions, get into crime, neglect their children and die young. Because infants of poor parents die more frequently, and children of poor parents are expected to work from their very toddler age, poor people have the most fertility (which, in turn, aggravates the poverty even further).

Gross domestic product and its fractionation. Although the GDP in India is a healthy $1.209 trillion (with a 6.7% growth rate in 2007/2008 fiscal year), economy in India is at best in a confused state. Most of the GDP is spent in agriculture (17.2%), industry (29.1%) and services (53.7%), leaving very little to health and education. 41.6% of population live below new international poverty line (i.e. < 1.25 US$/day purchasing power parity),¹³ which is an, however, improvement from 60% in 1981.

Population having access to safe water. While the share of those with access to an improved water source¹⁷ is 86%, the quality of service is poor and most users that are counted as having access receive water of dubious quality and only on an intermittent basis. In rural areas, the figure is 83%.

PQLI – Physical quality of life index - money can’t buy happiness. It is determined by an average of

All three have same weight. India scores a PQLI of 43.

The feel good factor, if analysed, has two components.

Health is an integral part of economic development of a country. Health and its maintenance is a major social investment. However, it has been shown conclusively that simple health measures, use of primary health care, aseptic delivery practices, improvements in education can improve health status of the community without any extra monetary input. A healthy population will, eventually, serve the country better and accelerate development.

The HDI indicates quality of human condition based on life expectancy at birth, per capita annual income (in US$ purchasing power parity¹⁸), educational attainment (adult literacy and mean school years). It varies between 0–1. In HDI rank, India is 134th in the world.¹⁹

To accomodate varying male: Female ratio in countries, and emphasize the differences in gender specific literacy, the UN has devised the Gender related development index. The principal difference from HDI is UN uses a different standard for male and female life expectancy, basically assuming that it is natural that women should live about 5 years longer than men.

The health system that most of the nations, including India, have set up after 1980 consists of three tiers, as recommended by “health for all” policy.

This is the bare necessity—Essential health care every citizen needs. It is the first level of contact between public and the health system. Most of common health problems should be served at this very level. This includes primary health center/subcenters. The nature of service is curative + preventive.

Diseases beyond the primary level are referred to secondary level which provides mainly curative service. It includes district hospitals, subdivisional hospitals, state hospitals, community health center (CHC—‘1st referral unit’)/rural hospitals. The level is called the ‘1st referral level’ because ideally, it should receive only those patients who have been referred from primary level.

It is superspecialty care. It includes medical colleges, regional hospitals and medical institutes (i.e. school of tropical medicine). This tire is also concerned with training, administration, planning and management of the whole system.

In the absence of a WHO definition, I will only cite those definitions of ‘disease’ which other people have mentioned.

Each disease usually begins with entry of the agent → subclinical phase → mild/moderate/severe clinical phase → recovery, death or disability (organ amputation/prosthetics/carrier states in case of communicable diseases, etc.) (Fig. 1.2). This is usually the spectrum of a disease.

Actually, there are four kinds of people in this world (Fig. 1.3).

Over the ages, our ideas of disease causation has gone a few paradigm shifts.

It is very embarrassing to classify diseases. Most names have been given irrationally by looking at a single sign or symptom (i.e. ‘diabetes mellitus’ meaning ‘frequent sweet urine’) or when more details were known, an underlying pathology (i.e. ‘myocardial infarction’). There is no consistency in the concept of what you call the disease. For example, a man with long standing diabetes mellitus developed hyperlipidemia, which accumulated as an atherosclerotic plaque in his left coronary artery, and culminated in thrombosis of that artery resulting in a myocardial infarction, ending up with left heart failure and pulmonary edema, ultimately the man dying of apnea. So what was his disease?

Defects in genome may lead to diseases, via enzyme deficiency and altered metabolism. Genetic diseases are on the rise, chiefly due to more exposure to radiation.

Congenital genetic diseases

19Acquired genetic diseases

Infections are the major chunk in developing countries. Agents which infect man are viruses, bacteria, protozoan, helminthes, fungi, arthropods and some algae. Infections may cause complications belonging to many other categories in this list.

Deficiency anemias, malnutrition, vitamin deficiencies, etc. fall in this category. Again, obesity be considered a diseases of excess.

Alzheimer disease, cirrhosis fall into the category of degenerative disease, i.e. replacement of tissue parenchyma by fibers/glia, etc.

Accidents and war are man-made epidemics.

The classification of psychiatric diseases has produced an entire offshoot from ICD, called the Diagnostic and Statistical Manual (DSM).

An attribute or exposure that is significantly associated with development of a disease. They are only suggestive and not absolute proof of disease occurrence. Also, they must be identified prior to disease occurrence. Risk factors are suspected from descriptive epidemiologic studies and established by analytic studies.

Air pollution, water contamination, traffic problem, urban congestion, etc. are risk factors to the health of the entire community.

Presence of risk factors in an individual/group make them more vulnerable to certain diseases. They can be identified by certain definite criteria and more attention is paid to them (risk approach).

It is the

Procedure

Collection of data (mainly health indicators) → Consolidation and interpretation of data (i.e. making out information from data – what are the facts behind the figures?) → Dissemination of appropriate plan in demand of changing health status → Action for control and prevention.

Monitoring may be said to be a small fraction of surveillance. It is the performance and analysis of routine measurements aimed at detecting changes in the environment/21health status of population.Thus we have monitoring on air pollution, growth and nutritional status. In most cases, monitoring is not a medical affair – technicians and instruments can very well measure dust in the air or MAC of a child. To interpret this data (as in surveillance) however, needs professionals.

In addition to providing socialized health care to its citizens, the responsibilities of the state also include programs and actions against public health problems—A disease that affects a large number of people, killing/disabling a lot of people and decreasing the productivity of the nation (tuberculosis, malaria, leprosy in India, to name a few). There are three steps, to be followed one after another, to win over a disease (Fig. 1.5; A = agent, H = host, E = environment).

The ‘agent’ remains in environment but to such a low level that it ceases to be a public health problem. A state of unstable equilibrium is maintained in the epidemiological triad. It is an ongoing operation and functions by primary and secondary prevention. Its objectives are:

This means interruption of transmission of disease – by any means. Even after elimination is achieved, apparently, hidden foci of infection may persist and unrecognized methods of transmission may also exist.

It means the wiping out of the agent from the environment. It is an absolute goal and have been achieved only for smallpox (May 1980) and Dracunculiasis (2000). Poliomyelitis and measles are serious contenders in line. The criteria for a disease to be eradicated are as follows:

Recall the definition of preventive medicine: Preventive medicine is the art and science of health promotion, disease prevention, disability limitation and rehabilitation (Fig. 1.6).

These are the activities directed to prevent the occurrence of disease in a human population. The aim is to prevent disease and prolong life.²¹

Those actions which halts the progress of a disease in an individual at the incipient stage and prevents further complications. It is indeed prevention because it prevents further spread of that disease from that individual.

All measures available to

Disability can be limited by proper treatment – in this case with MDT.

Rehabilitation:Combined use of:

There are four dimensions of rehabilitation

Science believes in generalizing the special, to make general rules that apply to everybody, from a limited number of observations. This is the only way research is possible, because it is not humanly possible to examine every human on this planet to verify if he has a set of femurs. When Vesalius cut up his very first corpse, he instantly made the decision that the human species, not just the specimen on his table, but the entirety of the human species, must have two femurs. Herein lies the mathematician’s dilemma. A formal proof, as iterated in pure mathematics, should not be based on induction (that is, no one specimen should be held representative of whole of the population). A proof must establish, by mathematical procedures, an identity between two sides of an equation. This kind of reasoning, however smart it may sound, is absurd in most kinds of research except pure mathematics. For the more mundane kind of research, we cannot examine whole populations and we have to deal with samples. A few questions immediately spring up—

Statistics is the answer to these questions.

The meaning of statistics can ultimately be altered by very easy steps. The simplest is to represent data in such a manner that your boss will find it to easy to comprehend and give you a raise.

There are only a few fundamental types of diagrams.

By definition, any set of rules for assigning numbers to attributes of objects is measurement. Not all measurement techniques are equally useful in dealing with the world, however, and it is the function of the scientist to select those that are more useful. The physical and biological scientists generally have well-established, standardized, systems of measurement, unlike social scientists.

The property of intervals is concerned with the relationship of differences between objects. If a measurement system possesses the property of intervals it means that the unit of measurement means the same thing throughout the scale of numbers. That is, an inch is an inch is an inch, no matter were it falls immediately ahead or a mile down the road.

A measurement system possesses a rational zero if an object that has none of the attribute in question is assigned the number zero by the system of rules. The object does not need to really exist in the “real world”, as it is somewhat difficult to visualize a “man with no height”. The requirement for a rational zero is this: If objects with none of the attribute did exist would they be given the value zero.

In the same article in which he proposed the properties of measurement systems, SS Stevens (1951) proposed four scale types. These scale types were nominal, ordinal, interval, and ratio. Each possessed different properties of measurement systems.

Nominal scales are measurement systems that possess none of the three properties discussed earlier. Nominal renaming scales apply random numbers (or words) to objects (i.e. social security numbers, classification of diseases). Nominal categorical scales apply a different number to each category of objects (i.e. Belgians = 1, Indians = 2, Irish = 3).

Ordinal scales are measurement systems that possess the property of magnitude, but not the property of intervals. The property of rational zero is not important if the property of intervals is not satisfied. Anytime ordering, ranking, or rank ordering is involved, the possibility of an ordinal scale should be examined. As with 29a nominal scale, computation of most of the statistics described in the rest of the book is not appropriate when the scale type is ordinal. Rank ordering people in a classroom according to height and assigning the shortest person the number “1”, the next shortest person the number “2”, etc. is an example of an ordinal scale.

Interval scales are measurement systems that possess the properties of magnitude and intervals, but not the property of rational zero (i.e. the height of a person). It is appropriate to compute the statistics described in the rest of the book when the scale type is interval.

Ratio scales are measurement systems that possess all three properties: Magnitude, intervals, and rational zero. The added power of a rational zero allows ratios of numbers to be meaningfully interpreted, i.e. the ratio of John’s height to Mary’s height is 1.32, whereas this is not possible with interval scales.

The use of sampling has already been underlined.

Random sampling is left entirely to nature’s own laws of entropy, and everyone has equal probability of being selected. It provides the greatest number of possible samples, but it is also most prone to produce a distorted sample. For example, out of fifty girls and fifty boys, a random sample of 20 has to be chosen. Now it is perfectly possible that the sample of 20 that we choose has exactly 10 girls and 10 boys. It is, however, much more probable for our sample to be distorted either way, i.e. we could select more girls than boys or vice versa. It is, by sheer chance, also possible that we select only girls, and that would be an embarrassingly distorted sample, not even close to representating the population.

If we really want to do a scientific study, let’s say about the pattern recognition skill differences between boys and girls, we must select pairs of a boy and a girl, who are identical in all aspects (age, mental growth, family background, etc.) except that one is a boy and other a girl. We could make a comparison only if such matching has been done.

Suppose we pick every 10th person from our hundred (i.e. 1, 11, 21, 31 … or 4, 14, 24, etc.), which reduces the number of possible samples (in our particular case, only 10 samples can now be chosen, beginning from 1, 11, 21 to 9, 19, 29). However, if the boys and girls are so arranged that every 10th person is a girl (i.e. if there is periodicity in the population and we resonate with that periodicity), we would end up with 10 girls again. This is the drawback of systematic sampling.

We could divide the population into reasonable groups (strata) and then takes samples from each group so that no group gets predilected (we could split our hundred into ‘boys’ stratum and ‘girls’ stratum, and then go on random/systematic sampling within each stratum; this way ensure that we do not end up with only girls or only boys in our sample). Stratification can be done on the basis of age, sex, religion or any other attribute.

We could also set up groups of 10 among our hundred (each group may include both boys and girls) and select one from each group. This kind of sampling is used in immunization survey among children.

Each sample of a universe differs from another sample, and this is unavoidable, omnipresent whim of nature.

Where the sample and population are identical in characteristic, statistical theory yields exact recommendations on sample size (the formulae are, however, not exactly nice looking, and perhaps best to avoid in this textbook). However, where it is not straightforward to define a sample representative of the population, it is more important to understand the cause system of which the population are outcomes and to ensure that all sources of variation are embraced in the sample. Large number of observations are of no value if major sources of variation are neglected in the study.

Consider the shoe sizes in a class. There will be few short ones, a few large ones, but most of the children will fall in between. Every data observed from nature has two opposing characteristics.

It defines the normal limits of a variable. Range of a biologic variable is worked out only after measuring the characteristic in large number of healthy persons of the same age, sex, class, etc. Range gives an idea of how big is the universe, but not anymore about the details.

A particular value x of a variable is said to be deviating from the mean by an amount x -. This is the deviation of x from mean. The mean deviation is the average of all such deviations.

It is the ∑(x - )²/η. The variance of a population shows how widely it is distributed. Suppose, in two different classes, the mean shoe size is same. In this 32case, the class with the more variance has a more varying set of students (i.e. there are more number of students who have a very small or very large shoe size) than the class with less variance. Variance is only a number, and its unit is the square of the unit of the thing we want to measure.

This is important. Standard deviation is the square root of variance.

For constant c and random variable x,

The standard deviation serves as the ‘unit’ of variability. We speak ‘the shoe size of this student is 3 standard deviations (i.e. 3 × 1.266) more than the mean, i.e. the shoe size is mean + 3 × standard deviation = 7.818 + 3 × 1.266 = 11.616.

As much as we are fond of data and patterns of data, there is always a limit to how much data we can collect, and at some point of time, we have to stop collecting data and do some hypothesizing. It would have been very fortunate if we could 33measure all the data about every aspect of everybody, but until that happens, we have to indulge in speculation and forecasting. The beauty of inferential statistics is that, not only does it allow you to make a reasonable prediction, but also allows you to specify the possible amount of error (i.e. “I am 93% sure that there is 13% chance of rain today”). Probability is a theory of uncertainty which deals with these speculations. It is a necessary concept because the world according to the scientist²³ is unknowable in its entirety. However, prediction and decisions are obviously possible. As such, probability theory is a rational means of dealing with an uncertain world.

Truth must ultimately be tested. The material sciences (physics, chemistry) usually provide us with the tools to conduct the tests, but it is statistics which tells how to interpret the test. Common to all tests is to find association between two events, i.e.

All tests must be

It is the ability of a test to yield the same results over and over, irrespective of variations in basis of test, method or skill. No test is wholly reproducible. Suppose you have diagnosed a man to have pulmonary tuberculosis by examining sputum smears. A fellow physician may wholly disagree with you, because, when he did the examination, either

A test is accurate when

This is the challenge: To distinguish truth from just another chance finding.

This is the most important aspect of a test from a clinical viewpoint. A positive predictive value is the probability of someone testing positive actually having the disease, i.e. a/(a + b). Similarly, a negative predictive value is the probability of not having the disease in someone testing negative = d/(c + d).

The positive predictive value is affected by the

Bayesian statistics states that the positive predictive value is much higher if the disease in question is very prevalent. In another words, the usefulness of a test, apart from an inherent quality of itself (the sensitivity and specificity), is also dependant upon how common the disease is. Suppose the prevalence of a disease in a certain area is P in a population of η; this means, the chance of any individual of that area of having the disease is P (the pretest probability). Now we do the test and get a positive result. Given the specificity and sensitivity of the test, what is the probability that the individual is truly diseased?

I mentioned earlier that inferential statistics allows you to predict both the probability of an event and the amount of error of that prediction. This section is to determine that amount of error.

The null hypothesis (H₀). It states that there is no relation between the two events tested.

Type I error (α). The error that happens when null hypothesis is rejected in spite of it being true (i.e. you wrongly diagnose an association between traveling to Goa and ulcerative colitis, or something equally bizzare). The probability of a Type I error happening in a test is called p value or α limit of the test.

The idea of the normal distribution is primary to hypothesis testing. In collecting data, if our sample is large enough, we tend to have a distribution much like that of our shoe size example (Fig. 1.12).38

When we connect the top of the bars, we get a curve like this (Fig. 1.13).

The standard normal curve is a member of the family of normal curves with μ = 0.0 and σ = 1.0. The value of 0.0 was selected because the normal curve is symmetrical around μ and the number system is symmetrical around 0.0. The value of 1.0 for σ is simply a unit value. The x-axis on a standard normal curve is often relabeled with multiples of σ and called z-scores.

Suppose a variable x has a mean and a standard deviation σ. It will produce a normal curve, no doubt. But it is easier, if we want to emphasize the variation rather than the actual values, to plot it in a standard normal curve by making the mean 0 and standard deviation 1 (Fig. 1.16).

Remember that mean is always dragged towards the tail of the distribution.

Each particular area bound between any two z-scores (any two vertical lines over the x-axis) is associated with a certain degree of probability, and all such areas are called confidence intervals. In continuum with our example of shoe sizes, what of those students who have a size of 11.5 or more? Could they be considered acromegalics, or perfectly ‘normal’ people? Look at the normal curve of shoe sizes again, the size 11.5 lies outside two standard deviations (11 in our curve). The area inside two standard deviations in a normal curve, as I have already illustrated, is 0.95. Thus the area outside 2 standard deviations is obviously, 0.05. This means that the person with a shoe size of 11.5 has a 0.05 probability (or 5%) chance of being normal.

We have mentioned that 95% of values lie within 2 standard deviations around the mean. This means, 5% of values lie outside (thus called ‘outliers’). This is called the alpha limit of two standard deviation. A p-value or probability value can be calculated for each interval in the normal curve (recall that the p-value is the probability of a Type I error, i.e. a false association is diagnosed). The p-value indicates the probability of a member from that interval being selected in a random sample. A p-value outside this limit ( < 0.05) is statistically significant, i.e. if the members of this interval (the last 5% area under the normal curve) appear in a random sample, that sample has 5% chance of being representative of the population. Similarly, p-value may be deduced for any confidence interval.

Not every variable (in fact, none) is distributed normally. For the real world with its variations, inequalities and heterogeneities, statisticians have found certain patterns of how certain events tend to happen. These ‘models’ of reality are known as ‘statistical distributions’.

where r is number of times we get a ‘head’ out of those n number of tosses, and we denote a ‘head’ as our success. Now let’s put Aside all this coin business and do some real research. Suppose Aspirin cures, and has been curing, most headaches (80% of the times) since time immemorial. Now you introduce a new drug ‘headgone’ that boasts 98 cures out of 100 patients who have tried it. Is it really any significant improvement over Aspirin?

which equals to

Suppose in the mean of a population (or universe, as we’ll call it) is μ. Each sample from this population has a different mean () value. These means, if plotted are found to be normally distributed around the universal mean μ. If we take any number of samples (each containing n members²⁷), then each sample will have its own mean . It is perfectly possible that we choose a sample from the lower end of the universe, i.e. only the shoe sizes between 6–8, so that we get a sample mean = 7. It is also possible that we get, in our sample, only the largest shoe sizes, giving a sample mean = 11. But if we go on taking random samples, chances are that we would encounter every shoe size in most of our samples. So the means of our samples could be any or all of 6, 6.5, 8, 8.5, 11.5 or any plausible value. If we go on taking infinite number of samples, we would, obviously, get an infinite number of sample means. The mean of these infinite number of means, as we will find out, will be equal or very close to the universal mean μ, and the sample means themselves will form a normal curve. This ‘normal curve of the sample means’ will, again, have the universal mean μ as its mean. This is the central limit theorem.

To determine whether a sample is representative, we need to know

Find the t-value corresponding to the degree of freedom in this table, which matches less than or equal to the value in our result (i.e. 5.7). That particular t-value in this table is 2.79, which indicates a p-value of < 0.05 (see the top row of the table). Thus, the difference of shoe size in this particular sample from the average of the class is statistically significant.

Suppose the mean shoe size in a class of 30 is 9.5. For a month, we apply growth hormone injections in each of the students and then measure their shoe sizes again. 45This time, we find the mean show size to be 10.3. Does this indicate a statistical difference?

While comparing the shoe sizes of two classes, we assume that there is no difference in shoe sizes at all between the two classes (the null hypothesis). Because the two classes are nor paired (the same student cannot read in two classes) neither are the number of students the same in two classes, we cannot measure the standard deviation of differences directly, as we did in the paired t-test. Thus find the pooled standard deviation of two classes, which is

It is the test applied where two groups of subjects, with differing characteristics, have to be tested for a common variable. They are first arranged in Table 1.7.46

We assume that shoe size is no indicator of acromegaly (the null hypothesis). Then the ones with small shoes are expected to have the same rate of acromegaly as those with large shoes (and that should be the prevalence of acromegaly in whole population in general). The incidence of acromegaly in whole population is a+c/(a + b + c + d). Thus expected numbers in the four cells are calculated likewise, i.e. expected number in cell ‘a’ is total number of students with shoe size > 11 × incidence of acromegaly in whole population = (a + b) × (a + c)/(a + b + c + d). Similarly, expected number in cell b = Total number of students with shoe size < 11 × incidence of ‘no acromegaly’ (normal children) in community = (c + d)×(b + d)/(a + b + c + d).

Similar to the t-test, the F test or ANOVA compares three or more samples. It is most useful when three or more groups have variable characteristics (like children with blood groups A, B, AB and O) and need to be compared over a common variable (whether blood group affects shoe size).

The correlation coefficient is the degree of association between two variables, i.e. if number of observations is n,

where a is the value of y when x = 0 (the intercept of the correlation line on the y-axis).

If data is not measurable in an interval scale (as we are used to) but in an ordinal scale (‘1st boy’,‘2nd boy’ or ‘Grade I cancer’,’ Grade II cancer’, etc.), then the degree of correlation between two such variables (i.e. ranking of boys in a class and ranking of the same boys in annual sports—as to see whether boys good in studies are also good in athletes) is measured by Spearman’s rank correlation coefficient ρ.

The Poisson distribution describes events that are very unlikely, or very random (like rate of disintegration of radioactive atoms). There are many other kinds of distributions, and more details of each, which are more appropriate in a textbook of statistics rather than this one.