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Chapter-12 Comparing groups: numerical Variables

BOOK TITLE: Research Methodology Simplified: Every Clinician a Researcher

Author
1. Parikh Mahendra N
2. Mukherjee Joydev
3. Hazra Avijit
4. Gogtay Nithya
ISBN
9789350250037
DOI
10.5005/jp/books/11435_12
Edition
1/e
Publishing Year
2010
Pages
8
Author Affiliations
1. Seth GS Medical College and Nowrosjee Wadia Maternity Hospital, Mumbai, Seth Gordhandas Sunderdas Medical College, Nowrosjee Wadia Maternity Hospital, Mumbai, Maharashtra, India; Shushrusha Citizens’ Cooperative Hospital, Mumbai, Maharashtra, India; Fertility Sterility, India; The Journal of Obstetrics and Gynaecology of India, Nowrosjee Wadia Maternity Hospital, Mumbai, Mumbai, Maharashtra, India, Mumbai, Seth GS Medical College and Nowrosjee Wadia Maternity Hospital, Mumbai, Maharashtra, India
2. North Bengal Medical College, West Bengal, India, RG Kar Medical College, Kolkota, RG Kar Medical College, Kolkata, India, RG Kar Medical College, Kolkata, RG Kar Medical College, Kolkata, West Bengal, India
3. Institute of Postgraduate Medical Education, and Research, Kolkata, Institute of Postgraduate Medical Education and Research, Kolkata, India, Institute of Postgraduate Medical Education and Research (IPGMER), Kolkata, West Bengal, India
4. Seth Gordhandas Sunderdas Medical College and King Edward Memorial Hospital, Mumbai, Maharashtra, India; Journal of Postgraduate Medicine, Seth GS Medical College and KEM Hospital, Mumbai, India, Department of Clinical Pharmacology, Seth GS Medical College and KEM Hospital, Mumbai, India
Chapter keywords

Abstract

Numerical data that are normally distributed can be analyzed with parametric tests, that is tests based on the parameters that define a normal distribution curve. If the distribution is uncertain, the data can be plotted as a normal probability plot and visually inspected, or tested for normality using one of a number of goodness of fit tests, such as the Kolmogorov-Smirnov test. The widely used Student’s t test has three variants. The one-sample t test is used to assess if a sample mean (as an estimate of the population mean) differs significantly from a given population mean. The means of two independent samples may be compared for a statistically significant difference by the unpaired or independent samples t test. If the data sets are related in some way, their means may be compared by the paired or dependent samples t test. The t test should not be used to compare the means of more than two groups. Applying the t test to compare groups in pairs in such a situation will increase the probability of type I error. The one-way analysis of variance (ANOVA) is employed to compare the means of three or more independent data sets that are normally distributed. Multiple measurements from the same set of subjects cannot be treated as separate unrelated data sets. Comparison of means in this scenario requires repeated measures ANOVA. It is to be noted that while a multiple group comparison test such as ANOVA can point to a significant difference, it does not identify exactly between which two groups the difference lies. To do this, an appropriate post hoc test is necessary. An example is the Tukey’s honestly significant difference test following ANOVA. If the assumptions for parametric tests are not met, there are non-parametric alternatives for comparing data sets. These include Mann-Whitney U test instead of unpaired Student’s t test, Wilcoxon’s matched pairs signed ranks test in lieu of paired Student’s t test, Kruskal-Wallis test as the non-parametric counterpart of ANOVA and the Friedman’s test instead of repeated measures ANOVA.

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