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2016 ; 61
(3
): 251-60
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Biostatistics Series Module 3: Comparing Groups: Numerical Variables
#MMPMID27293244
Hazra A
; Gogtay N
Indian J Dermatol
2016[May]; 61
(3
): 251-60
PMID27293244
show ga
Numerical data that are normally distributed can be analyzed with parametric
tests, that is, tests which are 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. Although it is possible to
compare groups in pairs, when there are more than two groups, this will increase
the probability of a 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 such a
situation 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, multiple group comparison needs to be followed up by an
appropriate post hoc test. An example is the Tukey's honestly significant
difference test following ANOVA. If the assumptions for parametric tests are not
met, there are nonparametric alternatives for comparing data sets. These include
Mann-Whitney U-test as the nonparametric counterpart of the unpaired Student's
t-test, Wilcoxon signed-rank test as the counterpart of the paired Student's
t-test, Kruskal-Wallis test as the nonparametric equivalent of ANOVA and the
Friedman's test as the counterpart of repeated measures ANOVA.
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