Parametric & Non-parametric Parametric Non-Parametric  A parameter to compare Mean, S.D.  Normal Distribution & Homogeneity  No parameter is compared Significant numbers in a category plays the role  No need of Normal Distribution & Homogeneity  Used when parametric is not applicable.

Parametric & Non-parametric Parametric Vs Non-parametric Which is good ? If parametric is not applicable, then only we go for a non-parametric Both are applicable, we prefer parametric. Why? In parametric there is an estimation of values. Null hypothesis is based on that estimation. In non-parametric we are just testing a Null Hypothesis.

Normality ? How do you check Normality ?  The mean and median are approximately same.  Construct a Histogram and trace a normal curve. Example ? Level of Significance / p-value / Type I error / α ? Degree of Freedom

Types of variables Independent variable Dependent variable Data representation 1.Continuous or Scale variable 2.Discrete variable Nominal Ordinal (Categorical)

Decide your test

Paired t-test Areas of application >> When there is one group pre & post scores to compare. >> In two group studies, if there is pre & post assessment, paired t is applied to test whether there is significant change in individual group. S = S.E. = t = S.E. Example

Unpaired/independent t-test Areas of application >> When there is two group scores to compare. (One time assessment of dependent variable). >> In two group studies, if there is pre & post assessment, paired t is applied to test whether there is significant change in individual group. After this, the pre-post differences in the two groups are taken for testing. Example

Areas of application ANOVA >> When there is more than two group scores to compare. Group A x Group B x Group C Post-HOC procedures after ANOVA helps to compare the in-between groups A x B, A x C, B x C Similar to doing 3 unpaired t tests Example

Wilcoxon Matched Pairs A Non-parametric procedure >> This is the parallel test to the parametric paired t-test  Before after differences are calculated with direction + ve or –ve  0 differences neglected.  Absolute differences are ranked from smallest to largest  Identical marks are scored the average rank  T is calculated from the sum of ranks associated with least frequent sign  If all are in same direction T = 0 Example

Mann Whitney U A Non-parametric procedure >> This is the parallel test to the parametric unpaired t-test  Data in both groups are combined and ranked  Identical marks are scored the average rank  Sum of ranks in separate groups are calculated  Sum of ranks in either group can be considered for U.  n 1 is associated with ∑R 1i, n 2 is associated with ∑R 2j Example

Median Test A Non-parametric procedure Similar to the cases of Mann Whitney >> This is the parallel test to the parametric unpaired t-test  Data in both groups are combined and median is calculated  Contingency table is prepared as follows

Kruskal Walis A Non-parametric procedure >> This is the parallel test to the parametric ANOVA >> ANOVA was an extension of 2-group t-test >> Kruskal Walis is an extension of Mann Whitney U  Data in all groups are combined and ranked  Identical marks are scored the average rank  Sum of ranks in separate groups are calculated Areas of application >> Areas similar to ANOVA >> Comparison of dependent variable between categories in a demographic variable Example

Mc Nemar’s Test Areas of application >> Similar to the parametric paired t-test, but the dependent variable is discrete, qualitative.

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