Parametric & Non-parametric

2. Parametric & Non-parametric Parametric • ØA parameter to compare • Mean, S.D. • Normal Distribution & Homogeneity Non-Parametric ØNo parameter is compared Significant numbers in a category plays the role ØNo need of Normal Distribution & Homogeneity ØUsed when parametric is not applicable.

3. 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.

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

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

6. Decide your test

7. Decide your test

8. 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

9. 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

10. ANOVA Areas of application >> 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

11. 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

12. 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. • n1 is associated with ∑R1i , n2 is associated with ∑R2j Example

13. 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

14. KruskalWalis A Non-parametric procedure >> This is the parallel test to the parametric ANOVA >> ANOVA was an extension of 2-group t-test >> KruskalWalis 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 Example >> Areas similar to ANOVA >> Comparison of dependent variable between categories in a demographic variable

15. 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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