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7440326.ppt

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Periyar University, Salem-11
Periyar University, Salem-11

This document provides an overview of parametric and non-parametric statistical tests. It explains that parametric tests make assumptions about the population distribution, comparing parameters like the mean and standard deviation, while non-parametric tests make no distributional assumptions and instead compare rankings or counts of observations. Specific tests discussed include the paired t-test, unpaired t-test, ANOVA, Wilcoxon matched pairs test, Mann-Whitney U test, median test, Kruskal-Wallis test, and McNemar's test. Examples are provided for each test.

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7440326.ppt
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 / ¦Á ? 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
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 ¨Cve ? 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. ? n1 is associated with ¡ÆR1i , n2 is associated with ¡ÆR2j 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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7440326.ppt

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7440326.ppt

  • 2. 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.
  • 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 ? ? The mean and median are approximately same. ? Construct a Histogram and trace a normal curve. Example ? Level of Significance / p-value / Type I error / ¦Á ? Degree of Freedom
  • 5. Types of variables Independent variable Dependent variable Data representation 1. Continuous or Scale variable 2. Discrete variable Nominal Ordinal (Categorical)
  • 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. 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
  • 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 ¨Cve ? 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 ¡ÆR1i , n2 is associated with ¡ÆR2j 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. 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
  • 15. Mc Nemar¡¯s Test Areas of application >> Similar to the parametric paired t-test, but the dependent variable is discrete, qualitative.