Parametric & Non-parametric

Parametric & Non-parametric

Parametric

Non-Parametric

Ø A parameter to compare Mean, S.D. Normal Distribution & Homogeneity

Ø No parameter is compared Significant numbers in a category plays the roleØ No need of Normal Distribution & HomogeneityØ 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-parametricBoth 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 ?

Ø The mean and median are approximately same.Ø 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 variableDependent variable

Data representation1. Continuous or Scale variable

2. Discrete variableNominal

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 –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. n1 is associated with ∑R1i , n2 is associated with ∑R2j

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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