parametric & non-parametric parametric non-parametric a parameter to compare mean, s.d. normal...
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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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