Non-parametric stats.

What are the parameters required to use a non-parametric test?

A nonparametric test should be used if... 

• You CANNOT assume a normal/Gaussian population/distribution 

• Variance is unequal 

• Have a very small sample 

• Have nominal or ordinal data

What is the ranking score concept used in non-parametric tests

Rank data out from smallest to largest 

• Smallest score = 1 

• Highest rank = n 

• If 2 or more scores have the same value, they’re given the average of the possible ranks 

What is a non-parametric test

• Less powerful because have a higher chance of type 2 error 

  • BUT more powerful with non-normal populations 

    • No outliers 

  • Power only an issue if you DON’T get statistical significance (null not rejected) 

• Most involve ranking scores (rather than comparing precise metric changes) 

What is a Mann-Whitney U-test

non-parametric version of student’s t-test 

• Requires at least ordinal scale  

• Doesn't look at the mean because looking at the median is more accurate 

• Test determines if the difference in the medians is large enough to be significant 

Procedure:  

• Combine both sets of scores and RANK them (farm boy example: ranked 1-20)

• Separate the ranks by group and add ranks together from each group 

• Perform test 

What is a Kruskal-Wallis one-way ANOVA

non-parametric version of ANOVA 

• Assumes ordinal data 

• Three or more INDEPENDENT groups 

• Test determines if the differences in the mean of the ranks is large enough to be significant 

Procedure:  

• Combine both sets of scores and RANK them 

• Separate the ranks by group and add ranks together from each group AND take average 

• Perform test 

Ex: Only state vs private had a statistically significant difference 

What is a Wilcoxon Matched pairs signed-ranks test

non-parametric version of paired t-test 

• Compares 2 paired groups (DEPENDENT) 

• Negative values are taken as the absolute version 

What is a Friedman test

non-parametric version of a repeated-measures ANOVA 

• Compares 3 or more paired groups (DEPENDENT) 

• Followed with a post-test 

What is the non-parametric equivalent of each parametric test

Look at image