Non-Parametric Hypothesis Testing
Suppose you don't know and cannot identify what form of distribution a certain piece of data demonstrates. How would you perform hypothesis tests on it? We know for normally distributed data, we can simply apply techniques such as ANOVA, t-test, and Z-test, right?
So, that brings us to the main question.
What is Non-Parametric Hypothesis Testing?
As you could guess from the name, "non-parametric tests" are used to analyze population distributions that don't have parameters. The absence of parameters translates to fewer assumptions when performing the different operations, making them quite simpler than parametric tests. It is out of the few assumptions made that they are commonly termed as "distribution-free tests".
Failure to make assumptions also means the data does not follow a normal distribution-the ideal point to apply non-parametric testing. Therefore, non-parametric tests are used as alternatives to parametric tests when we don't have to make any assumptions.
But how do we apply the technique?
Types of Non-Parametric Hypothesis Testing
Mann-Whitney U test
The Mann-Whitney U test is used as an alternative test method for the parametric "independent-samples t-test"-when the assumption for normality has been violated. Violation, in this case, implies assuming the dependent variable is normally distributed for each level of the independent variable.
This technique has a single null hypothesis with two distributions-because the independent variable has two levels (it is dichotomous).
Note that the Mann-Whitney U test has an optional assumption that the distribution is normal.
- If false, the null hypothesis becomes-both levels have equal MEANs
- If true, the null hypothesis becomes-both levels have equal MEDIANs
There are three acceptable levels of measurement in a Mann-Whitney U test.
- Ordinal level for ranked data
- Interval level where we have a meaningful difference between different points but does not have a true zero
- Ratio levels-it's similar to interval level, except that it has a true zero
Kruskal-Wallis ANOVA on Ranks
The Kruskal-Wallis hypothesis test is the non-parametric alternative to the parametric "one-way ANOVA". That's actually where the "Kruskal-Wallis ANOVA on ranks" name comes from. We apply this method when the data we are analyzing fails to meet the assumptions for one-way ANOVA.
The key assumption in Kruskal-Wallis ANOVA on ranks is that the distribution shapes are similar.
Note that the true and false conditions resemble those of the Mann-Whitney U test, as well as the three levels of measurement.
Wilcoxon Signed-Rank test
If you are familiar with the parametric "dependent/paired-samples t-test", then the "Wilcoxon Signed-Rank test" should be easy to understand because it is its non-parametric counterpart.
Like the Mann-Whitney U test, we use the Wilcoxon Signed-Rank test when our sample data does not meet the assumption of normality.
This technique has both the null hypothesis and the alternative hypothesis.
- Null Hypothesis-For a pair of samples, we have equal medians
- Alternative Hypothesis-For a pair of samples, we have unequal means
Friedman Repeated Measures test
True to its name, we use the Friedman repeated measures test when we have repeated measures, precisely-at least three measures or experimental conditions over a given period.
The method considers three conditions:
- No distractions
- Some level of distraction
- Greatest level of distraction
Therefore, we use the same data throughout the test period, under the same conditions, but we change the independent variable, which is the level of distraction.
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