2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

Demonstrate Kruskal-Wallis The average (mean) of TWO independent groups, interventions, or scores

Dependent Variable (outcome)

Independent Variable (Explanatory) One IV with three* or more levels (independent groups) * if only two, consider Mann Whitney U test instead

Ordinal/Ratio/ or Interval

The Kruskal-Wallis test is the non-parametric equivalent to the one-way ANOVA.

WHEN TO USE: Use the Krusla-Wallis when the normality test for the ANOVA is not met. Use the Kruskal-Wallis test to compare the medians of two or more samples to determine if the samples have come from different populations. It is sometimes called the one-way ANOVA on ranks. It extends the Mann- Whitney U test to more than two groups. In the Kruskal-Wallis, the distributions do not have to be normal and the variances do not have to be equal.

Graph it: The distributions of each group should have the same shape/variability. If not, you can only use this test to compare mean ranks. Before you use this test, do an exploration.

The test determines whether the medians of the groups are different. This test gives you an “ H ” statistic. The test will tell you if there is a significant difference between groups, but it won ’ t tell which groups are different. You have to run a post hoc test for that. Make sure a p-value correction for multiple testing is used in the post-hoc tests.

Assumptions

Check it

Assumptions not met?

Independent observations

Check data Check data

Friedman

Similar sample sizes

>5 data points per sample

Frequencies of group

HYPOTHESIS:

There are a couple of ways to test the hypothesis.

Null Hypothesis

Alternative hypothesis

H o : Mdn 1 - Mdn 2 = 0 OR H o : Mdn = Mdn 2

H a : Mdn 1 ≠ Mdn 2 (two tailed test) H a : Mdn 1 - Mdn 2 > 0 (one tailed, right-tailed) H a : Mdn 1 - Mdn 2 < 0 (one tailed, left tailed)

Example study: You want to find out socioeconomic status affects attitudes toward gas price increases. Your independent variable is socioeconomic status and you may have this in a range based on income (like low, middle, and wealty). The dependent variable is the point on a Liker scale (normally 5 point from strongly agree to strongly disagree.

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