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 Mann-Whitney U Test The average (mean) of TWO independent groups, interventions, or scores

Dependent Variable (outcome)

Independent Variable (Explanatory)

Ordinal/Continuous

Binary (Group)

The Mann-Whitney test is also known as the Mann-Whitney-Wilcoxon, the Wilcoxon rank sum test, or the Wilcoxon-Mann-Whitney U test.

WHEN TO USE: Use the Mann-Whitney test as an alternative to the independent t test when some assumption of the independent t test was violated. There are two types of Mann-Whitney U tests. If the distribution of the two groups have the same shape, the medians can be compared. If not, the test will compare the mean rank. TEST IT GRAPHICALLY: Before you use this test, do an exploration. Use box plots, confidence interval plots, and histograms. Essentially, you are using the visuals to determine which of the Mann- Whitney U test will be conducted. If the two groups have the same shape – the medians can be compared. If not, the test will compare mean rank. You need to understand which one to help you with the write-up.

Assumptions

Check it

Assumptions not met?

Non-normal distribution: Do the two groups have the same shape? If yes, compare medians. If NOT, compare mean ranks. The Mann Whitney U test is robust to violations to homogeneity of variance

Test it Graphically: Histograms of dependent variables per group

Use the Mann-Whitney test (also called the Wilcoxon rank sum test )

No need to test for homogeneity of variance

HYPOTHESIS:

In the two-sample t test, the null hypothesis is equal means; whereas in the Mann Whitney U test, it is equal medians. 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)

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