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

Independent t test Vs Mann-Whitney U test

COMPARING: The average (mean) of TWO independent groups, interventions, or scores

Variables: Dependent (outcome) variable + Independent (explanatory) variable Independent t test:

If data is normally distributed, use…

If data is ordinal or skewed distribution, use … Mann-Whitney test also called the Wilcoxon rank sum Test NON-PARAMETRIC TEST: The Mann- Whitney U test compares two independent groups when the dependent variable (outcome) is either ordinal or continuous but

Independent t-test

PARAMETRIC TEST: This student t test compares the means of two independent groups to determine if there is statistical evidence that the population means are significantly different Hypothesis: H o - The two-population means are equal H o : Mean 1-Mean 2 =0 or H o : Mean 1 = Mean 2 H a : µ1 > µ2 (one-tailed, right-tailed H a : µ1 <µ2 (one-tailed, left tailed) Data Requirements include: 1) dependent variable is continuous 2) independent variable is categorical 3) cases have values for dependent and independent 4) independent samples/groups 5) random sample 6) Sample size large (30+) OR Normal distribution (See note) 7) Homogeneity of variance (can use Levene’s test for this) 8) No outliers SPSS Steps 1) Analyze>Compare Means>Independent-Samples T Test The alternative H a include µ1 ≠ µ2 (two -tailed test) OR

not normally distributed. -Compares two medians

Hypothesis: Mdn = medians instead of means Ho: Mdn 1 - Mdn2 = 0 or Ho: Mdn = Mdn 2

The alternative H a include 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) Data Requirements include: 1) Dependent variable is ordinal or continuous 2) independent variable consists of two categorical, independent groups 3) independence of observations 4) Works for non-normal distributions, but

you should determine if the two distributions have the same shape

SPSS Steps Analyze>Nonparametric Tests>Legacy Dialogs> 2_Independent Samples

Example Study: Legutko, B. (2016). An exploration of the emergent leadership styles of fortune 500 executives as communicated in annual report letters to their shareholders Available from ProQuest Dissertations & Theses Global. (1854134498).

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