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

One way ANOVA Vs. Kruskal-Wallis Test

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

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

If data is normally distributed, use…

If data is ordinal or skewed distribution, use …

One-way ANOVA

Kruskal-Wallis Test

PARAMETRIC TEST: The one-way ANOVA is an omnibus test statistic and cannot tell you which specific groups were statistically significantly different from each other, only that at least two groups were significantly different. To determine further, use the post hoc test. Hypothesis: H o - The THREE+ population means are equal or µ 1= µ 2 = µ 3 Data requirements include : 1) Dependent variable measured as interval or ratio level (i.e. continuous). 2) independent variable consists of two or more categorical, independent groups. 3) Independence of observations (most serious assumption to fail). 4) No significant outliers 5) Dependent variable should be approximately normally distributed for each category 6) Homogeneity of variances (use Welch or Brown and Forsythe test) SPSS Steps Analyze>Compare Means>One-Way ANOVA (you will need post hoc test, most likely Tukey)

NON-PARAMETRIC TEST: Kruskal- Wallis is a nonparametric test to determine if there are statistically significant differences between two or more groups with an independent variable on a continuous or ordinal dependent variable. It uses medians. It only tells you that groups are different but not which ones. H0: population medians are equal. H1: population medians are not equal. Data requirements include: 1) Dependent variable measures at ordinal or continuous (interval or ratio). 2) independent variable consists of two or more categorical, independent groups. 3) Independence of observations (more of setting up design) 4) Distribution in each group have the same shape/variability. (If you violate this rule, you can only use this test to compare mean ranks) SPSS Steps (assuming 3 groups) Analyze>Nonparametric Tests> Independent Samples> Objective tab – customize analysis>Field tab – treatment in Groups and Test Field (insert your continuous variable>Setting tab-customize test, choose Krauskal-Wallis 1 way ANOVA (s samples) Hypothesis:

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