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 Independent t – test The average (mean) of TWO independent groups, interventions, or scores

Dependent Variable (outcome)

Independent Variable (Explanatory)

Continuous

Group

WHENTOUSE: Use the t-test to compares the means of two independent groups. Independent groups means that different people are in each group.

TEST IT GRAPHICALLY: Before you use this test, do an exploration. Use box plots, confidence interval plots, and histograms.

TEST NORMALITY NUMERICALLY: If you are uncomfortable assessing the normal distribution graphically, test it numerically. Almost all statistical software allows you to run exploratory statistics.

Assumptions

Check it

Assumptions not met?

Normal distribution: dependent variables should be normally distributed within each group

Test it Graphically: Histograms of dependent variables per group Test it numerically: Shapiro Wilk Levene’s test – default test for SPSS

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

Homogeneity of variance

Use bottom row of output – see illustration

INTERPRETATION:

There are a couple of ways to test the hypothesis. First review the null and alternative hypothesis.

Null Hypothesis

Alternative hypothesis

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

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

SAMPLE DATA DESCRIPTION:

The following study is a subset from Larson’s & Morris study: Sex and Salary: A survey of purchasing and supply professionals, answering the question, “ Are women still paid less than men for comparable work? ” The actual sample was large (over 300), but here is the subset of the data. The amounts are in thousands. Ten samples for each group.

Men: 81, 69, 81, 76, 76, 74, 69, 76, 79, 65 and Women: 78, 60, 67, 61, 62, 73, 71, 58, 68, 48

Let’s look at some of the output.

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