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 Paired-t test The average (mean) of TWO independent groups, interventions, or scores

Dependent Variable (outcome) Continuous (at least interval)

Independent Variable (Explanatory)

Time point 1 or 2/condition

WHEN TO USE: Use the paired – t test when the data is paired or matched. Examples include: Before and after, pre-test and post-test.

TEST IT GRAPHICALLY: Before you use this test, do an exploration. Use box plots, and histograms. Note: The histogram should be based on the paired difference. (However, if you plot a histogram for the before and after and they are normally distributed; chances are that the paired difference histogram will be normally distributed as well)

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 for the paired difference

Test it Graphically: A normality plot or boxplot of the differences, or Histogram of paired difference Test it numerically: Not necessary if sample size is high (our example dataset is large) If our sample size is small (under 20) use Shapiro Wilk

Wilcoxon signed rank

INTERPRETATION:

There are a couple of ways to test the hypothesis. First review the null and alternative hypothesis. The “d” stands for difference between the paired values

Null Hypothesis

Alternative hypothesis

(translate value to µ 1 - µ 2 into equivalent hypotheses) Form of the null hypothesis: H 0 : µ 1 – µ 2 = hypothesized value H o : µ d = 0 (two-tailed test) H o : µ d ≤ 0 (one -tailed test) H o : µ d ≥ 0 (one -tailed test) H o : µ d ≠ 0 (two -tailed test)

H a : µ d = hypothesized value H a : µ d > hypothesized value H a : µ d < hypothesized value H a : µ d ≠ hypothesized value

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