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

Paired t-test Vs. Wilcoxon Signed rank test

COMPARING: The average difference between paired (matched) samples

Variables: Dependent (outcome) variable: Continuous (at least interval)

Independent (explanatory) variable: time point 1 or 2/condition

If data is normally distributed, use…

If data is ordinal or skewed distribution, use …

Paired t-test

Wilcoxon signed rank test

PARAMETRIC TEST: The paired t test compares two population means when the samples are paired An example would be before and after measurements for a group of people. It is also called paired difference t test, the matched pairs t test, and repeated samples t-test Hypothesis: (translate value to µ 1 - µ 2 into equivalent hypotheses)

NON-PARAMETRIC TEST: The Wilcoxon signed rank test is a non- parametric test used to compare two related samples, matched samples or repeated measurements on a single sample to assess whether their population mean ranks differ. Hypothesis: (compares sample mean or median against a hypothetical mean or median)

Form of the null hypothesis:

H 0 : m = m 0

H 0 : m 1 – m 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 : m > m 0 H a : m < m 0 Ha: m ≠ m 0

Data requirements include : 1) The samples are paired.

Data requirements include: 1) Data must be matched. 2) The dependent variable must be continuous. 3) The paired samples are random and independent. 4) The distribution of the differences between the groups must be symmetrical.

2) Subjects must be independent. The n sample difference are from a random sample from a population of differences Measurements from one subject do not affect measurements for any other subject. 3)Both sample sizes are large (over 30) or the population distributions are approximately normal*. (Visually can use a normal probability plot or box plot of the differences to decide if assumptions of normality is reasonable). *use the differences between the paired value to test for normality and outliers.

Note: no assumption of normality

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