Nonparametric Tests with Ordinal Data

Chapter 18

> The sample data for the ordinal variable, accomplishment-related national pride, are skewed. This indicates the possibility that the underlying population distribution is skewed.

Spearman Rank-Order Correlation Coefficient

> When both variables are ordinal> Quantifies association> Calculating Spearman’s correlation

•Convert interval observations to rank-ordered observations

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2

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The Wilcoxon Signed-Rank Test

> A test for matched pairs is a nonparametric hypothesis test used when there are two groups, a within-groups design, and an ordinal dependent variable.

Steps for the Wilcoxon Signed-Rank Test

> Step 1. Identify assumptions> Step 2. State null and research hypotheses> Step 3. Determine characteristics of

comparison distribution> Step 4. Determine critical values> Step 5. Calculate the statistic> Step 6. Make a decision

Mann-Whitney U test> Nonparametric hypothesis test with two

groups, a between-groups design, and an ordinal DV

Steps for the M-W U

> Step 1. Identify assumptions> Step 2. State research and null

hypotheses> Step 3. Determine characteristics of

comparison distribution> Step 4. Determine critical values> Step 5. Calculate the statistic> Step 6. Make a decision

Formulae

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222

212 2)1())(( RnnnnU

Kruskal–Wallis H Test

> A nonparametric hypothesis test used for more than two groups a between-groups design, and an ordinal dependent variable.

Steps for the K-W H Test

> Step 1. Identify assumptions> Step 2. State research and null

hypotheses> Step 3. Determine characteristics of

comparison distribution> Step 4. Determine critical values> Step 5. Calculate the statistic> Step 6. Make a decision

Formulae

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Bootstrapping> A statistical process in which the original

sample data are used to represent the entire population.

> We repeatedly take samples from the original sample data to form a confidence interval.