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

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

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

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.