Non-parametric significance tests for two dependent samples are used when the researcher wants to study correlated, or matched, samples. This includes the before-after effect and matched paired studies: McNemar’s test, Test of Marginal Homogeneity, the Sign test, and Wilcoxon’s signed rank test. The McNemar test is the best test for dichotomous variables with two dependent sample studies. When a category of the sample is more than two, marginal homogeneity tests are appropriate; they are essentially an extension of the McNemar test for dependent samples. When the dependent variable samples are continuous in nature, then the sign and Wilcoxon tests are appropriate for two dependent sample studies.
McNemar test: People also call this test the symmetry McNemar chi-square test. The McNemar test assesses if a statistically significant change in proportions have occurred on a dichotomous trait at two time points on the same population.
The McNemar test uses the chi-square distribution based on this formula:
Degrees-of-freedom = (rows – 1) (columns – 1) = 1
Interpreting significance from the McNemar test: If the computed value of McNemar test is less than the critical value using the degree of freedom, then it will not be significant. If the p value shown by the output is less than the desired significant level, then the difference between the two dependent samples will be statistically significant; otherwise, it will be non- significant.
Questions Answered:
Is there a change in the proportion of voters prior to and following the press conference?
The marginal homogeneity test: The marginal homogeneity test is like the McNemar test, but with more than two categories. It assesses the marginal frequencies of rows and columns. Interpret it like the McNemar test: if the p-value is below the significance level, the means differ. If it is above, the means do not differ.
Questions Answered:
Is there a change in the proportion among raters’ agreement (low vs. medium vs. high) after the lecture?
The sign test: The sign test is used for dependent samples ordered in pairs, where the bivariate random variables are independent. It converts the variable cases into plus or minus signs (or ties, if applicable) and tests if the plus sign differs from the minus sign. Based on the result, we can conclude if the two dependent sample means are the same or different. The measurement scale is at least ordinal within each pair. The sign test is weaker because it only checks if a pair value is above or below the median. It does not measure the pair difference. To use the sign test in SPSS, click “Menu.” Select “Analysis,” then “Nonparametric.” Choose “Two Related Samples” and “Sign Test.”
Interpreting the sign test: If the p value of the sign test is less than the desired value, then the two dependent sample means will be different (rejecting the null hypothesis). If the p value of the sign test is more than the desired significant level, then the two sample means will be considered the same (not rejecting the null hypothesis).
Questions Answered:
Which product of soda (Pepsi vs. Coke) is preferred among a group of 10 consumers?
The Wilcoxon signed-rank test: The Wilcoxon test checks for significant differences in continuous variables measured twice. In SPSS, select “Analysis,” then “Nonparametric,” and choose “Two Related Samples” and “Wilcoxon.”
The SPSS output will also give information about the mean rank and the sum of ranks for the positive and negative sign. If the probability value is more than the desired value, than the Wilcoxon signed-rank test value will not be significant (not rejecting the null hypothesis). When that is the case, we can say that the median rank of the two dependent samples is the same. If the p value is less than the set significance value, then the median rank of the two dependent samples is the same (rejecting the null hypothesis)
Questions Answered:
Are IQ scores different from Kindergarten to 1st grade on the same group of 15 students?
Key terms and concepts
Assumptions:
Check out our online course for conducting a McNemar Test here.
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