There are some significance tests for two dependent samples, and these are namely the McNemar test, the Marginal homogeneity test, the sign test, and the Wilcoxon test.
The McNemar test assesses the significant difference between the two types of dependent samples in cases where the variables of the interest is dichotomous. The McNemar test is basically used by the researcher during the pre and the post studies in order to test for an experimental type of effect. The Marginal homogeneity test introduced for testing the significance of two dependent samples is nothing but an extended form of the McNemar test.
The sign test is used in cases when the variable of interest is continuous in nature. The Wilcoxon test is considered the most powerful test among all the tests.
The term ‘dependent’ in the significance tests for two dependent samples means the related, associated, or the correlated samples.
The McNemar test is also called the McNemar test for symmetry, or the McNemar symmetry chi square test. The variables of interest in the McNemar test are either of nominal or ordinal type. Since the calculation of the McNemar test is done using the chi square statistic, the data in the McNemar test is arranged in the form of cross tabs (i.e. in a 2X2 matrix form). In SPSS, the McNemar test can be conducted by selecting “descriptive statistics” from the analyze menu and then further clicking on the option of “Cross tabs” from this. From there, the researcher chooses the option of the “McNemar test” from the statistics button.
The Marginal homogeneity test is the same type of test as the McNemar test, except that in this case, the variables assume more than two types of the nominal variables.
The sign test for the two types of dependent samples is applied in those cases where the variable of interest is of ordinal type, or something higher than ordinal. The sign test assesses the sign (which can be positive, negative or tied) of the differences between the data pairs. In case both the samples do not differ significantly, then the numbers of the positive and the negative differences in the sign test are equivalent in both samples. Unlike the Wilcoxon test, the sign test does not measure the extent to which the difference exists between the pairs.
The Wilcoxon test can also be called the Wilcoxon signed rank test, or sometimes the Wilcoxon matched pairs test. The Wilcoxon test is regarded as more powerful than the sign test, as the Wilcoxon test takes more information into account as compared to the sign test. The Wilcoxon test is used in those cases where the variable of interest is of interval type.
There are certain assumptions that are made on the significance tests for two dependent samples:
- The McNemar test is used only in those cases where the variables are assumed to be dichotomous types of variables. The dichotomous types of variables in the McNemar test are assumed to be mutually exclusive or mutually exhaustive.
- All the tests under the significance tests for two dependent samples are assumed to be nonparametric tests, and therefore the significance tests for two dependent samples do not assume normal distribution or any other distribution of the population.
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