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A paired difference test is designed for situations where there is dependence between pairs of measurements (in which case a test designed for comparing two independent samples would not be appropriate). That applies in a within-subjects study design, i.e., in a study where the same set of subjects undergo both of the conditions being compared.
To test the null hypothesis, independent pairs of sample data are collected from the populations {(x 1, y 1), (x 2, y 2), . . ., (x n, y n)}. Pairs are omitted for which there is no difference so that there is a possibility of a reduced sample of m pairs. [4] Then let W be the number of pairs for which y i − x i > 0.
The Wilcoxon signed-rank test is a non-parametric rank test for statistical hypothesis testing used either to test the location of a population based on a sample of data, or to compare the locations of two populations using two matched samples. [1] The one-sample version serves a purpose similar to that of the one-sample Student's t-test. [2]
Paired samples t-tests typically consist of a sample of matched pairs of similar units, or one group of units that has been tested twice (a "repeated measures" t-test). A typical example of the repeated measures t -test would be where subjects are tested prior to a treatment, say for high blood pressure, and the same subjects are tested again ...
To illustrate, in a study with a sample of ten hares and ten tortoises, the total number of ordered pairs is ten times ten or 100 pairs of hares and tortoises. Suppose the results show that the hare ran faster than the tortoise in 90 of the 100 sample pairs; in that case, the sample common language effect size is 90%. [20]
The McNemar's test is a special case of the Cochran–Mantel–Haenszel test; it is equivalent to a CMH test with one stratum for each of the N pairs and, in each stratum, a 2x2 table showing the paired binary responses. [18] Multinomial confidence intervals are used for matched pairs binary data.
In the case of the degrees of freedom for the between-subject effects error, df BS(Error) = N k – R, where N k is equal to the number of participants, and again R is the number of levels. To calculate the degrees of freedom for within-subject effects, df WS = C – 1, where C is the number of within-subject tests.
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned).