Wilcoxom Flashcards
Nonparametric Tests
Besides the Chi-square test, all the other statistical tests (inferential tests) make assumption about the.
distribution of the population and associated parameters
Assumptions of the Wilcoxon Sign Rank Test
(i) Data are paired and come from the same population
(ii) Each pair is chosen randomly and independently
(iii) The data are measured at least, on an ordinal scale (cannot be nominal)
Observation
For the avoidance of doubt, I wish to reiterate that parametric statistics is a branch of statistics which assumes that the data under consideration come from a type of probability distribution and makes inference about the parameters of the distribution.
The normal distribution is a frequent assumption for the validity of the tests. This assumption was silent in the Chi-square test. In other words, apart from the Chi-square test, all the other tests done so far are valid only if the populations are normal or approximately normal.
If the assumption of normality or large samples is withdrawn, then it becomes impossible to apply parametric tests. In that case, we appeal to the nonparametric statistics, also called distribution-free statistics, they include:
Wilcoxon sigh-rank statistic, Wilcoxon rank-sum test, Mann Witney test, Kruskal Wallis test and runs test.
Wilcoxon sigh-rank statistic
The Wilcoxon sign-rank test is a
nonparametric statistical hypothesis test used in comparing two related samples (matched samples) or repeated measurements on a single sample to assess whether their population mean ranks differ. To this end, the Wilcoxon sign rank test is performed to test for significance of the difference between paired samples. The test is an alternative test for the paired t test (t test for matched sampled) when the population cannot be assumed to be normally distributed.
Note: The Wilcoxon sign-rank test is not the same as the Wilcoxon rank-sum test. The Wilcoxon rank-sum test is used for two independent samples.
Wilcoxon test statistics
Wilcoxon T (T^- or T ^+
