Chapter6 Flashcards
Cochran’s Q
This test is an extension of McNemar’s test and is basically a Friedman’s ANOVA for dichotomous data. So imagine you asked 10 people whether they’d like to shoot Justin Timberlake, David Beckham and Simon Cowell and they could answer only ‘yes’ or ‘no’. If we coded responses as 0 (no) and 1 (yes) we could do Cochran’s test on these data.
Friedman’s ANOVA
a non-parametric test of whether more than two related groups differ. It is the non-parametric version of one-way repeated-measures ANOVA.
Jonckheere-Terpstra test
this statistic tests for an ordered pattern of medians across independent groups. Essentially it does the same thing as the Kruskal-Wallis test (i.e., test for a difference between the medians of the groups) but it incorporates information about whether the order of the groups is meaningful. As such, you should use this test when you expect the groups you’re comparing to produce a meaningful order of medians.
Kendall’s W
this is much the same as Friedman’s ANOVA but is used specifically for looking at the agreement between raters. So, if, for example, we asked 10 different women to rate the attractiveness of Justin Timberlake, David Beckham and Brad Pitt we could use this test to look at the extent to which they agree. Kendall’s W ranges from 0 (no agreement between judges) to 1 (complete agreement between judges).
Kolmogorov-Smirnov Z
not to be confused with the Kolmogorov-Smirnov test that tests whether a sample comes from a normally distributed population. This tests whether two groups have been drawn from the same population (regardless of what that population may be). It does much the same as the Mann-Whitney test and Wilcoxon rank-sum test! This test tends to have better power than the Mann-Whitney test when sample sizes are less than about 25 per group.
Kruskal-Wallis test
non-parametric test of whether more than two independent groups differ. It is the non-parametric version of one-way independent ANOVA.
Mann-Whitney test
a non-parametric test that looks for differences between two independent samples. That is, it tests whether the populations from which two samples are drawn have the same location. It is functionally the same as Wilcoxon’s rank-sum test, and both tests are non-parametric equivalents of the independent t-test.
McNemar’s test
This tests differences between two related groups (see Wilcoxon signed-rank test and sign test), when nominal data have been used. It’s typically used when we’re looking for changes in people’s scores and it compares the proportion of people who changed their response in one direction (i.e., scores increased) to those who changed in the opposite direction (scores decreased). So, this test needs to be used when we’ve got two related dichotomous variables.
Median test
a non-parametric test of whether samples are drawn from a population with the same median. So, in effect, it does the same thing as the Kruskal-Wallis test. It works on the basis of producing a contingency table that is split for each group into the number of scores that fall above and below the observed median of the entire data set. If the groups are from the same population then these frequencies would be expected to be the same in all conditions (about 50% above and about 50% below).
Monte Carlo method
a term applied to the process of using data simulations to solve statistical problems. Its name comes from the use of Monte Carlo roulette tables to generate ‘random’ numbers in the pre-computer age. Karl Pearson, for example, purchased copies of Le Monaco, a weekly Paris periodical that published data from the Monte Carlo casinos’ roulette wheels. He used these data as pseudo-random numbers in his statistical research.
Moses extreme reactions
a non-parametric test that compares the variability of scores in two groups, so it’s a bit like a non-parametric Levene’s test.
Non-parametric tests
a family of statistical procedures that do not rely on the restrictive assumptions of parametric tests. In particular, they do not assume that the sampling distribution is normally distributed.
Pairwise comparisons
comparisons of pairs of means.
Ranking
the process of transforming raw scores into numbers that represent their position in an ordered list of those scores. The raw scores are ordered from lowest to highest and the lowest score is assigned a rank of 1, the next highest score is assigned a rank of 2, and so on.
Wald-Wolfowitz runs
another variant on the Mann-Whitney test. Scores are rank-ordered as in the Mann-Whitney test, but rather than analysing the ranks, this test looks for ‘runs’ of scores from the same group within the ranked order. Now, if there’s no difference between groups then obviously ranks from the two groups should be randomly interspersed. However, if the groups are different then one should see more ranks from one group at the lower end, and more ranks from the other group at the higher end. By looking for clusters of scores in this way, the test can determine if the groups differ.
