When you learned analysis of variance (ANOVA), it’s likely that the emphasis was on the ANOVA table, with its Sums of Squares and F tests, followed by a post-hoc test. But ANOVA is quite flexible in how it can compare means. A large part of that flexibility comes from its ability to perform many types of statistical contrast.
That F test can tell you if there is evidence your categories are different from each other, which is a start. It is, however, only a start. Once you know at least some categories’ means are different, your next question is “How are they different?” This is what a statistical contrast can tell you.
What is a Statistical Contrast?
A statistical contrast is a comparison of a combination of the means of two or more categories. In practice, they are usually performed as a follow up to the ANOVA F test. Most statistical programs include contrasts as an optional part of ANOVA analysis. (more…)
Exact and randomization tests are simple from a conceptual level and need fewer assumptions than traditional parametric tests. They do require substantial computing power, but nothing that can’t be handled by the computer you have today. (more…)
If you’ve ever run a one-way analysis of variance (ANOVA), you’re familiar with post-hoc tests. The ANOVA omnibus test only tells you whether any groups differ in their means. But if you want to explore which specific group mean is different from which, you need to follow up with a post-hoc test. (more…)
When you need to compare a numeric outcome for two groups, what analysis do you think of first? Chances are, it’s the independent samples t-test. But that’s not the only, or always, the best option. In many situations, the Mann-Whitney U test is a better option.
The non-parametric Mann-Whitney U test is also called the Mann-Whitney-Wilcoxon test, or the Wilcoxon rank sum test. Non-parametric means that the hypothesis it’s testing is not about the parameter of a particular distribution.
It is part of a subgroup of non-parametric tests that are rank based. That means that the specific values of the outcomes are not important, only their order. In other words, we will be ranking the outcomes.
Like the t-test, this analysis tests whether two independent groups have similar typical outcomes. You can use it with numeric data, but unlike the t-test, it also works with ordinal data. Like the t-test, it is designed for comparisons, and not for estimation or prediction.
The biggest difference from the t-test is that it does not compare means. The Mann-Whitney U test determines whether a random observation from one group tends to be higher (or lower) than a random observation from the other group. Imagine choosing two observations, one from each group, over and over again. This test will determine whether one group is more likely to have the higher values.
It has many advantages: It is a straightforward comparison of means. There are versions for similar and different variances in the two groups. Many people are familiar with it.
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Is it really ok to treat Likert items as continuous? 
And can you just decide to combine Likert items to make a scale? Likert-type data is extremely common—and so are questions like these about how to analyze it appropriately. (more…)
When your dependent variable is not continuous, unbounded, and measured on an interval or ratio scale, linear models don’t fit. The data just will not meet the assumptions of linear models. But there’s good news, other models exist for many types of dependent variables.
Today I’m going to go into more detail about 6 common types of dependent variables that are either discrete, bounded, or measured on a nominal or ordinal scale and the tests that work for them instead. Some are all of these.
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