ANOVA Assumptions

In this issue of the Journal of Visual Impairment & Blindness (JVIB), the article “Evaluating the use of tactile shapes in associative learning for people who are blind,” by Gupta, Mannheimer, Rao, and Balakrishnan reports the results of one-way ANOVA tests, but also notes results of something called “Levene’s test.” The mention of this test gives me a chance to talk about the assumptions behind a test like the one-way ANOVA. If readers will recall, a one-way ANOVA is a statistical test in which a dependent variable is compared across three or more groups. An example might be looking at the average height of people in North America, Africa, Europe, and Asia. An experimenter would collect a bunch of height data across those continents and could compare the average heights using an ANOVA test. But an experimenter should only use the ANOVA test if certain conditions are satisfied within the data. The first assumption is that the dependent measure is continuous, which means that it can have a value across a wide range and can have any value within that range. Height satisfies this requirement because people are a range of heights and can be any height within that range. The second assumption is that of normality, which is the assumption that the data for each group is drawn from a normally distributed population. A researcher could plot the heights of all the people in the dataset from each of the continents sampled and each sample should look like the standard bellshaped curve, with most heights being close to the average of the sample, and fewer people being much taller or much shorter. Plotting data is a quick way to check for normality. There are also statistical measures of normality. The shape of the bell curve has characteristics called “skewness” and “kurtosis.” One can think of skewness as how symmetrical the bell curve is and kurtosis as how pointy the curve is. If the bell curve of the plotted data is too lopsided (skewness of more than 1 or less than −1) or if it is too pointy (kurtosis of more than 3), then the sample of data is probably not normally distributed and another statistical test needs to be used. There are other tests that look at normality, but I will not get too deep in the weeds on that topic right now. The third assumption of data for an ANOVA test is that of independence, which means that the data in one group are not influenced by the data in another group and that the data in each group was gathered using random sampling. If height data from people in Turkey were included in both the European group and the Asian group, then those two groups would not be independent. Similarly, if a researcher only sampled people from Vancouver to represent all of North America, that would not be properly represented as a random sample of the continent. The final assumption of data for an ANOVA test is that of equal variances, and this is the point at which a test like Levene’s test comes into play. The assumption of equal variances means that the amount of spreading of scores in each group’s data is similar. Variance is calculated by adding the squared difference of each score from that score’s group average, then dividing that total by the number of scores in the group. It is related to SD because SD is the square Statistical Sidebar