The Levene test is less sensitive than the Bartlett test to departures from normality. If you have strong evidence that your data do in fact come from a normal, or nearly normal, distribution, then Bartlett's test has better performance.
The Levene test is defined as: H 0 :. The three choices for defining Z ij determine the robustness and power of Levene's test. By robustness, we mean the ability of the test to not falsely detect unequal variances when the underlying data are not normally distributed and the variables are in fact equal. By power, we mean the ability of the test to detect unequal variances when the variances are in fact unequal. Levene's original paper only proposed using the mean. Brown and Forsythe extended Levene's test to use either the median or the trimmed mean in addition to the mean.
They performed Monte Carlo studies that indicated that using the trimmed mean performed best when the underlying data followed a Cauchy distribution i. Using the mean provided the best power for symmetric, moderate-tailed, distributions. The research question for today is: is salary associated with region? We'll try to support this claim by rejecting the null hypothesis that all regions have equal mean population salaries. With regard to our data, independent observations seem plausible: each record represents a distinct person and people didn't interact in any way that's likely to affect their answers.
We'll inspect if our data meet this requirement in a minute. Last, homogeneity is only needed if sample sizes are sharply unequal. If so, we usually run Levene's test. The best way to do so is inspecting a histogram which we'll create by running the syntax below.
The combination of these last 2 points implies that we can not interpret or report the F-test shown in the table below. As discussed, we can't rely on this p-value for the usual F-test. This is a descriptive statistic that neither requires normality nor homogeneity. Now, if we can't interpret our F-test, then how can we know if our mean salaries differ?
Two good alternatives are:. As shown below, the Welch test rejects the null hypothesis of equal population means. Let's run it. On running our syntax, we get several tables. The second -shown below- is the Test of Homogeneity of Variances. This holds the results of Levene's test. Remember that we don't need equal population variances if we have roughly equal sample sizes.
A sound way for evaluating if this holds is inspecting the Descriptives table in our output. Because they're not roughly equal, we do need the homogeneity of variance assumption but it's not met by 2 variables. In this case, we'll report some alternative results Welch and Games-Howell but these are beyond the scope of this tutorial. We therefore compute the absolute differences between all scores and their group mean. The means of the absolute differences should be roughly equal over groups.
If that just sounds too weird , then try running the syntax below. It does exactly what I just explained. Thanks for reading! The "chi-square test" usually refers to the chi-square independence test and that's completely unrelated to Levene's test.
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