![]() ![]() If the result is significant, the group's have statistically different variances. This is your FK statistic that is evaluated against a chi-square distribution with degrees of freedom equal to (number of groups - 1). ![]() As discussed, we cant rely on this p-value for the usual F-test. The combination of these last 2 points implies that we can not interpret or report the F-test shown in the table below. Do this for all the groups, add them up, and divide by the total variance of all the z-scores. However, Levene’s test is statistically significant because its p < 0.05: we reject its null hypothesis of equal population variances. If your data fails this assumption, you may also need to use SPSS Statistics to carry out Levenes test of homogeneity of variance to determine where the problem may lie. You can test this assumption in SPSS Statistics using Boxs M test of equality of covariance. We then find a "mean square" for each group by taking its average z-score and subtracting the overall z-score, squaring the difference, and multiplying by the respective sample size of the group. Assumption 8: There is homogeneity of variance-covariance matrices. We obtain the average z-score for each group, as well as the overall average z-score, and the overall variance of the z-scores. Using the inverse normal distribution, we then convert these areas back into z-scores, taking the absolute value of any negative z-scores. By dividing each of these resulting ranks by the value 2(n+1), where n is the total number of data points across all groups, and then adding 0.5 to each result, each of the ranked residuals is "normalized" into an area under the normal curve. Rather than performing an ANOVA on these residuals, the FK test ranks these residuals from low to high (where a rank of 1 is given to the lowest data point), assigning the average value of any tied ranks. Essentially, it starts off the same way as a Brown Forsythe test for the ANOVA, obtaining the absolute deviations of each observation from its respective group median. It is a nonparametric way of comparing the variances of more than two groups that is very robust against non-normal data. Just thought I'd post a little more about the Fligner Killeen test. ![]()
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