![]() ![]() This is your FK statistic that is evaluated against a chi-square distribution with degrees of freedom equal to (number of groups - 1). Do this for all the groups, add them up, and divide by the total variance of all the z-scores. As Box (1953) said, 'To make the preliminary test on. 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. When the sample sizes are all the same (as in your case), or nearly the same, ANOVA is quite robust to heterogeneity of variance. 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. The course will spend of the time on ANOVA and on regression. It is a nonparametric way of comparing the variances of more than two groups that is very robust against non-normal data. The course is suitable for people who are looking to understand how ANOVA and regression works, apply these tools to their own data and interpret XLSTAT outputs. For example, if the assumption of homogeneity of variance was violated in your analysis of variance (ANOVA), you can use alternative F statistics (Welchs. To realize a two-sample comparison of variances test go to the menu bar Parametric Tests / Two-sample comparison of variances. If the variances are equal we can do a test to compare the averages. The trick is to convert your factorial design into a one-way design. However, the oneway command automatically performs a Bartlett’s test for homogeneity of variance along with a one-way anova. The anova command does not have a check for homogeneity of variance. Then we do a F-test to know if the variance are equal. To analyze a factorial anova you would use the anova command. Just thought I'd post a little more about the Fligner Killeen test. Setting up a Fisher's F-test in XLSTAT to assess the equality of variance of 2 samples. ![]()
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