The literature across the internet says that if Levene's Test is significant, then ANOVA and Post Hoc should not be applied. The data seems normal according to Kolmogorov-Smirnov and Shapiro-Wilk normality test. Both show the insignificant value for these tests. But the Levene's Test is also significant.
Should I opt for the Non-Parametric test like K Sample Test or go ahead with one-way ANOVA?
Do you mean the original Levene Test that is based on group means or do you mean the "Modified Levene Test" which is also called the Brown & Forsythe Test (based on group medians)?
With normal data, I would use Bartlett's Test to have more statistical power. With non-normal data, I would use the Brown & Forsythe Test (Modified Levene Test). If the latter test is significant, use Welch's ANOVA test in place of the ANOVA F test.
If you have non-normal data but equal population variances, use the Kruskal-Wallis test on the ranks.
If you have non-normal data and unequal population variances, transform the raw data to normal quantiles first, then test again for equal variances. If the variance test is still significant, use Welch's Test on the transformed data. If the variance test is not nonsignificant, use the standard ANOVA F test on the normal quantiles.
If the assumption of homogeneity of variance is violated, you can still use alternative procedures, which are designed for unequal variances (one possibility would be the Games-Howell Test, which is also implemented in SPSS (though not as the default option)). I hope this will help you a bit!
Do you mean the original Levene Test that is based on group means or do you mean the "Modified Levene Test" which is also called the Brown & Forsythe Test (based on group medians)?
With normal data, I would use Bartlett's Test to have more statistical power. With non-normal data, I would use the Brown & Forsythe Test (Modified Levene Test). If the latter test is significant, use Welch's ANOVA test in place of the ANOVA F test.
If you have non-normal data but equal population variances, use the Kruskal-Wallis test on the ranks.
If you have non-normal data and unequal population variances, transform the raw data to normal quantiles first, then test again for equal variances. If the variance test is still significant, use Welch's Test on the transformed data. If the variance test is not nonsignificant, use the standard ANOVA F test on the normal quantiles.
Hi,
Your question: When do I use the Levene's Test with one-way ANOVA?
Normally, we use the Levene's Test to test the Equality of Variances. Prior to the Anova test, the Levene's Test for Equality of Variances is to be performed. If the Levene test is positive ie., p - value
But Levene's test shows the homogeneity of the variance? Shouldn't the non-parametric tests be applied when there is an issue with the normality of the data?
hello, I am running a Levene's test currently and my result is P= 0.05. Can i still state there is not homogeneity of variance?
The normality assumptions is on the residuals of the model. So you need to make a QQ-plot of the residuals and assess visually is they are normally distributed. You could also do a test for this (but on the residuals). I find QQplots more informative.
The assumption of equal variance is also important but ANOVA is somewhat robust against deviations from this. If levene's test is just barely significant I would let it pass. You can also check equal variances visually by creating a plot of residuals vs predicted values. This should reveal no structure and a shapeless cloud of points. The range of your residuals should be the same for all predicted values, otherwise the variances are not equal. If the problem is big (very sign p-values for Levene's) you could try log scaling or square root scaling of your observations. This could fix the problem. Also look for outliers/errors in the data...
Raid Amin, could you please give the references for your suggestions so I can cite them in my paper?
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