I think I am on the right track, but I would rather know.
Initially, when the results of Levene's and Shapiro's were significant at 95%, I tested and investigated the data in various ways. I used Fligner, Anderson, Kolmogorov, and Lilliefors - what I found was consistent results. All of the tests returned a p-value between .01 and .05.
- Levene's p < .02581
- Shapiro's p < .03673
- ANOVA p < .0001265
*** All tests of the distribution were assessed with the residuals.
My initial thought and question now - I know that there is no reason to discount a p-value in some imaginary world of only 95% matters - because that is the opposite of intelligent (being as professional as I can here) --
Is it accurate to say that if the assumptions are not significant at 99% (therefore fail to reject) and the ANOVA is significant at the 99% CI, the assumptions are not violated, and the results of the ANOVA are reliable?
If not, what else can I look for to get a better understanding? Where did I go wrong?
** Outliers? Using the Mahalanobis distance, there were none. Using GVLMA, all the assumptions were met. (That is another little world of 'very interesting.')
For clarity, I've added the variance visualized. The vertical, dashed black lines indicate the five groups. The red background reflects the widest to the narrowest range among the groups' variance. The red horizontal line is the trend line, not a line marking zero (although it does both, here).
A boxplot of the residuals: