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I want to know what to look for in a boxplot, when we want to check for homogeneity of variances among groups, which is an assumption in ANOVA. I used this codes to get a boxplot: '''boxplot(log(PhiPS2)~elevation, data = ecophy_df)''' enter image description here

So, I want to know

  1. In this plot, the means are different, also we have some outliers too. Does this mean my data is non-homogeneous? What to look for in this box-plot to check for homogeneity?

  2. Is there other way to check for homogeneity(visually), because the leveneTest and Barlett Test, is showing very low p-value.

  3. How to read this graph, probably it is another way to check homogeneity? enter image description here

Or this graph?

enter image description here

  1. Do we need to check for homogeneity of variance with residuals rather then the data, like we do for normality test. If that's so we need to have a boxplot of residuals between groups, right?

Thanks in advance.

scholar101
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    Welcome to Cross Validated! Look at this page for an explanation of plots that help with quality control in linear models. The residuals vs fitted plot is the "boxplot of residuals between groups" that you seek when there is a single categorical predictor variable. But why are you treating a continuous predictor like elevation as a 10-level categorical predictor? See this page. A smooth continuous fit (e.g., with a regression spline or other generalized additive model) is typically better. – EdM Nov 28 '23 at 15:48
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    You can find answers at https://stats.stackexchange.com/questions/255863, https://stats.stackexchange.com/questions/33028, and this site search for good answers concerning boxplots and heteroscedasticity. (Most of those hits are directly relevant to your questions.) – whuber Nov 28 '23 at 15:55

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