I have seen many presentations with One-Way Plots produced using the "Fit Y by X" platform with categorical X and continuous Y, some of which have red boxplots while other has green mean diamonds.
It would be helpful to have further clarification on the following:
- What is the difference between these two display options?
- When is a boxplot more appropriate than a mean diamond (and vice versa)?
- Are the other display options that should be considered instead of box plots or mean diamonds?
Thanks!
The details about what green diamonds cover can be found at: https://www.jmp.com/support/help/14-2/mean-diamonds-and-x-axis-proportional.shtml
The details about what box plots cover can be found at: https://www.jmp.com/support/help/14-2/outlier-box-plot.shtml
If you got a green diamond it is because you run an ANOVA test. It also means you are assuming the response (y-axis) is normally distributed for each group in the x-axis. Besides, you are assuming the response has the same - similar in practical terms - variance for each group. Then, ANOVA tests whether all group means are equal. The diamonds are meant to help you visualize the result of the ANOVA test.
The box plot has nothing to do with a test. In fact, it is a tool that helps you do exploratory (visual) analysis before you decide to run a test, if ever. For instance, it provides you visual evidence that the variability of the response across groups is similar or not similar at all, or that the response is skewed for some groups but not for others. Sometimes visual evidences are more informative than a formal test. The box of the plot contains the innermost 50% of the response distribution, it gives you an idea of spread - much like variance does - without the impact of outliers. If the boxes of two groups don't overlap or barely do so, it tells you - without a test - that you should not expect the response for these two groups to be the same - similar to rejecting the ANOVA hypothesis of equal means. The presence of outliers may explain why the variance (or std deviation) of one group is larger than those of others while the box size of this group is similar to the box size of other groups. To sum up, you use the box plot when you want to make your point visually - not using a formal test like ANOVA or the test of unequal variances.
