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In my data set, I've run a 2-way ANOVA with interaction. Found the interaction term to be non-significant. I re-ran the ANOVA without the interaction, and got the results that both my explanatory variables are significant.

In essence, the resulting plot looks like this: enter image description here

What would be an efficient way to recapitulate the statistical result on such a graph? Should I split the graphs by gender? By courses? Both?

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  • $\begingroup$ Math courses and gender are the explanatory variables, but what is your response variable? $\endgroup$ Apr 21 '17 at 15:11
  • $\begingroup$ In this example, test scores $\endgroup$ Apr 21 '17 at 15:15
  • $\begingroup$ I am sorry I didn't see score labelled on the y-axis. Is it correct to assume that the score is not for a course. $\endgroup$ Apr 21 '17 at 15:18
  • $\begingroup$ I like your graph. In the good old days before the printing press was invented, scientists such as Galileo and da Vinci would integrate text and graphics. Tufte has argued that we should get back to doing that. Therefore, I would recommend putting some inferential statistics in text form in your graph. Perhaps in the lower right. Although Box Plots usually don't include means, I like versions that do when presented with inferential statistics testing mean differences. $\endgroup$
    – David Lane
    Apr 21 '17 at 18:38
  • $\begingroup$ @DizietAsahi Since there was not answer in here: Did you come up with a solution yourself $\endgroup$ Dec 11 '17 at 10:57
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The resulting plot looks fine to me: You show that there is a main effect of class type: Calculus scores are higher than the other two. You also show the main effect of gender: Males tend to do better than females. And your insignificant moderation is also shown here: The pattern of males performing better than females is the same across all types of classes; the pattern of Calculus being higher than Algebra+Geom being higher than Algebra alone is the same for both men and women.

The problem with splitting the graphs by gender or by course is that you wouldn't be able to see the main effects of gender or course on these new graphs—information that you want to present to the reader. I think the figure you have captures your results nicely.

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    $\begingroup$ Thanks @Mark. The question is how to indicate (with stars ***) the degree of statistical significance of the differences, so that someone skimming the figures of the paper would get the info without having to refer to the text $\endgroup$ Apr 21 '17 at 17:47

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