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I have this output from a R ANOVA analysis and the graph attached. I want to verify if the interpretation for the scenario is correct?

                      Estimate   Std. Error z value Pr(>|z|)   
(Intercept)             1.7918     0.6236   2.873  0.00206 **
typeHigh               -1.5911     0.7687  -2.070  0.01847 * 
statusBlack            -1.2528     0.7843  -1.597  0.11018   
typeHigh:statusBlack    2.4384     1.0628   2.294  0.01177 * 
  1. Line 4 of result -- The difference between the status: Black and Gray is different for the type: Low vs High. Here, At low: black decreases w.r.t to gray and at high it increases w.r.t to gray

  2. Line 1 of result -- How do I interpret the first line alone?

  3. Finally, is it correct to say that as we go from low to high: Gray decreases significantly i.e. Gray in "Low" is different from Gray in "High". Also, does black increase significantly i.e. Black in "Low" is different from Black in "High".

  • $\begingroup$ I ran a glm negative binomial function, so the values are from the estimate. Ignore those $\endgroup$ – Biotechgeek Jul 24 '19 at 16:43
  • $\begingroup$ negative binomial and ANOVA are totally different things. Then my first comment based on ANOVA is wrong. $\endgroup$ – user158565 Jul 24 '19 at 17:03

A significant effect in an ANOVA analysis is interpreted as: At least one level of the categorical variable has a mean, which is significantly different from at least one other level. It tells you nothing regarding which group is different from any other group.

When a categorical by categorical interaction is added to the model the groups are broken down into their memberships on both variables. In your case, the 4 groups would be: low and black, low and grey, high and black, & high and grey.

The interaction coefficient simply tells you that one of those 4 groups means is statistically significantly different from at least one other.

To understand which group is different, many methods exist. p-value corrected pairwise tests can be used, dummy coded regression models, or simply graphical methods.

  • $\begingroup$ The model is not ANOVA, it is based on negative binomial, as OP said in the comment. $\endgroup$ – user158565 Jul 24 '19 at 17:51
  • $\begingroup$ I see that, but also see that they say to ignore that output. I provide an answer to the question asked, and the 4 points put forth in the OP. $\endgroup$ – Roman_Numerals Jul 24 '19 at 19:20

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