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In testing gender difference on the relationship between variable A and B,

  • A is the covariate (or independent variable)
  • B is the dependent variable
  • Gender is the factor

As I understand it, if there is a significant interaction between the covariate and factor, then the analysis should be stopped as this violates an assumption of ANCOVA.

My question is: What next?

(I am asking this question because most text books only deal with non-significant interaction, hence there is very little guidance on what to do next if the interaction is significant, as in my case.)

Does the above violation of the assumption mean that I cannot do any further statistical test? (This may be a blessing in disguise for me!)

Can I draw a scatter plot of A and B with different colours for male and females and then discuss the slopes? (This will make intuitive sense to my target audience.)

The goal of my project is to see if the relationship between A and B is affected by gender.

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  • $\begingroup$ How is that a problem? Move away from ANCOVA into a general linear regression setup. $\endgroup$ – varty Nov 21 '11 at 6:41
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    $\begingroup$ @Adhesh, all of your last 4 or 5 questions go round in a circle. You seem to have stumbled on something. What might it be? What is the aim of your study, after all? If that is to see if the relationship between A and B is affected by gender then the significant interaction showed you that. $\endgroup$ – ttnphns Nov 21 '11 at 7:19
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    $\begingroup$ @ttnphns I'm not convinced of this conclusion. It's not because I think you're wrong--you could very well be correct--but because nowhere in this whole constellation of questions have I seen any evidence that the data have been explored and examined for appropriateness of the statistical analyses. The presence of a significant interaction raises questions about potential lack of fit of the model. We should take the interaction merely as the first piece of evidence of nonlinearity, not as the final model. All conclusions are doubtful until that is investigated. $\endgroup$ – whuber Nov 21 '11 at 15:54
  • $\begingroup$ @whuber, I make no conclusions at all. Adheshs's questions simply leaves an impression on me that there is no headway in the questions asked one after another. $\endgroup$ – ttnphns Nov 21 '11 at 17:33
  • $\begingroup$ @ttnphns The conclusion I referred to, and am not convinced of, is "If that is to see if the relationship between A and B is affected by gender then the significant interaction showed you that." $\endgroup$ – whuber Nov 21 '11 at 20:23
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This is not a problem. If you know that you want to see if the A-B relationship differs by sex, do a regression that compares the A-B relationship in different sexes. The interaction is the whole point.

As a by-product, this analysis will tell you what the intercept and slopes are in the different sexes, which you can add to your scatterplot.

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  • $\begingroup$ In this case this might be the best way to foster understanding of the problem, even though some would call it a little less "elegant" statistically speaking. $\endgroup$ – rolando2 Mar 31 '12 at 13:01
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I think you're using the wrong textbooks! :-).

ANOVA, ANCOVA and linear regression are all the same model. In matrix algebra, each is written:

$Y = XB + e$

where $Y$ is a vector of the dependent variable, $X$ is a matrix of the independent variables, $B$ is a parameter vector to be estimated and $e$ is error.

Did your text point that out?

Also, the idea of stopping an analysis if an interaction is significant is nonsensical, and a good text will cover what to do. What is true is that main effects can be hard to interpret in the presence of a large interaction (whether that interaction is significant or not). To be specific, in the presence of an interaction (large or small, significant or not) the parameter estimate for each main effect is the effect when the other variable involved in the interaction is 0.

In your case, you have

$ DV = b_0 + b_1*Gender + b_2 * IV + b_3*IV*Gender$.

So, if gender is coded 0 for males and 1 for females, then $b_2$ is the parameter estimate for IV for males. For females, the estimated effect of IV is $b_2 + b_3$

The question to ask next is not whether $b_3$ is significant but whether it is big enough to make a difference, substantively.

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    $\begingroup$ +1 Good points and good guidance. We could (and should) go even further: if interaction makes a substantial difference, then what else could be done to further improve the model? Is the model even appropriate for these data? (One way that interactions can become significant is when the independent variable should really be re-expressed in a nonlinear fashion.) The significant interaction becomes a flag that alerts us to the need for further investigation. $\endgroup$ – whuber Nov 21 '11 at 15:58
  • $\begingroup$ Can I just stop after finding the significant interaction and draw scatter plots of A and B with gender in the mix (as explained in the Question?) (I have actually done this with regression lines for males and females and it makes a lot of sense, I think!) $\endgroup$ – Adhesh Josh Nov 21 '11 at 22:07
  • $\begingroup$ @Adhesh - I think the tone of the "can I?" and "should I?" questions may be rubbing people the wrong way, but i agree that the plots you describe will be effective in giving you the opportunity to look into the issue whuber raises about nonlinear relationships. $\endgroup$ – rolando2 Mar 31 '12 at 13:06

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