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I am currently helping a friend with some statistical analysis.

There is a main hypothesis, for which a significant relationship can be shown. Lets call the predictor variable A and the predicted variable B. Her sample size is 200 people. However the distribution of the sexes is very uneven, i.e. there are 150 women and only 50 men.

There also is a significant relationship in her data between gender and the predicted variable B. Furthermore if all factors are analyzed together, the significance of the relationship between A and B drops below the alpha-level.

Is it possible that the unevenness of the sample can somehow influence the result in this case? Or is there some other effect that explains this situation. If so what is this effect called (assuming it is known). Maybe the stronger relationship between gender and B is shadowing the relationship between A and B or something like that.

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About your 3rd paragraph---"between sex and the predicted variable B and the sex"---do you mean there is some correlation between A and gender, and B and gender? – chl♦ Dec 3 '11 at 22:30
@chl: sorry, I guess I was missing some english words, when I typed this. I tried to edit to make this a little clearer. I am not sure about a correlation between variable A and gender. The interaction was tested using an ANOVA. The ANOVA of A and B was significant and the ANOVA between gender and B was significant. For an ANOVA with A, gender and B only the relationship between gender and B were significant, so the presence of gender in the analysis destroyed the significance for A and B. I hope it is more clear this way. – LiKao Dec 3 '11 at 22:50

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Because you have more women in the sample you will be able to characterize the distributions of A, B, and the relationship between the two, more precisely for women than for men. If the relationship between A and B is the same for men and women, it will be more statistically significant for women.

Why don't you run your regression predicting B with both A, gender, and A*gender and report the results. Also tell us what you think you can say based on it, because otherwise you will end up copying what people say, gaining a correct answer, but not true understanding

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I am not sure what you mean by "predicting B with both A, gender, and A*gender". If I encode gender as 1/0, then wouldnt A*gender be zero for some parts of the group. Also, the main interest of this study is about the relationship between A and B. There seem to be some effects of gender on B, which have been studied before (althoug the results are not coherent). The problem is that the relationship between A and B is destroyed, when gender is used as well, and I am not sure what this means for rejecting the hypothesis (because it is not significant in this case). – LiKao Dec 4 '11 at 16:33
By A*gender I meant to suggest you include an interaction of A and gender. This term would allow you to see how the relationship between A and B differs among men and women. You should go beyond the simple question of: "Is the relationship between A and B statistically significant?" and try to learn everything your data can tell you about this relationship. The model you use to predict B depends on, among other things, on what B is... continuous and normally distributed, dichotomous, ordinal, etc. Please give us statistical output and then attempt to interpret it. – Michael Bishop Dec 4 '11 at 17:40

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