# Contradiction between significant effect in multiple regression, but non-significant t-test on its own

I ran a multiple regression using 10 independent variables and the single dependent variable (consumer complaining behaviour). One of those independent variables was gender. The $R^2$ for the model itself was $.157 (F= 20.50, p = .000)$ which whilst not the highest $R^2$ score was at least significant. Down in the coefficients table Gender $(\beta = -.083, p = .006)$. As my supervisor explained it is a significant score that accepts the alternative, and has a negative relationship with CCB. Interpretively, it would mean men are more likely to complain than women (men = 1 women = 2).

Now I got a bit curious and did a t-test to test the difference in means and as it turns out there is no significant difference between the gender groups.

This is where I'm getting a bit confused... I'm not sure how I'm meant to interpret these results. It just seems like maybe they contradict each other?

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The multiple regression model controls for other sources of variability in the DV, whereas in the t-test, all of that variability is lumped into the error term. Thus, the t-test has lower statistical power to detect the effect. Under the assumption that the effect is real, however, the t-test would show 'significance' with a sample that was large enough.

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Gung already gave a good answer. I would also add that in a model with 10 covariates, it's very easy to obtain small, sometimes spurious, effects, just because your other variables are absorbing so much variance. I would examine some effect size metrics (such as delta R^2) for your gender effect to help you determine whether your gender effect is real.

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At the risk of sounding a bit silly... where on the SPSS output would I find the delta R^2? –  user14189 Sep 19 '12 at 3:10
If you're using the General Linear Model routine, I believe one of the options is "show measures of effect size" or something similar to that. SPSS should then show several effect size measures next to the tests of your model parameter estimates (i.e., your tests of the gender and other effects). –  Patrick S. Forscher Sep 19 '12 at 3:21