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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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  • $\begingroup$ At the risk of sounding a bit silly... where on the SPSS output would I find the delta R^2? $\endgroup$
    – user14189
    Sep 19, 2012 at 3:10
  • $\begingroup$ 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). $\endgroup$ Sep 19, 2012 at 3:21
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In the model gender is one of 10 covariates. It has some influence on the response complaining in conjunction with the other covariates. But by itself it makes less of a difference and is not a statistically significant difference.

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  • $\begingroup$ By 'but by itself it makes less of a difference and is not a statistically significant difference' are you referring to the -.083? I mean I have other variables with around .255 and .277 so I guess I'm wondering where the cut-off is. $\endgroup$
    – user14189
    Sep 19, 2012 at 3:13
  • $\begingroup$ No I am talking about the mean response for males - mean response for female which is determined not to be significant based on the t test. $\endgroup$ Sep 19, 2012 at 3:36

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