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I have a question regarding the interpretation of multiple dummy variables based on one categorical variable in a regression:

Suppose I have a categorical variable called ‘race’ which has four categories: white, black, Indian and Asian. For this categorical variable, I’ve created four separate dummy variables: white, black, Indian and Asian.

I now run a multiple regression which includes three (white, black, Indian) of the four dummy variables created above; one (Asian) is left out to set the reference category/dummy to compare the others to.

In the output, one dummy variable is significant (Indian) but the other two aren’t (white & black). My question is; what exactly does this mean?
As far as I understand it means that the one dummy variable that is significant (Indian) is of more significant influence on the model than the (reference) dummy that was left out (Asian).
But what do the two dummy variables (white & black) mean that are not significant? Does it mean they have no significant influence than the (reference) dummy variable that was left out (Asian)?

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As you said: it basically means that there is a difference in your dependent variable between your reference race (Asian in your case) and people of Indian race.

The non-significance of the other two indicates that you haven't been able to detect such a difference between the other two races and the reference race (which of course does not mean that there isn't one). So no difference in the dependent variable detected for black vs Asian, and no difference in the dependent variable detected for white vs Asian.

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  • $\begingroup$ Many thanks for your prompt reply (I gave you an upvote, but my reputation is less than 15 so sadly it isn't visible). What do you mean exactly by: "which of course does not mean that there isn't one"? Do you mean that, even though in this particular regression there is no significance difference between these two races and the reference race, if I would compare these (non significant) two races against each other, there might be a significance difference between them after all? Many thanks! $\endgroup$ – Freek Apr 26 '17 at 9:06
  • $\begingroup$ Indeed there might be a difference between black vs white, which you won't detect with this regression because Asian is the reference category. That is not what I meant, though. What I meant is that even if there is a difference between say black and Asian, you may not be able to detect it because it's small or you have a small sample size (and consequently large standard errors) $\endgroup$ – Maarten Punt Apr 26 '17 at 9:53
  • $\begingroup$ Once again, thanks for your reply! Ah, OK, I think I get it. Could another reason why I'm unable to detect it be that the net effect of black is (way) smaller than Indian, so that black becomes insignificant? $\endgroup$ – Freek Apr 26 '17 at 10:30
  • $\begingroup$ Hmm that I do not know exactly. I would say no, unless black and Indian are correlated. In fact, I think if the effect of Indian is larger than that of black, controlling for Indian effects would make a small black effect easier to detect, rather than harder. If black becomes significant once you drop Indian from your regressors, then black is probably just picking up the original Indian effect (see [here] stats.stackexchange.com/questions/88635/…) $\endgroup$ – Maarten Punt Apr 26 '17 at 10:44

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