Wald test results against Confidence Interval

[Alistair Rowe]

Hi, I am trying to test and see whether the marginal effect of IP_HomeO is equal to one. At the 95% CI level, it is contained within the interval so I obviously fail to reject my hypothesis that IP_HomeO is not equal to one.

However, when I then do a joint Wald test of IP_HomeO = 1 and constant = 0, my prob > chi2 is statistically significant allowing me to reject the null of IP_HomeO = 1.

I am a bit confused now - how can I reject that IP_HomeO = 1 when it is included in the confidence interval before? I am not sure if I am interpreting the Wald test wrong or over complicating it for myself.

Apologies for the image of output - I was not sure how to get stata code format in my submission.

Any assistance would be greatly appreciated.

[Leonardo Guizzetti]

You are comparing apples and oranges.

Apples: Margins reports the transformed estimated marginal means, and the hypothesis test corresponds to the null hypothesis that Pr(y)=0.

Oranges: -test- performs a hypothesis test on the regression model coefficient(s). The individual coefficient estimates are precise enough to show that they are quite different from the hypothesized values of 0 and 1 (from your joint test), so it's not surprising that a joint test would then also be statistically significant.

Out of curiosity, is there a specific reason you are testing this specific joint test? I have my suspicions about what you might be getting at, but I don't want to make any assumptions.

[Alistair Rowe]

Thanks Leonardo, that makes sense. IP_HomeO is the implied probability of a football team winning the game (probability derived from betting odds).

To ascertain market efficiency, it needs to be that IP_HomeO = 1, as that would indicate betting odds correctly predict actual probabilities of match results (my dependent variable, =1 if team wins, =0 if team loses). _cons needs to = 0, as that shows no other variables would add info to the prediction.

I was using margins as it is easier to interpret probit results that way I thought

Appreciate your response