# Discrepency between p value and confidence interval in glm [duplicate]

Consider estimating the binomial success parameter using glm.

glm(cbind(3,10)~1, family = binomial()) # 3 successes, 10 failures


The table is

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  -1.2040     0.6583  -1.829   0.0674 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance:  0.0000e+00  on 0  degrees of freedom
Residual deviance: -3.2646e-24  on 0  degrees of freedom
AIC: 4.7333

Number of Fisher Scoring iterations: 3


Note that the model fails to reject the null at the 5% significance level. However, if I then estimate the confidence interval for this model I get

     2.5 %     97.5 %
0.06302025 0.49511505


Note now that the null value is outside the confidence interval, and we should reject the null hypothesis. Some documentation reading reveals there is another method called confint.default based on asymptotic normality which returns the following confidence interval

                2.5 %    97.5 %
(Intercept) 0.07626731 0.5215448


Does R use asymptotic normality in the glm coefficient table but profile likelihood when I call confint? What else may explain this discrepancy?

• The point estimate doesn't fall within either confidence interval - have you described what you've done correctly? Nov 20, 2019 at 21:34
• Oh, I see, the CI's are for odds, not log odds. Nov 20, 2019 at 21:41