Using glm() as substitute for simple chi square test

You can use an offset: glm with family="binomial" estimates parameters on the log-odds or logit scale, so $\beta_0=0$ corresponds to log-odds of 0 or a probability of 0.5. If you want to compare against a probability of $p$, you want the baseline value to be $q = \textrm{logit}(p)=\log(p/(1-p))$. The statistical model is now

$$\begin{split} Y & \sim \textrm{Binom}(\mu) \\ \mu & =1/(1+\exp(-\eta)) \\ \eta & = \beta_0 + q \end{split}$$

where only the last line has changed from the standard setup. In R code:

• use offset(q) in the formula
• the logit/log-odds function is qlogis(p)
• slightly annoyingly, you have to provide an offset value for each element in the response variable – R won’t automatically replicate a constant value for you. This is done below by setting up a data frame, but you could just use rep(q,100).

x = rbinom(100, 1, .7)
dd <- data.frame(x, q = qlogis(0.7)) 
summary(glm(x ~ 1 + offset(q), data=dd, family = "binomial"))