I'm trying to get a handle on the concept of overdispersion in logistic regression. I've read that overdispersion is when observed variance of a response variable is greater than would be expected from the binomial distribution.
But if a binomial variable can only have two values (1/0), how can it have a mean and variance?
I'm fine with calculating the mean and variance of successes from x number of Bernoulli trials. But I cannot wrap my head around the concept of a mean and variance of a variable that can only have two values.
Can anyone provide an intuitive overview of:
- The concept of a mean and variance in a variable that can only have two values
- The concept of overdispersion in a variable that can only have two values