Binary vs Binomial data

This section focuses on the distinction between binary and binomial data.

For binary regression, all the data in our outcome variable has to be a 0 or a 1. For example, the correct variable below:

participant	question	correct
1	1	1
1	2	0
1	3	1
...	...	...

But we can re-express this information in a different way, when we know the total number of questions asked:

participant	questions_correct	questions_incorrect
1	2	1
2	1	2
3	3	0
...	...	...

To model data when it is in this form, we can express our outcome as cbind(questions_correct, questions_incorrect)