Interview – content
Skills-based – content
Integrity – criterion because while this is likely to have “face validity” it may not actually predict theft, etc. so if it causes disparate impact the company may be held liable. However, having face validity is good because it decreases the chances of it being challenged because it “looks” like it’s related to the job.
Personality – criterion
Job Knowledge – content
Math or reading – it depends, if the job requires direct application of certain math or reading skill proficiency levels, then you can probably use a content approach. But if it’s intent is to measure general intelligence to determine how quickly someone will be trained, you’ll need to establish criterion-related validity.
The key is how much of an inferential leap do you need to make? The larger the leap the less likely content validity is able to be used.