Validating a paper questionnaire in a web-based format I would like to validate a commonly used questionnaire for internet-based administration.  What statistical tests should I be using?
 A: The following are two complementary strategies that you could adopt.
1. Conduct your own empirical validation:
A simple strategy would be to run some form of experiment.
Randomly assign half of your participants to web based completion and the other half to paper based completion.
Then, examine whether statistical properties of the questionnaire are the same across administration formats; e.g., item mean, item standard deviation, intercorrelations between items, etc.
You may find structural equation modelling approaches useful.
You'll also need a sufficiently large sample size because you are effectively trying to prove the null hypothesis.
Other designs would also be possible. For example, you could get participants to complete both versions and counterbalance for order. This mixed design would have more power for a given sample size but would suffer the potential confound of carry-over effects.
2. Rely on existing research literature
There's been a lot of research looking at consistency of web based and paper based formats.
Over the while I've read research on online-paper consistency for personality tests, ability tests, questionnaires, and more.
I don't have specific references on hand, but you should do a literature review to gather  relevant evidence from analogous existing studies.
In general, you'd want to think about the reasons why you would expect differences. For example, I've seen cases where data collected online is more noisy than face-to-face data.
You also need to consider what you mean by "questionnaire". A questionnaire can be mail, face-to-face, self-administered but with an investigator in the room, and so on.
