Thank you @Mila Ilieva for your compliments! I hope I get intresting answers too.

Depends what you mean by internal reliability. In the old days people might have run Cronbach's alpha without thinking (it is fine for binary data, if doing it by hand there is a formula to make it easier). Now I think people consider more what they mean by "internal reliability." So what do you mean? Do you believe your scale is unidimensional? If you just want one number, the median odds ratio (or log odds ratio, or loads of other 2x2 association measures) might be appropriate. But, in order for anyone to answer (other than someone not knowing how to press follow, so saying that as if it is an answer) you should say what you mean.

Hi Wumi,

The issue is how to preserve construct vaidity (among many other things). Cronbach's alpha is the correct approach, but you have to do some basic pre-liminary checks before calculating CA. You have to do factor analysis, check the results, decide whteher the factor loadings comply with the standards. Then you can calculate Cronbach's Alpha. Mind that there are conventions as thresholds. Have fun.

Kind Regards

Rob

Daniel Wright Thanks for your contribution. By "internal relaibility" I mean internal consistency, that is, how well this "CPTED elements audit and site assessment checklists questionnaire" is actually measuring what I want it to measure. The scale cannot be unidimesional. When a question has two possible responses (e.g. Yes/No), we consider it dichotomous; right?

Rob Christiaanse Thanks for your contribution. But this (Cronbach's alpha) was strongly opposed by a reviewer (no alternative statistical tool(s) was offered). However, what then, if factor loadings did not comply with the standard? Is this an indication for actual lack of consistency among items in the questionnaire even when alpha's value is above 0.60? Which other statistical tool(s) is analogous to Cronbach's α and very applicable in this situation?

Kuder Richardson 20. (Though the Cronbach's Alpha and KR20 values for dichotomous variables would be the same as there is no question of partial credit).

Wumi Badiora , a "scale" can be unidimensional with binary observed items. This is the assumption made often with IRT (item response theory), though many say this assumption should not be made (e.g., http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/latent-trait-test-score-models.pdf). It is that there is only one latent trait influencing the probability of how people answer different items (and if you want this trait to be categorical, try latent class analysis). On what you mean by internal consistency, how the individual items relate, this is NOT what Cronbach's alpha measures. It is about the scale, so tends to increase if you do things like ask a question several times. To see how well the typical item predicts the rest, there are methods in IRT, but if you don't want to use latent variables and want something that will be understood by readers, you could do something like for each item, calculate the difference between those answer one way versus the other on the sum of the other responses (reverse scoring where appropriate). This will give you a number for each item in an understandable metric.

As far as the reviewer's comment, some people like omega_T rather than alpha.

Viswa Chandu Thank you for your suggestion. I will try the statistical tool.

Daniel Wright Thank you for your detailed explanation. I want something that will be well understood by readers. So, I will try to calculate (the reverse scoring) the difference between those answer one way versus the other on the sum of the other responses.

Wumi Badiora The statistics Viswa Chandu mentioned will do for your purposes. Because you referred to CPTED which is a quite complicated multi i.e. interdisciplinary approach, I thought that your model must have have some multi variable construct . As said Kuder Richardson 20 will do.

Daniel Wright Rob Christiaanse Viswa Chandu

Can you please also add a (at least short) explanation of the consistency test: the KR-20 test measures how good the different items/constructs of a questionnaire/check-list fit to different groups (e.g. Five CPTED strategies); in the sense that the different items could be "merged" to one of the strategies ?

Cronbach's alpha is usually used to check the consistency of a new merged variable consisting of several items. Is that correct?