Hello Kaylee,

That's a lot of questions! Here are some possible answers.

1. If you're trying to determine whether a given sample manifests some attribute, trait, or characteristic, to a non-zero extent, then you'll need: (a) a measure of that attribute; (b) a sample, ideally a probability sample from your target population; and (c) if the usual assumptions apply (normality, independence, interval strength scores), then a one-sample t-test could evaluate whether your sample reflects a level of 0 for the attribute (or any other specific constant you have in mind) as the null hypothesis value. Though it sounds like semantics, we never "prove" anything with statistics, unless you have data for the entire population on the variable(s) of interest.

2. This one can become quite complicated. PI, or any construct, may in reality be contributed to by multiple (latent) variables (e.g., it's multidimensional), or it may be unidimensional. That's part of the reason that factor analysis (whether exploratory or confirmatory) is so important a tool in questions like this. If you have developed the indicators/items to measure PI and your attempt to identify structure suggests 3 distinct factors/components (you didn't say whether you used PCA or common factor analysis: common factor analysis is likely the better choice here), then you could: (a) use all three latent variables (e.g., treat PI as a multivariate attribute); (b) try a higher-order factor model to see if a second-order factor captures the three that you have identified; or (c) go back to your item set and judge whether one of the three factors/components is closest in line with your chosen definition of PI (and just use that single latent variable).

3. I would disagree with your friend's advice; while an estimate of score reliability is a useful indicator of technical quality, there is no substitute for confirmation that the scale (however constructed) measures the target construct and not something else.

Good luck with your work!

Dear Kaylee Ra ,

I'm really impressed by David Morse 's answer. Maybe I can just add something small regarding your Likert variables.

Factor analysis often combines several items measured by Likert variables (e.g. strongly disagree to strongly agree) into a single scale variable. This is actually the definition of a Likert scale.

Your other "qualitative" variable that has 7 answers should be treated as ordinal data is there is a clear ordering between the answers, otherwise it should be treated as a nominal variable. Nominal variables cannot be used in factor analysis.

David Morse has given you good advice. In addition to making sure that you doing the factor analysis with a Common Factors model, I would also recommend using an oblique (correlated factors) rotation rather than Varimax, because it is unlikely that your factors are uncorrelated in the real world.

Beyond that, I would recommend looking at the "scree" of your factors, rather than just using the defaults values that are producing the current selection of three factors. This is fairly straightforward, so you should be able to find good advice on the internet about doing scree tests in factor analysis.

Finally, you should examine the variables that make up each of the factors to make sure that they are not picking up on the difference between items with 5 versus response categories.