So, it appears that this is a repeated measures design, correct? Another question regards how you conceived of the 13 ordinal questions. Perhaps they are Likert-type, and perhaps you intend to sum them, or perhaps not. It does make a difference. If summed, then a psychometric step that you should do is to address reliability. You can get an easy estimate of that from coefficient alpha. Of course it is also possible that you see these 13 items splitting into two or three subscales, in that case, you would need to address that question for each. I assume that validity will be addressed as well, but seems beyond the scope of this question.

Then, beyond that, I would guess that your question regards the difference(s) between Ss in the A and B treatments. Therein, assuming assumptions are met, you can pursue standard repeated measures statistical analysis. If you only have two (A and B) levels of the repeated measure, you will not need to be concerned about the otherwise somewhat pesky sphericity assumption, and can simply use a "paired" t-test for any such scale, keeping in mind that if there are multiple scales, some attention is needed to accumulating Type I error-rate with multiple hypothesis tests.

If on the other hand , you intend to treat all of these 13 ordinal variables separately, without know why, I would discourage that, both because of the limited stability of the individual items, but also due to the error-rate problem I mentioned.

My best on your research,

John

I think there are two different elements to your question, one concerning repeated measures and another concerning how to handle Likert-scored variables. As John Morris suggests, you can resolve the issues around the ordinal-level measurement in your Likert-scored items by combining them into a scale. Because there have be so many questions here about this topic, I have compiled at set of resources to address it:

https://www.researchgate.net/post/How_can_one_help_people_create_simple_scales_from_Likert-scored_items

With what I understand to be 13 items, the per-hypothesis error correction will make it such that only a VERY large effect can be significant if you treat these items indidvidually, and use a Bonferroni correction. As these items apparently arise from a longer instrument that I presume uses summed the Likert-type items, I still believe that you will be best to sum the items, and to consider whether the reduced scale manifests enough reliability to be useful. Note that the reliability, as any other statistic, will be unstable due to the small sample size, but it is not biased by that.

You need power. Unless the distributions are far from assumptions, I would still use a paired-t.

JDM

If you only have a total of 10 research participants, then you are correct that you should not do EFA with 13 items.

Beyond that, such a small sample size will make it very difficult to find any significant results, regardless of the statistic that you use, due to the low power (large confidence intervals) for your results.