Methodological Question
In a research question, we need to find out whether two groups A/B are equally engaged in using an app given a single different variable:
We have $\approx12$ people, so $6$ tired people and $6$ rested people. We want to maybe disprove that their engagement with an app (measured from a number based research question) can be said to fail the null hypothesis: Group A and B have equal mean engagement, i.e. they might be equally likely to use the app based on the data.
We have found that using A/B-testing, one can use Welch's $t$-test to get a statistic to estimate this question. The question is whether this has obvious pitfalls, and if so since it has many calculations (https://en.wikipedia.org/wiki/Welch%27s_t-test), are there other pitfalls that need another question after performing the test, in order to not make an error by calculation?
Otherwise, is there a reason why Welch, which is popular, is not appropriate? Finally, what happens if we collect data on more than one app, say six? Is the a way to handle six outcomes in one method, or is this merely six reproductions of the same method?
Research Question
The impact of cognitive fatigue on a subjective perception of usability Hypothesis: F is expected to impact negatively on the subjective perception of usability, meaning that tired users are going to experience more cognitive load and perceive the usability tasks as more complicated.