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I am proposing a cross-sectional study that measures two variables.

Variable A is measured using a questionnaire that returns a value at an interval scale.

Variable B is measured as a dichotomous yes/no response (i.e. it is nominal).

Suppose that literature suggests that A is a predictor of B (say, increased A is conceptually expected to affect the response to B being "yes"). Since this would imply that the conceptual framework considers A, a continuous numeric variable, as predicting B, a dichotomous outcome, it seems that logistic regression would be the appropriate test to be used.

My question is: Are there conceptual grounds for choosing to utilize an independent samples t-test utilizing B as a grouping variable and comparing the means of A between the groups?

Would the conceptual framework of A being the independent variable and B being the dependent variable still hold if a t-test were to be performed? For example, if I conclude that "A is significantly different between the groups B(yes) and B(no)," is it valid to claim that an association exists between them that is consistent with literature?

The conflict here is that there seems to be an assertion (from what I've read) that independent samples t-tests should only be done if the grouping variable is the independent variable. However, I can say that reversing the framework into one that claims B as independent would not conceptually make sense. Perhaps this is all trivial and ultimately based on convention/argumentation/justification of the test to be used?

andrewt
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  • Welcome to CV. Doesn't https://stats.stackexchange.com/questions/159110/logistic-regression-or-t-test/159203#159203 answer your question? If not, why not? – whuber Jul 18 '23 at 14:35
  • Quite related and extension of the first link – Dave Jul 18 '23 at 14:40
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    A nicety of the logistic model approach is that it easily extends to multivariate comparisons of means. See this for discussion of a method proposed by Peter O'Brien. – Frank Harrell Jul 18 '23 at 14:46
  • @whuber: I guess the itch I still need to scratch (or be convinced is not a problem at all) is that age has a different quality to variable B. While the directionality between age and response in the link seems to be ambiguous, the directionality of A->B in my example is established. It is with this conceptual link where my confidence in utilizing a t-test falters, even though I can wrap my head around how the hypothesis it answers can still yield logically valid results. Another concern is that both values will be measured at the same time, instead of one being used to select a sample. – andrewt Jul 18 '23 at 15:01
  • The apparent duplicate explains the difference between the t-test and logistic regression. Neither models anything about causality or a "directionality." Although it's unclear what you mean by "different quality to," the models differ according to which variable's conditional distribution is important for you to analyze -- again, I believe, as explained in the duplicate. – whuber Jul 18 '23 at 15:52

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