I want to evaluate in a choice test if the individuals choose between two options, A and B. The test is carried out on 20 individuals (10 males and 10 females) for 5 minutes and the time, in seconds, that each individual spends in each of the options is recorded. Since the time that an individual spends in one option determines the time that it spends in the other option, there is no statistical independence. To solve this problem we plan to use only the time that individuals spend in option A and subtract 150 seconds from the records (expected time under the null hypothesis of no choice between A and B) and run a linear model with sex as a factor and evaluate the intercept and the intercept difference with the other sex. I think that by using only the time in only one of the options we get around the problem of the non-independence of the records. If someone has analyzed essays of this type I would appreciate comments on this and if it seems appropriate or if it has any slip that we missed... Thanks in advance!
I find that a more simple and direct direct way would be to express the proportion of time spent on option A and evaluate it with a generalized linear model with quasibinomial family specs.
for example in R
binmodel = glm(Proportion ~ Sex, data, family='quasibinomial')
The dotted line in the plot shows the Ho expectation.
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