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I have data from human participants who had to estimate the probability of an event happening under conditions A and B. They used a slider on an interval of 0-1 where 0 means the event is not gonna happen and 1 means the event is definitely gonna happen.

The raw data is the x axis of cursor position along this horizontal scale.

I want to know if there is a difference in these human-estimated probabilities between conditions A and B.

If responses were "event happens / doesn't happen" I would use logistic regression. If responses were on a likert scale, I would use ordered categorical regression.

My plan is to convert the cursor coordinates into a probability between 0-1. Then convert this into log odds. Then use generalised linear regression on the log odds assuming an identity link and a gaussian error distribution.

Would this do? Is there a more elegant alternative?

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You can simply feed the coordinates into a standard t test. Or convert them into probability estimates first. This will test a difference in means between your two conditions. You can use a paired t test if each participant was tested under both conditions, or not if not.

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  • $\begingroup$ The way I understand it, a t test would look for a difference in means because it would assume that the data are normally distributed, which is far from the case here. I think maybe a non-parametric test, like a Wilcoxon test, would be suitable on the raw data, but I'm not sure how much. $\endgroup$
    – petyar
    May 10, 2021 at 5:52
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    $\begingroup$ No, not at all! t tests do not assume a normal distribution. That is an unfortunate urban legend that will never be eradicated. See t-test when the data population is not normally distributed. $\endgroup$
    – Stephan Kolassa
    May 10, 2021 at 6:09

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