We see that the p-value is about 0.05. So there appears to be some evidence of an association. But can we infer causation here? Is gender bias causing this observed difference? The response to the...

We see that the p-value is about 0.05. So there appears to be some evidence of an association. But can we infer causation here? Is gender bias causing this observed difference? The response to the original paper claims that what we see here is similar to the UC Berkeley admissions example. Specifically they state that this _“could be a prime example of Simpson’s paradox; if a higher percentage of women apply for grants in more competitive scientific disciplines, then an analysis across all disciplines could incorrectly show”evidence” of gender inequality.“_ To settle this dispute, create a dataset with number of applications, awards, and success rate for each gender. Reorder the disciplines by their overall success rate. Hint: use the reorder function to reorder the disciplines in a first step, then use gather, separate and spread to create the desired table.