The question may be framed nonspecifically as an investigation of possible associations between party affiliation and mathematical reasoning across contexts. As a hypothetical example, suppose a researcher is interested in how Democrats and Republicans perform differently in a short mathematics test when it is expressed in two different contexts, involving either healthcare or the military. In general, p-values are based on what would have happened under other possible data sets. In an ironic twist, p-values are now often used to lend credence to noisy claims based on small samples. Fisher offered the idea of p-values as a means of protecting researchers from declaring truth based on patterns in noise. The concept of p-values was originally developed by statistician Ronald Fisher in the 1920s in the context of his research on crop variance in Hertfordshire, England.
The idea is that when p is less than some prespecified value such as 0.05, the null hypothesis is rejected by the data, allowing researchers to claim strong evidence in favor of the alternative.
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