# After bootstrapping regression analysis, all p-values are multiple of 0.001996

I'm running various multiple regression analyses in SPSS 27, and with those that are not bootstrapped, the p-values vary such that I do not find the same p-value twice within a regression (e.g., the p-values will be 0.000012435, 0.0053868, 0.000000013845, and so on). However, I bootstrapped some of these regressions (bca, 500 samples), and all p-values listed under the table that indicates the bootstrapped results are multiples of 0.001996 (e.g., 0.001996, 0.003992, 0.007984). Are these legitimate p-values? Or is this an error on the part of SPSS? In either case, are these p-values "report-able", or should I use the p-values of the non-bootstrapped regression results?

The values you got were multiples not of 0.002, but of 0.001996. This turns out to be pretty much exactly equal to 1/501. The reason for this discrepancy of 1, is that the "regular" p-value calculated from a bootstrap has a bias. The regular formula is $$\hat{p}=\frac{x}{N}$$, where $$x$$ is the number of bootstrap-sampled coefficients that were larger than your observed value, and $$N$$ is the number of bootstrap samples. The bias-corrected formula is $$\hat{p}=\frac{x+1}{N+1}$$. So, any p-value resulting from this formula will be an integer multiple of $$\frac{1}{N+1}$$, which in your case is 1/501.