A researcher found that his statistic was significant at the p < .001 level, indicating it was "more" significant than if the significance level was found to be p < .01.

Statistical significance does not indicate degrees of "more" or "less" significant; it simply means that the result is unlikely to have occurred by chance below the specified p-value threshold. Both p < .001 and p < .01 indicate significance, but do not imply a comparative degree of significance.