Читать книгу Applied Univariate, Bivariate, and Multivariate Statistics - Daniel J. Denis - Страница 80

At this point, the conscientious reader may very well be asking the following question: If the significance test is so misleading and subject to misunderstanding and misinterpretation, how does it even make sense as a test of anything? It would appear to be a nonsensical test and should forever be forgotten. The fact is that the significance test does make sense, only that the sense that it makes is not necessarily always scientific. Rather, it is statistical. To a pure theoretical statistician or mathematician, a decreasing p‐value as a function of an increasing sample size makes perfect sense—as we snoop a larger part of the population, the random error we expect typically decreases, because with each increase in sample size we are obtaining a better estimate of the true population parameter. Hence, that we achieve statistical significance with a sample size of 500 and not 100, for instance, is well within that of statistical “good sense.” That is, the p‐value is functioning as it should, and likewise yielding the correct statistical information.

However, statistical truth does not equate to scientific truth (Bolles, 1962). Statistical conclusions should never be automatically equated with scientific ones. They are different and distinct things. When we arrive at a statistical conclusion (e.g., when deciding to reject the null hypothesis), one can never assume that this represents anything that is necessarily or absolutely scientifically meaningful. Rather, the statistical conclusion should be used as a potential indicator that something scientifically interesting may have occurred, the evidence for which must be determined by other means, which includes effect sizes, researcher judgment, and putting the obtained result into its proper interpretive context.