The Art of Statistical Thinking by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 0000000000000
Published: 2023-04-06T12:06:21+00:00

“No scientific worker has a fixed level of significance at which from year to year, and in all circumstances, he rejects hypotheses; he rather gives his mind to each particular case in the light of his evidence and his ideas.”

While Fisher did recommend 0.05 as a benchmark threshold for a small sample analysis, it seems he never intended it to be used as a universal threshold. A part of the deep problem we have is this 0.05 threshold recommended for a small sample analysis is still being routinely and mindlessly used in the era of big data.

Neyman and Pearson

The next generation of pioneers were Jersey Neyman and Egon Pearson, who introduced a decision-theoretic approach to hypothesis testing in their paper published in 1933. They introduced the alternative hypothesis in addition to the null hypothesis and concepts such as the level of significance (Type I error rate), statistical power, and Type II error rate. The sample size and the level of significance are critical elements in their method, and they should be chosen before the researcher observes the data. These choices also determine the critical values or critical regions where the researcher accepts the null hypothesis or the alternative hypothesis. Note that “accepting a hypothesis does not mean that you believe in it, but only that you act as if it were true.”[v][5] According to their teaching, the sample size and the level of significance should be chosen in explicit consideration of the losses or consequences of incorrect decisions.

As we have seen in this chapter, the concepts such as Type I error rate, Type II error rate, and statistical power are important for the paradigm of Neyman and Pearson and largely because it has a substantive alternative hypothesis that specifies the population value we are testing for. This is the point that was different from Fisher’s method and the method being adopted in modern statistics.

In addition, these pioneers recommended inferential statistics as an aid to make the final decision. The inferential outcome should not drive the whole decision process. They recommend being “modest and thoughtful” in making statistical decisions, evaluating the outcome of statistical inference carefully considering all information.

Null ritual

The statistical methods adopted by modern statistical researchers are rather different from the teaching of the above pioneers. It is called “the null ritual” by Gigerenzer (2004) in his article, “Mindless Statistics”. Following his description, the null ritual is conducted in the following way:

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