I am looking for information on the history of the development of statistical significance formulae, the mathematical calculations and why they were chosen.
I would also like to learn the same about effect size.
Thanks!
Depends what you mean by statistical significance. Several books cover the history of statistics and probability pre-1900 (Stigler's History of Statistics and Hacking's Emergence of Probability, being two of the most well known). For more on the past 100 years, Gigerenzer's Empire of Chance is excellent. There are others, but I'll let other commentators list their favorites.
If you mean statistical significance as just the approaches of Fisher, Neyman, Pearson, etc., to hypothesis testing and p values, their papers are available, and much discussion of them (actually, Gigerenzer is the author of one on this, something like the Id, Ego, and Super-Ego of statistical reasoning ... heh, its here (http://www.mpib-berlin.mpg.de/en/institut/dok/full/gg/ggstehfda/ggstehfda.html)). Another is Lehmann's Fisher, Neyman, and the creation of classical statistics.
John -
Good inquiry and good answer by Daniel.
The p-value may be the most misunderstood statistical concept ever, and has resulted in a great many erroneous conclusions. I suspect that is why you are interested in the historical development of this tool. You will find a great deal written on this topic. If you follow the history, I think that you will see it has resulted in much discussion of technical points regarding the null hypothesis, that I think have detracted greatly from practical usage. It seems that many more people are finally coming to that conclusion, and thus, as you noted, "effect size" has gotten some notice. The problem is that a p-value is a function of sample size. For a given level, say 0.05, to reject a null hypothesis, increase your sample size. To 'accept' (fail to reject it), decrease your sample size. Yet in much of the literature you will see a given level, often 0.05, used without regard to this. That is why a power analysis or other sensitivity analysis is needed for each application.
There are many practitioners who do not like dealing with statisticians because too many statisticians may go off on a theoretical tangent, and ignore the practical aspects of real world problem solving. I hope that you will find that the trend has finally moved toward practical problem solving in your historical study of "significance." (The word "significance," in my opinion, is so distorted that I have generally tried to make clear that in a problem solving effort, I looked for what was "substantial," and avoided "significance.")
The attached letter was with regard to an article by Richard Royall, who also wrote a book on 'significance,' as I recall.
Cheers - Jim
Article Practical Interpretation of Hypothesis Tests - letter to the...
Prof. James, thank you for the substance of substancial, I find it concrete, simple and substantial!
Roberto
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as already mentionned by Daniel above, Gigerenzer's The Empire of Chance is a wonderful book on the history of statistics
enjoy the chapter attached below !
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i would also add Desrosières' masterpiece,The Politics of Large Numbers (Harvard University Press), which covers the history of social statistics
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The text Statistics (especially the 1979 first edition)by Freedman, Pisani, and Purvis provides a good review of the development of the idea of statistical significance.
Thank you all. I had started out trying to find out what the step-by-step calculations for both Statistical Significance and Effect Size, hoping to better understand each concept better. I then realized that looking at the history of the concepts and their development would probably be a better way to get to the answer. I thank you all for your generosity of time, knowledge and resources!
Thanks Markovic, Danny and Manuel! I will read through these suggestion articles.