On Men and Ideas: Fisher vs. Pearson

05 Friday Oct 2018

Posted by egarcia in Correlation Coefficients, Data Mining, Fisher Transformations, Mathematics, Statistics and Mathematics

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Fisher, Fisher vs. Pearson, Pearson, Royal Statistical Society

Ronald Aylmer Fisher was considered an outsider by the statistical establishment of his time.

The links below (1-3) show his struggles & nuances with Karl Pearson, his son Egon, Bowley, their followers, and the Royal Statistical Society (RSS). His life was a story of accomplishments and noise (deceptions and nasty RSS politics). He was too ahead of his time.

That reminds me of the struggles of another maverick: Benoit Mandelbrot. Eventually and like Mandelbrot, Fisher greatness was recognized. Also like Mandelbrot, he was able to boost the signal-to-noise of his career and life.

Most statisticians consider Fisher the Father of Modern Statistics (https://en.wikipedia.org/wiki/Ronald_Fisher), even when he was not allowed to teach Statistics at the University of Cambridge (they tried to silence Fisher).

Yes, scientists too can be demeaning to other scientists, more for personal reasons than for ideas and the Scientific Method. After all, they are also mostly carbon units called “humans”.

1. Fisher in 1921 https://projecteuclid.org/download/pdfview_1/euclid.ss/1118065041

2. Fisher vs Pearson: A 1935 Exchange from Nature
http://physics.princeton.edu/~mcdonald/examples/statistics/inman_as_48_2_94.pdf

3. Fisher: The Outsider
R. A. Fisher: how an outsider revolutionized statistics

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Regression & Correlation Calculator: Updates and Improvements

14 Friday Sep 2018

Posted by egarcia in Algorithms, calculators, Data Mining, Fisher Transformations, Mathematics, Statistics and Mathematics

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Correlation Coefficients, Pearson Correlation, Spearman Correlation

Regression & Correlation

We have updated and improved our Regression & Correlation Calculator to demonstrate, as shown in the above figure, that a Spearman’s Correlation Coefficient is just a Pearson’s Correlation Coefficient computed from ranks.

The tool uses an algorithm that converts values to ranks and averages any ties that might be present before calculating the correlations. This comes handy when we need to compute a Spearman’s Correlation Coefficient from ranks with a large number of ties.

We have explained in the “What is Computed?” section of the page’s tool that as the number of ties increases the classic textbook formula for computing Spearman’s correlations

Spearman's Correlation Coefficient

increasingly overestimates the results, even if ties were averaged.

By contrast, computing a Spearman’s as a Pearson’s always work, even in the presence or absence of ties.

To illustrate the above, consider the following two sets:

X = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Y = [1, 1, 1, 1, 1, 1, 1, 1, 1, 2]

using Spearman’s classic equation r_s = 0.6364 ≈ 0.64.
By contrast, r_s = 0.5222 ≈ 0.52 when computed as a Pearson coefficient derived from ranks. This is a non trivial difference.

Accordingly, we can make a case as to why we should ditch for good Spearman’s classic formula.

We also demonstrate in the page’s tool why we should never arithmetically add or average Spearman’s correlation coefficients. The same goes for Pearson’s.

Early articles in the literature of correlation coefficients theory failed to recognize the non-additivity of Pearson’s and Spearman’s Correlation Coefficients.

Sadly to say, this is sometimes reflected in current research articles, textbooks, and online publications. The worst offenders are some marketers and teachers that, in order to protect their failing models, resist to consider up-to-date research on the topic.

PS. Updated on 09-14-2018 to include the numerical example and to rewrite some lines.