Below, a very simple example to illustrate the use of statistical
tests in the Social Sciences. It is from the Paris-Sorbonne series
I have been going through. The math is mind-bending but the
example sane enough to pull it all together.
The test in question: Student's t-test. (I love it: Student
never existed, but the test was designed by someone working
for a beer manufacturer...). A summary of the test and findings.
In a business with 32 employees, we want look at the relationship between
salary and years of service. With a correlation of 0.4, is this significant.
We have used variance as r in the Pearson test.
The t-test tells us that it is, with a possible error less than 5%.
Equally interesting. With a r^2 of 0.16, only 16% of the effect (ie salary) is being
accounted for. This is the coefficient of determination at work.
That is weak...
Correlation Coefficient | Types, Formulas & Examples (scribbr.com)
* * *
Working from Karl Popper: 'all swanns' are white is a null hypothesis.
One should not seek to establish such a thing, At best, one can show that
some aren't ie if we find pink ones...
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