In 1969, Psychologist Jacob Cohen released his book ‘Statistical Power Analysis for the Behavioral Sciences’. In this book Jacob Cohen introduced the Effect Size for the first time and explained how to use it.
So, how did Jacob Cohen, the inventor of the Effect Size, use it?
Quick translation – I noticed that people in the Behavioral Sciences sometimes did badly designed experiments because they didn’t understand Statistics well enough, so, I decided to help them by making some easy look-up tables.
Quick translation – There are four ways to do Power Analysis, but two of them are rarely needed. The two main ways you need to check your experiment before you do it are, firstly, check the Statistical Power is high enough or alternately check you have planned to test enough people.
Quick translation – To use the Statistical Power tables, you need to know the number of people in your experiment, the Statistical Significance you want and the Effect Size.
And here is a Statistical Power table from Jacob Cohen’s book, notice the Effect Size (d) at the top. There are dozens of pages of these tables in his book.
And here he gives an example of how to use the Statistical Power tables.
The other thing you need to check is the Sample Size.
Quick translation – The other way to check your experiment is with the Sample Size table. To use this your need the Statistical Power, the Statistical Significance and the Effect Size.
And here is a Sample Size table, notice the Effect Size (d) at the top. Again there are dozens of pages of these tables in the book.
And he gives an example of how to use the Sample Size table.
Now, every modern user of the Effect Size cites Cohen and they always quote him about small, medium and large effects. This gives the impression that they are just continuing his work, yet, they are using it in a completely different way to him.
Jacob Cohen, the inventor of the Effect Size, used it to check the Statistical Power and the Sample Size of an experiment before you did the experiment. He did this using look-up tables.