Everyday effect size problems come down to one relationship between control sample mean, experimental sample mean, control standard deviation and experimental standard deviation. This calculator turns those numbers into pooled standard deviation, correlation coefficient and effect size, with the working shown so you can check the result rather than simply trust it.
What Is the Effect Size Calculator?
The effect size calculator turns a set of measurements into pooled standard deviation, correlation coefficient and effect size, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the Effect Size Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with control sample mean set to 10, experimental sample mean set to 5, control standard deviation set to 2, the calculator returns pooled standard deviation of 70.72482, and effect size of 0.0707, and correlation coefficient of 0.03533. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out pooled standard deviation?
Enter control sample mean, experimental sample mean, control standard deviation and experimental standard deviation. The calculator then works through the relationship and reports pooled standard deviation, correlation coefficient and effect size.
What does the effect size actually calculate?
It takes control sample mean, experimental sample mean, control standard deviation and experimental standard deviation and converts them into pooled standard deviation, correlation coefficient and effect size using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter control sample mean?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.