# Quantitative : 3 Arm : Single Measurement : Calculator

There are several sample size calculators available on the web. The following is one such calculator:

http://math.yorku.ca/SCS/Online/power/

Recall that Jill is interested in testing whether or not the mean tumor size for each treatment group are equal. Jill wants to know how many mice she needs in each group in order to detect a difference of 1.5, 1.75, 2.0, or 2.25 standard deviations at a significance level of 0.05 and a power of at least 80%.

The following is an example of how Jill used the online calculator along with her results.

## Zoomed In

Jill is interested in comparing three treatments (one of which is the control). She is not interested in the interaction between any of the treatments, hence the number of levels of effect 'A' is 3 (for the two treatments and the control) and the number of levels of effect 'B' is 1. Jill wants the level of significance to be 0.05, and she is interested in four different levels of the effect size (1.5, 1.75, 2.0, 2.25). Using this information Jill is able to fill out the table in the following way.

## Interpretation

From the above output Jill can see that in order to obtain at least 80% power she will need at least 10 mice per group to detect a difference of 1.5 standard deviations. In fact the power would actually be 81.7%. If however she only needs to detect a difference of 2 standard deviations then a sample of 6 mice per group will give her a power of 80.5%. Jill should keep in mind though that accidents happen and its probably best to use a few more mice than needed.

-- ErinEsp - 28 Feb 2010