calculating sample size

[roblox]

Hi

I am a research project virgin, & I'm having a hard time understanding how you estimate your sample size.

My project entails performing a muscle strength test on three different groups of individuals (with varying physical characteristics). You either 'pass' or 'fail' the strength test.

The book says Power should be 80%, significance level 0.05, and 'specify the variability of the observations if you have a numerical variable'... but I don't have a numerical variable do I(?), just a catagorical Y or N.

What can I do?

Thanks

Rob

[bryangoodrich]

The variability has to do with what it is you are calculating. While your test is binary, your value of interest is not. Suppose you want the mean for a group. If your group size were equally 10 in each group, and group A, B, and C had 4, 7, and 5 successes, respectively, then we simply divide each success count by the group size. Of course, we don't know this numerical value. We don't know the size in our experiment. Nevertheless, we can specify certain parameters about the experiment, like how much variability we are willing to accept.

As an example, consider Kutner, et al. "Applied Linear Statistical Models" example (p 719, 5th ed.). A company owning a large fleet of trucks wishes to determine whether or not four different brands of snow tires have the same mean tread life (in thousands of miles). it is important to conclude that the four brands of snow tires have different mean tread lives when the difference between the means of the best and worst brand is 3 (thousand miles) or more. Thus, the minimum range specification is \delta = 3. It is known from past experience that the standard deviation of the tread lives of these tires is approximately \sigma = 2. Then we use the ratio \frac{\delta}{\sigma} to help us determine n. For small values of the ratio we have significant requirements on sample size. However, the sample sizes shrink considerably as the ratio grows. This makes sense because if we're more loose with our range requirements, we don't need a large sample size. The smaller the ratio, the more precision we're after, which always requires more size.

Now, the ratio can grow either by accepting a larger range of variation (delta) or there being a smaller standard deviation. You really can't control the latter! However, if you define the variation in terms of standard deviations (say, 2 standard deviations is your minimum range specification), then \frac{\delta}{\sigma} = \frac{k\sigma}{\sigma} = k. I'm not saying I have a formula for you to plug-and-chug, but this should answer your question about specifying the variability of the observations. You need to know what your observations are about. It isn't about each trial of the experiment. it is about what you are trying to observe from that experiment (say, mean number of successes). Those are certainly numerical. It is referred to as the effect size (http://en.wikipedia.org/wiki/Effect_size), and what choice of it you should make is variable. If your text provides something on this, I suggest following that.