John C. Pezzullo

To estimate sample size in biostatistics, you must state the effect size of importance, or the effect size worth knowing about. If the true effect size is less than the “important” size, you don’t care if the test comes out nonsignificant. With a few shortcuts, you can pick an important effect size and find out how many participants you need, based on that effect size, for several common statistical tests.

Biostatistics, in its present form, is the cumulative result of four centuries of contributions from many mathematicians and scientists. Some are well known, and some are obscure; some are famous people you never would’ve suspected of being statisticians, and some are downright eccentric and unsavory characters.

One of the reasons (but not the only reason) for running a multiple regression analysis is to come up with a prediction formula for some outcome variable, based on a set of available predictor variables. Ideally, you’d like this formula to be parsimonious — to have as few variables as possible, but still make good predictions.

Two quite different ideas about probability have coexisted for more than a century. These probability approaches, which differ in several important ways, are as follows: The frequentist view defines probability of some event in terms of the relative frequency with which the event tends to occur. The Bayesian view defines probability in more subjective terms — as a measure of the strength of your belief regarding the true situation.

Modern statistical software makes it easy for you to analyze your data in most of the situations that you’re likely to encounter (summarize and graph your data, calculate confidence intervals, run common significance tests, do regression analysis, and so on). But occasionally you may run into a problem for which no preprogrammed solution exists.

You can calculate the standard error (SE) and confidence interval (CI) of the more common sample statistics (means, proportions, event counts and rates, and regression coefficients). But an SE and CI exist (theoretically, at least) for any number you could possibly wring from your data — medians, centiles, correlation coefficients, and other quantities that might involve complicated calculations, like the area under a concentration-versus-time curve (AUC) or the estimated five-year survival probability derived from a survival analysis.

While many programs, apps, and web pages are available to perform power and sample-size calculations, they aren’t always easy or intuitive to use. Because spreadsheets like Excel are readily available and intuitive, it’s convenient to have a single spreadsheet that can perform power and sample-size calculations for the situations that arise most frequently in biological and clinical research.

In biostatistics, when comparing paired measurements (such as changes between two time points for the same subject) using a paired Student t test, the effect size is expressed as the ratio of Δ (delta, the mean change) divided by σ (sigma, the standard deviation of the changes). Another, perhaps easier, way to express the effect size is by the relative number of expected subjects with positive versus negative changes.