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.

This is one time you don't need any formulas because you shouldn't attempt to calculate standard errors or confidence intervals (CIs) for regression coefficients yourself. Any good regression program can provide the SE for every parameter (coefficient) it fits to your data. The regression program may also provide the confidence limits for any confidence level you specify, but if it doesn't, you can easily calculate the confidence limits using the formulas for large samples.

The so-called “one-way analysis of variance” (ANOVA) is used when comparing three or more groups of numbers. When comparing only two groups (A and B), you test the difference (A – B) between the two groups with a Student t test. So when comparing three groups (A, B, and C) it’s natural to think of testing each of the three possible two-group comparisons (A – B, A – C, and B – C) with a t test.

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.