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.

The end result of a statistical significance test is a p value, which represents the probability that random fluctuations alone could have generated results that differed from the null hypothesis (H0), in the direction of the alternate hypothesis (HAlt), by at least as much as what you observed in your data. If this probability is too small, then H0 can no longer explain your results, and you're justified in rejecting it and accepting HAlt, which says that some real effect is present.

The aims or goals of a study are short general statements (often just one statement) of the overall purpose of the trial. For example, the aim of a study may be "to assess the safety and efficacy of drug XYZ in patients with moderate hyperlipidemia." The objectives are much more specific than the aims. Objectives usually refer to the effect of the product on specific safety and efficacy variables, at specific points in time, in specific groups of subjects.

The theory of statistical hypothesis testing was developed in the early 20th century and has been the mainstay of practical statistics ever since. It was designed to apply the scientific method to situations involving data with random fluctuations (and almost all real-world data has random fluctuations). Following are a few terms commonly used in hypothesis testing.

Over the years, as computing has moved from mainframes to minicomputers to personal computers to hand-held devices (calculators, tablets, and smartphones), statistical software has undergone a similar migration. Today you can find statistical software for just about every intelligent (that is, computerized) device there is (with the possible exception of smart toasters).

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.