40 PART 1 Getting Started with Biostatistics

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» ^{The average value of a measurement may be different from zero (or from}

some other specified value). For example, the average reduction in pain level

measurement in surgery patients from post-surgery compared to 30 days

later may have an effect that is different from zero (or so we would hope)!»

» ^{Two numerical variables may be associated (also called correlated). For}

example, the taller people are on average, the more they weigh. When two

variables like height and weight are associated in this way, the effect is called

correlation, and is typically quantified by the Pearson correlation coefficient

(described in Chapter 15).

Honing In on Hypothesis Testing

The theory of statistical hypothesis testing was developed in the early 20th

­century. Among other uses, it was designed to apply the scientific method to data

sampled from populations. In the following sections, we explain the steps of

hypothesis testing, the potential results, and possible errors that can be made

when interpreting a statistical test. We also define and describe the relationships

between power, sample size, and effect size in testing.

Getting the language down

Here are some of the most common terms used in hypothesis testing:»

» ^{Null hypothesis (abbreviated H}0^{): The assertion that any apparent effect}

you see in your data is not evidence of a true effect in the population, but is

merely the result of random fluctuations.»

» ^{Alternate hypothesis (abbreviated H}1 ^{or H} Alt^{): The assertion that there}

indeed is evidence in your data of a true effect in the population over and

above what would be attributable to random fluctuations.»

» ^{Significance test: A calculation designed to determine whether H}0 ^can

reasonably explain what you see in your data or not.»

» ^{Significance: The conclusion that random fluctuations alone can’t account for}

the size of the effect you observe in your data. In this case, H0 must be false,

so you accept HAlt.»

» ^{Statistic: A number that you obtain or calculate from your sample.»}

» ^{Test statistic: A number calculated from your sample that is part of perform-}

ing a statistical test. It can be for the purpose of testing H0. In general, the test