36 PART 1 Getting Started with Biostatistics

statisticians can describe quantitatively how these random fluctuations behave

using mathematical equations called probability distribution functions. Probability

distribution functions describe how likely it is that random fluctuations will

exceed any given magnitude. A probability distribution can be represented in sev-

eral ways:»

» ^{As a mathematical equation that calculates the chance that a fluctuation}

will be of a certain magnitude. Using calculus, this function can be integrated,

which means turned into another related function that calculates the proba-

bility that a fluctuation will be at least as large as a certain magnitude.»

» ^{As a graph of the distribution, which looks and works much like a}

histogram.»

» ^{As a table of values indicating how likely it is that random fluctuations will}

exceed a certain magnitude.

In the following sections, we break down two types of distributions: those that

describe fluctuations in your data, and those that you encounter when performing

statistical tests.

Distributions that describe your data

Here are some common distributions that describe the random fluctuations found

in data analyzed by biostatisticians:»

» ^{Normal: The familiar, bell-shaped, normal distribution is probably the most}

common distribution you will encounter. As an example, systolic blood

pressure (SBP) is found to follow a normal distribution in human populations.»

» ^{Log-normal: The log-normal distribution is also called a skewed distribution.}

This distribution describes many laboratory results, such as enzymes and

antibody titers, where most of the population tests on the low end of the

scale. It is also the distribution seen for lengths of hospital stays, where most

stays are 0 or 1 days, and the rest are longer.»

» ^{Binomial: The binomial distribution describes proportions, and represents the}

likelihood that a value will take one of two independent values (as whether an

event occurs or does not occur). As an example, in a class held regularly

where students can only pass or fail, the proportion who fail will follow a

binomial distribution.»

» ^{Poisson: The Poisson distribution describes the number of occurrences of}

sporadic random events (rather than the binomial distribution, which is for

more common events). Examples of where the Poisson distribution is used in

biostatistics is where the events are not as common, such as deaths from

specific cancers each year.