CHAPTER 9 Summarizing and Graphing Your Data 125

The smooth curve in Figure 9-5a shows how SBP values are distributed in an infi-

nitely large population. The height of the curve at any SBP value is proportional to

the fraction of the population in the immediate vicinity of that SBP. This curve has

the typical bell shape of a normal distribution.

The histogram in Figure 9-5b indicates how the SBP measurements of 60 study

participants randomly sampled from the population might be distributed. Each

bar represents an interval or class of SBP values with a width of ten mmHg. The

height of each bar is proportional to the number of participants in the sample

whose SBP fell within that class.

Log-normal distributions

Because a sample is only an imperfect representation the population, determining

the precise shape of a distribution can be difficult unless your sample size is very

large. Nevertheless, a histogram usually helps you spot skewed data, as shown in

Figure  9-6a. This kind of shape is typical of a log-normal distribution

(Chapter  25), which is a distribution you often see when analyzing biological

measurements, such as lab values. It’s called log-normal because if you take a

logarithm (of any type) of each data value, the resulting logs will have a normal

distribution, as shown in Figure 9-6b.

Because distributions are so important to biostatistics, it’s a good practice to pre-

pare a histogram for every numerical variable you plan to analyze. That way, you

can see whether it’s noticeably skewed and, if so, whether a logarithmic transfor-

mation makes the distribution normal enough so you can use statistics intended

for normal distributions on your data.

FIGURE 9-6:

Log-normal

data are

skewed (a), but

the logarithms

are normally

distributed (b).

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