A New View of Statistics

© 1997 Will G Hopkins

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Summarizing Data:
PRECISION OF MEASUREMENT continued

 HOW MANY DIGITS?
Stats programs routinely crank out 8-figure accuracy for computed statistics. Your data are hardly ever good enough to justify that sort of precision. In any case, too many digits make data hard to comprehend, and most people hate numbers! So when you present your statistics in print or on a slide, it's important to show as few digits as possible.

Most statistics need either two significant digits (the first two digits), or two decimal places when the number is less than 1.0:

Percentages:

73%, 7.3%, 0.73%

Correlations:

0.97, 0.23, 0.05

Relative risks or odds ratios:

12, 2.4, 0.64

Effect sizes:

2.6, 0.51, 0.07

SDs usually need two significant digits. The mean must match the precision of the SD:

23500 ± 1300 (not 23538 ± 1341 etc.)
  2350 ± 130
    235 ± 13
   2.35 ± 0.13
 0.235 ± 0.013

The SD in descriptive statistics for height, weight, and age can often be shown with just one significant digit. After all, it doesn't really matter whether your subjects were 67 ± 5 or 67.3 ± 5.4 kg in weight:

height: 178 ± 7 cm
weight: 67 ± 5 kg
age: 23 ± 4 y

Naturally, if weight was an outcome variable, you would need to show two significant figures.

To avoid clutter in a table or figure, indicate statistical significance with * or **, and include *p < 0.05 or **p < 0.01 somewhere in the table or figure. Otherwise exact p values are preferable, and don't go to more than two significant digits: p = 0.007, 0.04, 0.35. See later for more about p values and statistical significance.

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Last updated 12 Sept 98