Math 445—Important Things to Think About When Writing About Statistics

(For this class and for the rest of your life.)

1. Distributions are described and compared via 1) graphs, 2) numerical summaries, and 3) worded (full-sentence) interpretations. Throughout the course we will talk about the distribution of a variable or an estimator. In any graphical display of a distribution, look for the overall pattern and for any striking deviations from that pattern. The overall pattern of a distribution can be described by its shape, center, and spread (i.e., variability). Recall for skewed distributions, the 5-number summary (minimum, first quartile, median, third quartile, maximum) is a more informative numerical summary than the mean and standard deviation. For symmetric (particularly mound-shaped) distributions, the mean and standard deviation provide enough numerical information. (Note: It’s fine to report the 5-number summary, mean, and standard deviation—this covers the bases for any distribution. Just recognize where to focus your attention when writing about the analysis.)

2. Always put your analysis in context. That is, include information on the individuals being measured, the variable being measured, and the units of measurement (no floating numbers in space!). After you have written your analysis, ask yourself whether a stranger could read your words and completely understand the topic and the context.

Here is an example progression from poor statistical writing to strong statistical writing:

The median is 75.

The median is 75 beats per minute.

The median resting heart rate is 75 beats per minute.

The median resting heart rate of patients is 75 beats per minute.

The median resting heart rate of recent patients at the Makemewell Clinic is 75 beats per minute.

3. In a similar vein, be specific (rather than general) in your descriptions, linking them to the setting of the problem.

Here is an example progression from general (and non-informative) statistical writing to specific statistical writing:

The data are skewed.

The data are skewed right.

The distribution of resting heart rates is skewed right.

The distribution of resting heart rates of recent patients at the Makemewell Clinic is skewed right.