Common Errors in Statistics (and How to Avoid Them), 4th Edition

WHAT IS A HYPOTHESIS?

A well-formulated hypothesis will be both quantifiable and testable, that is, involve measurable quantities or refer to items that may be assigned to mutually exclusive categories. It will specify the population to which the hypothesis will apply.

A well-formulated statistical hypothesis takes one of two forms:

1. Some measurable characteristic of a defined population takes one of a specific set of values.

2. Some measurable characteristic takes different values in different defined populations, the difference(s) taking a specific pattern or a specific set of values.

Examples of well-formed statistical hypotheses include the following:

• For males over 40 suffering from chronic hypertension, a 100 mg daily dose of this new drug will lower diastolic blood pressure an average of 10 mm Hg.
• For males over 40 suffering from chronic hypertension, a daily dose of 100 mg of this new drug will lower diastolic blood pressure an average of 10 mm Hg more than an equivalent dose of metoprolol.
• Given less than 2 hours per day of sunlight, applying from 1 to 10 lbs of 23-2-4 fertilizer per 1000 square feet will have no effect on the growth of fescues and Bermuda grasses.

“All redheads are passionate” is not a well-formed statistical hypothesis, not merely because “passionate” is ill defined, but because the word “all” suggests there is no variability. The latter problem can be solved by quantifying the term “all” to, let’s say, 80%. If we specify “passionate” in quantitative ...