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

INTERVAL ESTIMATES

Brother Adel—who, I will hazard a guess, is a statistician—sent me a message criticizing my emails for being of varying lengths and not symmetrical like the hems of dresses in vogue this year. Adel says that in order for the lengths of my emails to be even, they must show evidence of natural distribution. According to him, natural distribution means that 95 percent of the data contained therein will center around the mean (taking into consideration of course the standard deviation), while the percentage of data outside the area of normal distribution on both sides of the mean does not exceed 2.5 percent in either direction, such that the sum total of standard deviation is 5 percent.

—Rajaa Alsanea in The Girls of Ryadh

Point estimates are seldom satisfactory in and of themselves. First, if the observations are continuous, the probability is zero that a point estimate will be correct and equal the estimated parameter. Second, we still require some estimate of the precision of the point estimate.

In this section, we consider one form of interval estimate derived from bootstrap measures of precision. A second form, derived from tests of hypotheses, will be considered in the next chapter.

A common error is to create a confidence interval of the form (estimate − k * standard error, estimate + k * standard error). This form is applicable only when an interval estimate is desired for the mean of a normally distributed random variable. Even then, k should be determined ...