Question

Efficiency of the Sign Test Refer to Table 13-2 on page 600 and identify the efficiency of the sign test. What does that value tell us about the sign test?

Short answer

The efficiency rating of the sign test is equal to 0.63.

This means that while keeping all other things constant, the non-parametric sign test will require a sample of 100 observations to achieve the same result as compared to the requirement of only 63 observations if the parametric t-test is applied.

Step-by-step solution

Given information

A sign test is the non-parametric counterpart of the t-test.

State the efficiency of the sign test

The sign test is the non-parametric counterpart of the parametric t-test.

The efficiency of the sign test is equal to 0.63, obtained from the mentioned Table 13-2.

This has the following implication.

While keeping all other things constant, the sign test will require 100 sample observations to achieve the same results as compared to the requirement of only 63 observations while applying the t-test.

Thus, if the sample data, as well as their populations, meet the required conditions, a t-test will be more efficient than the sign test.