In Step 3 of the sign test, what does S represent?

In Step 3 of the sign test, what does S represent?

• A. Take the more frequent sign and call this S.
• B. Sum all signs regardless of frequency.
• C. Take the less frequent sign and call this S.
• D. Use the number of positive signs as S.

Answer: (C)

In a sign test for paired data, you look at the direction of each difference (positive or negative) and ignore any zeros. The test then uses the count in the less frequent direction, called S, because under the null hypothesis both directions are equally likely. So S is the number of differences that fall in the direction with fewer signs (the smaller count of positives or negatives). The total number of nonzero differences, n, is used with S in the binomial test to determine significance. This focus on the smaller count makes the test symmetric for a two‑tailed assessment.

In a sign test for paired data, you look at the direction of each difference (positive or negative) and ignore any zeros. The test then uses the count in the less frequent direction, called S, because under the null hypothesis both directions are equally likely. So S is the number of differences that fall in the direction with fewer signs (the smaller count of positives or negatives). The total number of nonzero differences, n, is used with S in the binomial test to determine significance. This focus on the smaller count makes the test symmetric for a two‑tailed assessment.