In a sign test, which option correctly describes S?

In a sign test, which option correctly describes S?

• A. The total number of observations.
• B. The less frequent sign among plus and minus.
• C. The sum of all signs.
• D. The threshold for significance.

Answer: (B)

In a sign test you look at the direction of each paired difference and convert them to plus or minus signs, ignoring any ties. You then count how many plus signs there are and how many minus signs there are. S is defined as the smaller of these two counts. This matters because, under the null hypothesis, plus and minus signs should be about equally likely, so the strength of the result is reflected in how imbalanced the counts are—and taking the smaller count provides a symmetric measure for testing with the binomial distribution. The total number of observations is the number of non-tied differences, not S, and the significance threshold comes from comparing S to binomial-critical values (or computing a p-value), not from S alone.

In a sign test you look at the direction of each paired difference and convert them to plus or minus signs, ignoring any ties. You then count how many plus signs there are and how many minus signs there are. S is defined as the smaller of these two counts. This matters because, under the null hypothesis, plus and minus signs should be about equally likely, so the strength of the result is reflected in how imbalanced the counts are—and taking the smaller count provides a symmetric measure for testing with the binomial distribution. The total number of observations is the number of non-tied differences, not S, and the significance threshold comes from comparing S to binomial-critical values (or computing a p-value), not from S alone.