How are ties treated in the sign test?

How are ties treated in the sign test?

• A. They are counted as positive signs.
• B. They are counted as negative signs.
• C. They are ignored.
• D. They are included in the calculation as zero.

Answer: (C)

In a sign test you’re looking at the direction of differences between paired observations, not how big those differences are. For each pair, you note whether the second value is higher or lower than the first, giving a plus or minus sign. A tie, where the two values are equal, doesn’t tell you anything about direction, so it isn’t counted at all. Keeping only the nonzero differences preserves the test’s basis on counting signs (positive vs negative) under the null hypothesis, and including ties would complicate or bias the analysis. So ties are ignored.

In a sign test you’re looking at the direction of differences between paired observations, not how big those differences are. For each pair, you note whether the second value is higher or lower than the first, giving a plus or minus sign. A tie, where the two values are equal, doesn’t tell you anything about direction, so it isn’t counted at all. Keeping only the nonzero differences preserves the test’s basis on counting signs (positive vs negative) under the null hypothesis, and including ties would complicate or bias the analysis. So ties are ignored.