How is a significant S value interpreted with respect to the critical value?

How is a significant S value interpreted with respect to the critical value?

• A. If S is greater than the critical value, the result is significant.
• B. If S equals the critical value, the result is not significant.
• C. If S is less than or equal to the critical value, the result is significant.
• D. If S is zero, the result is automatically significant.

Answer: (C)

In this kind of test, the critical value defines the boundary of the rejection region for the S statistic. Small values of S indicate a result more extreme than would be expected under the null hypothesis, so you reject H0 when the observed S is at or below the critical value. If S is larger than that cutoff, the data aren’t extreme enough to conclude significance. The value being zero isn’t automatically significant; it would only be significant if zero lies within the rejection region for the given sample size and alpha level.

In this kind of test, the critical value defines the boundary of the rejection region for the S statistic. Small values of S indicate a result more extreme than would be expected under the null hypothesis, so you reject H0 when the observed S is at or below the critical value. If S is larger than that cutoff, the data aren’t extreme enough to conclude significance. The value being zero isn’t automatically significant; it would only be significant if zero lies within the rejection region for the given sample size and alpha level.