What does the Wald-Wolfowitz runs test look for in the ranked data?

What does the Wald-Wolfowitz runs test look for in the ranked data?

• A. It looks for difference in means between two groups.
• B. It tests for variance equality.
• C. It tests correlation between ranks.
• D. It looks for runs of scores from the same group within the ranked order to determine whether groups differ.

Answer: (D)

The essential idea is to examine how two groups are arranged when all observations are ordered. You pool both samples, rank the combined data, and keep track of which group each rank came from. A run is a consecutive sequence of ranks from the same group. If the two samples come from the same distribution, the order of group labels should be random, producing a typical number of runs. If one group tends to have higher (or lower) values, you’ll see longer runs of that group and fewer runs overall. So this test uses the observed number of runs to decide whether the groups differ in their distributions. That’s why it’s not about differences in means, variances, or correlations between ranks. It’s about whether the sequence of group memberships in the ranked data is more or less orderly than would occur by chance, which signals a difference between the groups.

The essential idea is to examine how two groups are arranged when all observations are ordered. You pool both samples, rank the combined data, and keep track of which group each rank came from. A run is a consecutive sequence of ranks from the same group. If the two samples come from the same distribution, the order of group labels should be random, producing a typical number of runs. If one group tends to have higher (or lower) values, you’ll see longer runs of that group and fewer runs overall. So this test uses the observed number of runs to decide whether the groups differ in their distributions.

That’s why it’s not about differences in means, variances, or correlations between ranks. It’s about whether the sequence of group memberships in the ranked data is more or less orderly than would occur by chance, which signals a difference between the groups.