Wald-Wolfowitz Runs Test II

A scientist collected data on the body lengths of 30 baboons approaching a water source.

So, the Wald-Wolfowitz test can determine if the sequence in which baboons approached the water source is random or relates to their body length.

Here, the null hypothesis states that the data are in a random sequence, whereas the alternative hypothesis states the data are not in a random sequence.

For these numerical data, the runs—G—are computed by assigning binary signs to the values greater and lesser than the median 74.5.

Here, the value of G is 17.

Notice that the number of values smaller than the median—n₁ — and greater than the median—n₂ — are less than 20.

So, the critical values at α = 0.05 can be obtained from the standard table.

The Wald-Wolfowitz test is two-tailed. So, to reject the randomness, the test statistic needs to be beyond the range of critical values.

Here, G falls within this range, providing evidence in favor of the null hypothesis.