 
Runs tests
Onesample runs test & the WaldWolfowitz test
Worked example 3
Time (hours) from treatment to lambing 
Control (C) 
Treated (T) 
45 87 123 120 70 
51 71 42 37 51 78 
51 49 56 47 58 
= 89.0  = 53.7 
This example uses the same data on the effect of drug treatment on the length of time from treatment to lambing that we used in Unit 8 with the ttest. There we first used an equalvariance ttest on the log transformed data, having first checked for equality of variances with the Fratio test. We obtained a Pvalue of 0.00986, which suggested that treatment was providing a significant reduction in lambing time. The unequalvariance ttest on the raw data gave a nonsignificant Pvalue of 0.0823, reflecting the erratic behaviour of the unequal variance ttest when sample sizes are very different.

Since we have two independent samples with skewed distributions we decide (admittedly rather unwisely) to use the WaldWolfowitz test. The ranked combined sample is shown below:
Ranked combined sample 
37 T 
42 T 
45 C 
47 T 
49 T 
51 T 
51 T 
51 T 
56 T 
58 T 
70 C 
71 T 
78 T 
87 C 
120 C 
123 C 
The number of runs (r) = 6, the number of control animals (m) = 5 and the number of treated animals (n) = 11. Since both n and m are < 20 we cannot use the normal approximation. Using Siegel's tables the observed value (6) is neither equal to nor smaller than the value in table F (4). Hence the result is not significant (P > 0.05).
One should note that even if the test result had been significant, interpretation would have been difficult. The interest in the trial was clearly to assess the effect of the drug on the 'average' lambing time, whether assessed by the median or the mean. The WaldWolfowitz test could only have indicated whether there was any difference between the distributions.


