#### Worked example 3

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 *t*-test. There we first used an equal-variance *t*-test on the log transformed data, having first checked for equality of variances with the *F*-ratio test. We obtained a * P*-value of 0.00986, which suggested that treatment was providing a significant reduction in lambing time. The unequal-variance *t*-test on the raw data gave a non-significant P-value of 0.0823, reflecting the erratic behaviour of the unequal variance *t*-test when sample sizes are very different.

**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 |
| |

Since we have two independent samples with skewed distributions we decide (admittedly rather unwisely) to use the Wald-Wolfowitz 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 Wald-Wolfowitz test could only have indicated whether there was any difference between the distributions.