Study design

In considering what to do it was realised that the data that had already been collected in the experiment could be used to estimate the total sample size needed to detect statistically significant differences between the three diets, and that this might help with the decision.

The sample size n needed to detect significant differences between two means is determined from the formula:

Moving the terms around so that n is on the left hand side, we get

where is the difference between two means; s² is the estimated pooled variance among individuals within groups and t is the value of the t-statistic, say for P = 0.05.

An estimate for s² could be derived from the first two batches of the experiment. Also, from values obtained for the mean milk yields from the first two batches for the three diets, preliminary estimates could be obtained for means in the above formula.