Study questions

1. Checking of raw data was not done. Plot line graphs across time for each goat and determine whether there are any odd values. If there are, what would you do with them? Do the lines give any indications of any trends in milk yield that may help in understanding the pattern?

2. In this study an estimate of variance s² was available. Discuss in general terms how you might determine sample size if no estimate of s² is available.

3. Suppose that Option 4 was chosen but rather than assign 4 goats to each diet, 6 were assigned to the (A + B) group and 3 to each of B and C. Assuming s²=1653, calculate the minimum difference in means between A+B (12 goats) and C and B pooled (18 goats) that will need to be observed for the difference in means to be significant (P<0.05). Is this less than the difference that needs to be observed given 10 and 20 goats in the respective groups?

4. Suppose that measurements on milk yield had not been taken before the experiment started. Using the estimate of residual variance without adjustment for covariance, namely 7476 g², estimate the sample size that would need to be achieved in Option 4 given equal numbers in the three groups.

5. The smaller the variance s² the fewer animals are needed to detect significant differences between means. Discuss other ways, in addition to the existence of a pre-treatment covariate period, in which the variability among goats might be minimised.