Question

An experiment to investigate the effects of various dietary starch levels on milk production was conducted on four cows. The four diets, T1, T2, T3, and T4, (in order of increasing starch equivalent), were fed for three weeks to each cow and the total yield of milk in the third week of each period was recorded (i.e. third week to minimize carry-over effects due to the use of treatments administered in a previous period). That is, the trial lasted 12 weeks since each cow received each treatment, and each treatment required three weeks. The investigator felt strongly that time period effects might be important (i.e earlier periods in the experiment might influence milk yields differently compared to later periods). Hence, the investigator wanted to block on both cow and period. However, each cow cannot possibly receive more than one treatment during the same time period; that is, all possible cow-period blocking combinations could not logically be considered. The randomization scheme and data are shown in the table below

Cow Cow 2 Cow 3 Cow 4 Period T4 (192) T1 (195) T3 (292) T2 (249) Period 2 T1 (190) T4 (203) T2 (218) T3 (210) Period 3 T3 (214) T2 (139) T1 (245) T4 (163) Period 3 T2 (221) T3 (152) T4 (204) T1 (134)

1. Write down the model for this analysis.

2. Which type of design is this?

3. Use ANOVA to analyze the effects of four diets.

4. Construct 95% Tukey’s pairwise comparisons of the diets and report your findings.

Answer 1

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