Comparison of butterfat content in milk from different breeds of cow (You will be marked on: 1) Getting the proper R output and plots, 2) Validity of your statistical conclusions and interpretations) Hand et al. (1994) report butterfat percentages for milk from 5 different breeds of cow (Original source: Sokal and Rohlf (1981)). Here we will investigate possible differences in the butterfat content between the breeds by running an ANOVA and then carrying out post-hoc pairwise comparisons. The data set we will use (contained in 2050_F21_Hand_Butterfat_Adapted) is a modified version of the original data set. It contains average butterfat percentages for samples of 8 two-year old cows from each of the breeds. You *must* use the data from the given file, and not from any other source. a) Plot side-by-side boxplots of the data (in one plot). Label the plot appropriately. b) Carry out a one-way (one factor) ANOVA in R. Give an appropriate conclusion to the ANOVA F test. c) In R, carry out pairwise tests using the Tukey procedure with a family-wise error rate of = 0.05. Give: The R output. A table that contains 2 columns (putting the sample means in increasing order): 1) Breed, 2) Yi SE( Yi) (include the symbol - do not actually carry out an addition and subtraction. Mean SE is often seen in journal articles.) Use the pooled estimate of the variance in your standard error calculation. Also include the "same letter" method of illustrating the results of pairwise comparison procedures, letting "a" represent the group containing the largest mean(s). For example, see Table 3 in da Silva-Castiglioni et al. (2010) (we looked at this in class), but put the breed means in increasing order in the table!

Data:

Butterfat	Breed
4.44	Ayrshire
4.37	Ayrshire
4.25	Ayrshire
3.71	Ayrshire
4.08	Ayrshire
3.9	Ayrshire
4.11	Ayrshire
4.37	Ayrshire
4.29	Canadian

5.24	Canadian
4.43	Canadian
4	Canadian
4.29	Canadian
4.85	Canadian
4.66	Canadian
4.4	Canadian
5.3	Guernsey
4.5	Guernsey
4.59	Guernsey

4.83	Guernsey
4.55	Guernsey
4.97	Guernsey
5.38	Guernsey
5.39	Guernsey
3.79	Holstein-Fresian
3.66	Holstein-Fresian
3.38	Holstein-Fresian
3.71	Holstein-Fresian
3.94	Holstein-Fresian

3.59	Holstein-Fresian
3.55	Holstein-Fresian
3.55	Holstein-Fresian
5.75	Jersey
5.14	Jersey
4.76	Jersey
5.18	Jersey
4.22	Jersey
5.98	Jersey
4.85	Jersey

6.55

Jersey