Exercise New
- The table below gives the coagulation times for samples of blood drawn from 16 animals receiving four diets A, B, C, and D. The diets were randomly allocated to the animals and their actual numbers are mentioned in the superscripts in parentheses. The blood samples were taken and tested in random order.
|
Diet (treatment) |
|
A |
B |
C |
D |
|
62(13) |
63(12) |
68(16) |
56(8) |
|
60(2) |
67(9) |
66(7) |
62(3) |
|
63(11) |
71(15) |
71(1) |
60(6) |
|
59(10) |
64(14) |
67(4) |
61(5) |
- Decompose the data and of the sums of squares. Is there evidence to indicate real differences among the mean values associated with the different treatments (diets)?
- Now assume that the real data are the coagulation times for samples of blood drawn from 24 animals (not 16) receiving four diets A, B, C, and D. The values are given in the table below, again with the actual numbers of the animals mentioned in the superscripts in parentheses. As you see from the table, the design was not balanced, i.e. the number of observations for the various treatments are not equal.
|
Diet (treatment) |
|
A |
B |
C |
D |
|
62(20) |
63(12) |
68(16) |
56(23) |
|
60(2) |
67(9) |
66(7) |
62(3) |
|
63(11) |
71(15) |
71(1) |
60(6) |
|
59(10) |
64(14) |
67(17) |
61(18) |
|
|
65(4) |
68(13) |
63(22) |
|
|
66(8) |
68(13) |
64(19) |
|
|
|
|
63(5) |
|
|
|
|
59(24) |
a. Perform again the analyses mentioned in the question 1 above.