A study was conducted to compare the effect of three levels of digitalis on the

Question

A study was conducted to compare the effect of three levels of digitalis on the level of calcium in the heart muscle of dogs. A description of the actual experiment procedure is omitted, but it is sufficient to note that the general level of calcium uptake varies from one animal to another so that comparison of digitalis levels (treatments) had to be blocked on heart muscles. That is, the tissue for a heart muscle was regarded as a block and comparisons of the three treatments were made within a given muscle. The calcium uptakes for the three levels of digitalis, A, B, and C, were compared based on the heart muscle of four dogs. The results are shown below:

Dogs
1 2 3 4

A C B A
1342 1698 1296 1150

B B A C
1608 1387 1029 1579

C A C B
1881 1140 1549 1319

Approximately how many replications are required for each level of digitalis (how many blocks) so that the error of estimating the difference in mean response for a pair of digitalis levels is less than 20, with a probability of .95? Assume that additional observations would be made within a randomized block design.

Explanation / Answer

I. State Hypotheses Treatments: H0: µ1=µ2=µ3 Alternative: At least two of the means differ. If rejected, level of digitalis was affecting calcium levels. Blocking: H0: µ1=µ2=µ3=µ4 Alternative: At least two of the means differ If rejected, then blocking was important in this experiment. Balanced Data from Randomized Complete Block 2001 The GLM Procedure Class Level Information Class treat block Number of observations Levels 3 4 Balanced Data from Randomized Complete Block 2001 The GLM Procedure Dependent Variable: calcium Source Model Error Corrected Total Sum of Squares R-Square 0.991346 Source treat block Source treat block There are two test statistics, one for treatments and one for blocking. Thus there are two p- values. If we reject the null for treatments, we then do a multiple comparisons procedure on the variable of interest – in this case treat. DF 5 697592.1667 6089.5000 6 11 703681.6667 Coeff Var 2.251697 Type I SS DF 524177.1667 173415.0000 2 3 Type III SS DF 2 3 524177.1667 173415.0000 Root MSE 31.85776

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