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 experimental 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 heart muscle of a dog was regarded as a block, and comparisons of the three treatments were made within a given muscle. The calcium uptake for the three levels of digitalis, A, B, and C was compared using the heart muscle of four dogs. The results follow:

Dogs	1	2	3	4
	A	C	B	A
	147	169	129	125
	B	B	A	C
	162	138	132	157
	C	A	C	B
	188	124	154	131

Complete an INITIAL analysis of this question

Answer 1

Answer:

Given that,

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 experimental 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 heart muscle of a dog was regarded as a block, and comparisons of the three treatments were made within a given muscle.

The calcium uptake for the three levels of digitalis, A, B, and C was compared using the heart muscle of four dogs. The results follow:

To find the various sum of square (SS). We arrange the given table as follow:

Treatment	Block				Treatment Total (Ti)	Ti2
	1	2	3	4
A	147	124	132	125	528	278784
B	162	138	129	131	560	313600
C	188	169	154	157	668	446224
Block Total (Bj)	=497	=431	=415	=413	=1756
Average Bj2	247009	185761	172225	170569

Correlation Factor (CF):

=256961.3

Raw  

Therefore,

Total SS(TSS)= Raw SS-CF

=261394-256961.3

=4432.667

SS Treatment (SST):

=2690.667

SS Block (SSB) :

=1560

Error SS (SSE)=TSS-SST-SSB

=182

Hypothesis : Treatment

H₀ :

H₁ : All 's are not equal.

Block:

H₀ :  

H₁ : All 's are not equal.

ANOVA table;

Source	DF	SS	MS	F	P
Treatment	2	2690.667	1345.33	44.35	0.000
Block	3	1560	520	17.14	0.002
Error	6	182	30.33
Total	11	4432.667

From the analysis, the p-values for the treatment and block are less than 0.05 level of significance. Hence, we reject both the null hypothesis for treatment and block.

So, we can conclude that at least one digital level has a statistically significant mean level of calcium in the heart muscle of the dogs at the 0.05 level of significance.

Further, the blocks are not homogeneous at the 0.05 level of significance.