In order to determine the efficacy and lethal dosage of cardiac relaxants, anest

Question

In order to determine the efficacy and lethal dosage of cardiac relaxants, anesthetized guinea pigs are infused with a drug (the treatment) till death occurs. The total dosage required for death is the response; smaller lethal doses are considered more effective. There are four drugs, and ten guinea pigs are chosen at random for each drug. Lethal dosages follow.

1: 18.2 16.4 10.0 13.5 13.5 6.7 12.2 18.2 13.5 16.4

2: 5.5 12.2 11.0 6.7 16.4 8.2 7.4 12.2 6.7 11.0

3: 5.5 5.0 8.2 9.0 10.0 6.0 7.4 5.5 12.2 8.2

4: 6.0 7.4 12.2 11.0 5.0 7.4 7.4 5.5 6.7 5.5

Determine which drugs are equivalent, which are more effective, and which less effective.

Explanation / Answer

One-way ANOVA: Dose versus Drug

Source DF SS MS F P
Drug 3 265.48 88.49 9.87 0.000
Error 36 322.93 8.97
Total 39 588.41

S = 2.995 R-Sq = 45.12% R-Sq(adj) = 40.54%

Comment: The estimated p-value is 0.000. Hence, we can conclude that at least one drug has the significant effect than remaining drugs.

Grouping Information Using Tukey Method

Drug N Mean Grouping
1 10 13.860 A
2 10 9.730 B
3 10 7.700 B
4 10 7.410 B

Means that do not share a letter are significantly different.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Drug

Individual confidence level = 98.93%

Drug = 1 subtracted from:

Drug Lower Center Upper -----+---------+---------+---------+----
2 -7.739 -4.130 -0.521 (--------*--------)
3 -9.769 -6.160 -2.551 (--------*--------)
4 -10.059 -6.450 -2.841 (--------*--------)
-----+---------+---------+---------+----
-8.0 -4.0 0.0 4.0

Drug = 2 subtracted from:

Drug Lower Center Upper -----+---------+---------+---------+----
3 -5.639 -2.030 1.579 (--------*--------)
4 -5.929 -2.320 1.289 (--------*--------)
-----+---------+---------+---------+----
-8.0 -4.0 0.0 4.0

Drug = 3 subtracted from:

Drug Lower Center Upper -----+---------+---------+---------+----
4 -3.899 -0.290 3.319 (--------*--------)
-----+---------+---------+---------+----
-8.0 -4.0 0.0 4.0

Grouping Information Using Tukey Method

Drug N Mean Grouping
1 10 13.860 A
2 10 9.730 B
3 10 7.700 B
4 10 7.410 B

Means that do not share a letter are significantly different.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Drug

Individual confidence level = 98.93%

Drug = 1 subtracted from:

Drug Lower Center Upper  
2 -7.739 -4.130 -0.521
3 -9.769 -6.160 -2.551  
4 -10.059 -6.450 -2.841
Comment: THe confidence interval does not include zero. Hence, drug 1 has significant difference effect from drugs 2,3 and 4.

Drug = 2 subtracted from:

Drug Lower Center Upper
3 -5.639 -2.030 1.579   
4 -5.929 -2.320 1.289
Comment: THe confidence interval includes zero. Hence, drug 2 does not have significant difference effect from drugs 3 and 4.       

Drug = 3 subtracted from:

Drug Lower Center Upper  
4 -3.899 -0.290 3.319   
Comment: THe confidence interval includes zero. Hence, drug 3 does not have significant difference effect from drugs 4.   

From the above analysis drugs 2, 3 and 4 are equivalent. Drug 1 has more effective and drugs 4 has less effective.

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