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

Question

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

What is being asked here? is this a multiple comparison 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.

Explanation / Answer

The R code to do this analysis is:

data <- c(18.2, 16.4, 10, 13.5, 13.5, 6.7, 12.2, 18.2, 13.5, 16.4, 5.5, 12.2, 11, 6.7, 16.4, 8.2, 7.4, 12.2, 6.7, 11, 5.5, 5, 8.2, 9, 10, 6, 7.4, 5.5, 12.2, 8.2, 6, 7.4, 12.2, 11, 5, 7.4, 7.4, 5.5, 6.7, 5.5)
drug <- as.factor(c(rep(1,10),rep(2,10),rep(3,10),rep(4,10)))
table <- data.frame(data,drug)
aov1 <- aov(data~drug, data=table)
summary(aov1)
TukeyHSD(aov1, "drug", ordered = TRUE)

The output is:

data <- c(18.2, 16.4, 10, 13.5, 13.5, 6.7, 12.2, 18.2, 13.5, 16.4, 5.5, 12.2, 11, 6.7, 16.4, 8.2, 7.4, 12.2, 6.7, 11, 5.5, 5, 8.2, 9, 10, 6, 7.4, 5.5, 12.2, 8.2, 6, 7.4, 12.2, 11, 5, 7.4, 7.4, 5.5, 6.7, 5.5)
> drug <- as.factor(c(rep(1,10),rep(2,10),rep(3,10),rep(4,10)))
> table <- data.frame(data,drug)
> aov1 <- aov(data~drug, data=table)
> summary(aov1)
Df Sum Sq Mean Sq F value Pr(>F)
drug 3 265.5 88.49 9.865 6.91e-05 ***
Residuals 36 322.9 8.97   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> TukeyHSD(aov1, "drug", ordered = TRUE)
Tukey multiple comparisons of means
95% family-wise confidence level
factor levels have been ordered

Fit: aov(formula = data ~ drug, data = table)

$drug
diff lwr upr p adj
3-4 0.29 -3.3173943 3.897394 0.9963493
2-4 2.32 -1.2873943 5.927394 0.3224748
1-4 6.45 2.8426057 10.057394 0.0001496
2-3 2.03 -1.5773943 5.637394 0.4390060
1-3 6.16 2.5526057 9.767394 0.0002860
1-2 4.13 0.5226057 7.737394 0.0195604

The ANOVA result show that there is a difference in drugs, which means that the drugs are not equivalent.

The Tukey test shows that the drug 1 is different from all the others at 0.05 level of significance.

So the most effective is drug 1 and the least effective is drug 4.

Yes it is a multiple comparion question

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