One kind of dioxin, called (TCDD), was once thought to cause cancer and birth de
ID: 3265713 • Letter: O
Question
One kind of dioxin, called (TCDD), was once thought to cause cancer and birth defects, but subsequent research showed it to have only mild toxic effects except at a very high exposure levels. About 10 years ago, a study published in a leading journal in environmental science reported the levels of TCDD of 20 Massachusetts Vietnam veterans who may have been exposed to Agent Orange during the war. The TCDD levels in plasma and in fat tissue are listed below. The goal of the study was to learn how these two population mean levels compared. (a) For this cohort of individuals, why might it be of interest to learn about how the mean TCDD levels compare in plasma and fat tissue? (b) Acknowledging that this is a matched-pairs set up (first explain why), analyze this data to answer the research question in part (a). State all conclusions in plain English. (c) Explain what advantages this matched pairs design has over an experiment that would require two independent samples of veterans.Explanation / Answer
(a) We might be interested to know the relation between the mean level of TCDD in Plasma and that in fat tissue for the population of veterans.
(b) Here both the sample (TCDD level in Plasma and TCDD level in Fat Tissue) are drawn from the same set of individuals, so, it is a type of Bivariate Sample, where the samples are taken from an indentical set. So, the level of TCDD in plasma and fat tissue will be correlated., That's why it is a a match paired set up where we will conduct a paired t-test to conduct the test of hypothesis for equality of means.
We will conduct the test in R.
Write the following code in R to import the data and do the paired t-test.
Code:
plasma<-c(2.5,3.1,2.1,3.5,3.1,1.8,6,3,36,4.7,6.9,3.9,4.2,1.6,7.2,1.8,20,2,2.5,4.1)
fat<-c(4.9,5.9,4.4,6.9,9,4.2,10,5.5,41,4.4,7,2.9,4.6,1.4,7.7,1.1,11,2.5,2.3,1.5)
cor(plasma,fat)
t.test(plasma,fat,mu=0, paired = TRUE,conf.level = 0.95)
/* End of Code */
Output:
> plasma<-c(2.5,3.1,2.1,3.5,3.1,1.8,6,3,36,4.7,6.9,3.9,4.2,1.6,7.2,1.8,20,2,2.5,4.1)
> fat<-c(4.9,5.9,4.4,6.9,9,4.2,10,5.5,41,4.4,7,2.9,4.6,1.4,7.7,1.1,11,2.5,2.3,1.5)
> cor(plasma,fat)
[1] 0.9280636
> t.test(plasma,fat,mu=0, paired = TRUE,conf.level = 0.95)
Paired t-test
data: plasma and fat
t = -1.2809, df = 19, p-value = 0.2156
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-2.3969777 0.5769777
sample estimates:
mean of the differences
-0.91
>
/* End of Output */
We see that, the p-value of the test is 0.2156, which is greater than 0.05. So, we conclude that, there is no statistical evidence to support that mean TCDD level in Plasma and Fat Tissue differ.
c) In the matched paired design we don't need the assumption of equal variance for the two population. Which is an advantage over two independent samples.
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