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Chapter 10: Problem 30

Treatment In a 2018 study by Zhu et al. reported in The Lancet, researchers conducted an experiment to determine the efficacy and safety of the drug dorzagliatin in the treatment of patients with Type 2 diabetes. In this double-blind study, patients were randomly assigned to one of two treatment groups (drug or placebo) and the glucose levels of the two groups were compared after 12 weeks. If we test whether treatment group is associated with glucose level, are we doing a test of homogeneity or a test of independence?

Short Answer

Expert verified
The described scenario in the exercise is best analysed by using a test of independence.

Step by step solution

01

Understanding the Scenario

In the given scenario, an experiment is conducted with patients divided into two groups: one group receiving the drug dorzagliatin and the other a placebo. The glucose levels of the two groups are compared after 12 weeks. The conjecture is whether the treatment group affects the glucose level i.e., whether there is an association between the treatment group and glucose level.
02

Understanding a Test of Homogeneity

A test of homogeneity is used when the aim is to determine if different groups or populations have the same proportions for a categorical outcome. In this context, it could be applied if we were comparing the proportion of patients with different glucose levels in the drug and placebo groups separately.
03

Understanding a Test of Independence

A test of independence is applied to determine if there is a significant relationship between two categorical variables in one population. In our scenario, we are looking to see if there is a relationship between the two variables, treatment group (drug or placebo) and glucose level.
04

Choosing the Appropriate Test

Comparing the definitions, we see that we are trying to determine if there is a relationship between treatment group and glucose level. This scenario aligns more with a test of independence, because: 1) We are dealing with one population (patients with Type 2 diabetes split into drug or placebo group), 2) Our two variables - treatment group and glucose level - are categorical variables and the relationship between them is being investigated.

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Most popular questions from this chapter

In Montreal, Canada, an experiment was done with parents of children who were thought to have a high risk of committing crimes when they became teenagers (Tremblay et al., 1996 ). Some of the families were randomly assigned to receive parental training, and the others were not. Out of 43 children whose parents were randomly assigned to the parental training group, 6 had been arrested by the age of \(15 .\) Out of 123 children whose parents were not in the parental training group, 37 had been arrested by age 15 . a. Find and compare the percentages of children arrested by age \(15 .\) Is this what researchers might have hoped? b. Create a two-way table from the data, and test whether the treatment program is associated with arrests. Use a significance level of \(0.05\). c. Do a two-proportion \(z\) -test, testing whether the parental training lowers the rate of bad results. Use a significance level of \(0.05\). d. Explain the difference in the results of the chi-square test and the twoproportion \(z\) -test. e. Can you conclude that the treatment causes the better result? Why or why not?

A large number of surgery patients get infections after surgery, which can sometimes be quite serious. Researchers randomly assigned some surgery patients to receive simple antibiotic ointment after surgery, others to receive a placebo, and others to receive just cleansing with soap. If we wanted to test the association between treatment and whether patients get in infection after surgery, would this be a test of homogeneity or of independence? Explain. (Source: Hospitals Could Stop Infections by Tackling Bacteria Patients Bring In, Study Finds, New York Times, January \(6,2010 .\) )

The Perry Preschool Project data presented in exercise \(10.39\) can be divided to see whether there are different effects for males and females. The table shows a summary of the data for males (Schweinhart et al. 2005 ). $$\begin{array}{lcc} & \text { Preschool } & \text { No Preschool } \\\\\text { HS Grad } & 16 & 21 \\\\\text { HS Grad No } & 16 & 18\end{array}$$ a. Find the graduation rate for males who went to preschool, and compare it with the graduation rate for males who did not go to preschool. b. Test the hypothesis that preschool and graduation are associated, using a significance level of \(0.05\). c. Exercise \(10.40\) showed an association between preschool and graduation for just the females in this study. Write a sentence or two giving your advice to parents with preschool-eligible children about whether attending preschool is good for their children's future academic success, based on this data set.

Rats had a choice of freeing another rat or eating chocolate by themselves. Most of the rats freed the other rat and then shared the chocolate with it. The table shows the data concerning the gender of the rat in control. $$\begin{array}{lcc} & \text { Male } & \text { Female } \\\\\hline \text { Freed Rat } & 17 & 6 \\\\\text { Did not } & 7 & 0 \\ \hline\end{array}$$ a. Can a chi-square test for homogeneity or independence be performed with this data set? Why or why not? b. Determine whether the sex of a rat influences whether or not it frees another rat using a significance level of \(0.05\).

The Perry Preschool Project discussed in exercises \(10.39\) to \(10.41\) found that 8 of the 58 students who attended preschool had at least one felony arrest by age 40 and that 31 of the 65 students who did not attend preschool had at least one felony arrest (Schweinhart et al. 2005). a. Compare the percentages descriptively. What does this comparison suggest? b. Create a two-way table from the data and do a chi-square test on it, using a significance level of \(0.05\). Test the hypothesis that preschool attendance is associated with being arrested. c. Do a two-proportion \(z\) -test. Your alternative hypothesis should be that preschool attendance lowers the chances of arrest. d. What advantage does the two-proportion \(z\) -test have over the chi-square test?
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