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In December 2001 , the Department of Veterans Affairs announced that it would begin paying benefits to soldiers suffering from Lou Gehrig's disease who had served in the Gulf War (The New york Times, December 11,2001 ). This decision was based on an analysis in which the Lou Gehrig's disease incidence rate (the proportion developing the disease) for the approximately 700,000 soldiers sent to the Gulf between August 1990 and July 1991 was compared to the incidence rate for the approximately 1.8 million other soldiers who were not in the Gulf during this time period. Based on these data, explain why it is not appropriate to perform a formal inference procedure (such as the two-sample \(z\) test) and yet it is still reasonable to conclude that the incidence rate is higher for Gulf War veterans than for those who did not serve in the Gulf War.

Short Answer

Expert verified
Formal inference procedures like the two-sample \(z\) test rely on specific assumptions that are not met in this scenario, such as random and independent sampling and roughly equal variances. However, given the actual measurements of incidence rates in both groups, we can compare them directly and note a clear difference, making it reasonable to conclude that Gulf War veterans have a higher incidence rate of Lou Gehrig's disease.

Step by step solution

01

Understanding the exercise

The problem provides information about two groups: veterans that served in the Gulf War, and those that did not. The incidence rate of Lou Gehrig's disease in these groups is being compared. However, we can't apply a standard test of significance such as a two-sample \(z\) test. In this situation, it's important to identify why formal statistical procedures aren't applicable.
02

Recognizing limitations of statistical tests

Formal statistical tests like a two-sample \(z\) test, are designed to compare two samples drawn from the same population to assess if a significant difference exists between them. These tests rest on assumptions about the data, such as the samples being independently and randomly selected, and having roughly equal variances. In this scenario, these conditions are not met. Comparing soldiers deployed to the Gulf and those who were not doesn't constitute independent or random sampling. Moreover, the large discrepancy in the sizes of the two groups (700,000 versus 1.8 million) suggests that variance may not be approximately equal.
03

Forming a reasonable conclusion

Despite not being able to carry out a formal inference procedure, it's still reasonable to conclude that the incidence rate of Lou Gehrig's disease is higher among Gulf War veterans. This conclusion can be reached by observing the raw data and recognizing that the incidence rate is indeed higher in the Gulf War group. Since the incident rates are actual measurements and not estimates, we can directly compare them without a formal test. Therefore, even without the ability to prove causation or to quantify the measure of the difference, it's evident that a difference exists in the incidence rates of the two groups.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Incidence Rate Comparison
In the realm of research, the comparison of incidence rates focuses on understanding how frequently a specific event, such as the development of a disease, occurs in different groups. For this exercise, we are comparing the incidence rate of Lou Gehrig's disease among Gulf War veterans with those who did not serve in the Gulf.

The incidence rate is a crucial measure in epidemiology, representing the number of new cases of a disease in a population over a certain period. It helps researchers assess and compare disease risk across different populations. To compare these rates accurately, researchers look at the proportion of new cases in each group.
  • Gulf War veterans: Approximately 700,000 individuals were examined for disease incidence.
  • Non-Gulf War veterans: The incidence rate is established from a much larger group of about 1.8 million soldiers.
Analyzing the data involves observing the raw incidence rates. Even without complex formal tests, if one group shows a clearly higher incidence, it implies a greater risk or vulnerability within that group.
Limitations of Statistical Tests
Statistical tests, like the two-sample \(z\) test, help determine if there is a statistically significant difference between two group means. However, these tests come with assumptions. In the context of the Gulf War veterans study:
  • Random and Independent Sample Selection: These tests require each group to be random samples from the same population. The samples must be independent. Here, different environmental and historical contexts make these samples more complex.
  • Equal Variance: The assumption that both groups have similar variances does not hold, especially considering the huge sample size difference (700,000 vs. 1.8 million). Large imbalances can influence the variance.
Due to these constraints, using standard statistical inference techniques like the \(z\) test might not be appropriate. Instead, simply comparing the observed incidence rates directly can still provide valuable insights into differences between the groups.
Military Health Studies
Studies on military health are crucial as they help address specific health concerns related to unique exposures veterans may experience. Military personnel can be subject to different stressors, environments, and potential chemical exposures, influencing long-term health outcomes.

The Gulf War veterans' study highlights why such research is so essential:
  • Environmental Exposure: Veterans may have encountered conditions or chemicals not present in non-deployed groups, which can affect incidence rates of diseases like Lou Gehrig's.
  • Policy and Decision Making: Findings from these studies impact veteran benefits and healthcare policies. For instance, recognizing a higher disease incidence among Gulf War veterans led to new benefit entitlements.
Through ongoing research and better understanding of veteran health, military health studies aim to improve healthcare measures and support services for former military personnel.

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Most popular questions from this chapter

The director of the Kaiser Family Foundation's Program for the Study of Entertainment Media and Health said, "It's not just teenagers who are wired up and tuned in, its babies in diapers as well." A study by Kaiser Foundation provided one of the first looks at media use among the very youngest children \(-\) those from 6 months to 6 years of age (Kaiser Family Foundation, \(2003,\) www .kff.org). Because previous research indicated that children who have a TV in their bedroom spend less time reading than other children, the authors of the Foundation study were interested in learning about the proportion of kids who have a TV in their bedroom. They collected data from two independent random samples of parents. One sample consisted of parents of children age 6 months to 3 years old. The second sample consisted of parents of children age 3 to 6 years old. They found that the proportion of children who had a TV in their bedroom was . 30 for the sample of children age 6 months to 3 years and .43 for the sample of children age 3 to 6 years old. Suppose that the two sample sizes were each 100 . a. Construct and interpret a \(95 \%\) confidence interval for the proportion of children age 6 months to 3 years who have a TV in their bedroom. Hint: This is a one-sample confidence interval. b. Construct and interpret a \(95 \%\) confidence interval for the proportion of children age 3 to 6 years who have a TV in their bedroom. c. Do the confidence intervals from Parts (a) and (b) overlap? What does this suggest about the two population proportions? d. Construct and interpret a \(95 \%\) confidence interval for the difference in the proportion that have TVs in the bedroom for children age 6 months to 3 years and for children age 3 to 6 years. e. Is the interval in Part (d) consistent with your answer in Part (c)? Explain.

Suppose that you were interested in investigating the effect of a drug that is to be used in the treatment of patients who have glaucoma in both eyes. A comparison between the mean reduction in eye pressure for this drug and for a standard treatment is desired. Both treatments are applied directly to the eye. a. Describe how you would go about collecting data for your investigation. b. Does your method result in paired data? c. Can you think of a reasonable method of collecting data that would not result in paired samples? Would such an experiment be as informative as a paired experiment? Comment.

Each person in a random sample of 228 male teenagers and a random sample of 306 female teenagers was asked how many hours he or she spent online in a typical week (Ipsos, January 25, 2006). The sample mean and standard deviation were 15.1 hours and 11.4 hours for males and 14.1 and 11.8 for females. a. The standard deviation for each of the samples is large, indicating a lot of variability in the responses to the question. Explain why it is not reasonable to think that the distribution of responses would be approximately normal for either the population of male teenagers or the population of female teenagers. Hint: The number of hours spent online in a typical week cannot be negative. b. Given your response to Part (a), would it be appropriate to use the two- sample \(t\) test to test the null hypothesis that there is no difference in the mean number of hours spent online in a typical week for male teenagers and female teenagers? Explain why or why not. c. If appropriate, carry out a test to determine if there is convincing evidence that the mean number of hours spent online in a typical week is greater for male teenagers than for female teenagers. Use a .05 significance level.

The paper "The Truth About Lying in Online Dating Profiles" (Proceedings, Computer-Human Interactions [2007]\(: 1-4)\) describes an investigation in which 40 men and 40 women with online dating profiles agreed to participate in a study. Each participant's height (in inches) was measured and the actual height was compared to the height given in that person's online profile. The differences between the online profile height and the actual height (profile - actual) were used to compute the values in the accompanying table. $$ \begin{array}{ll} \text { Men } & \text { Women } \\ \hline \bar{x}_{d}=0.57 & \bar{x}_{d}=0.03 \\ s_{d}=0.81 & s_{d}=0.75 \\ n=40 & n=40 \end{array} $$ For purposes of this exercise, assume it is reasonable to regard the two samples in this study as being representative of male online daters and female online daters. (Although the authors of the paper believed that their samples were representative of these populations, participants were volunteers recruited through newspaper advertisements, so we should be a bit hesitant to generalize results to all online daters!) a. Use the paired \(t\) test to determine if there is convincing evidence that, on average, male online daters overstate their height in online dating profiles. Use \(\alpha=.05\) b. Construct and interpret a \(95 \%\) confidence interval for the difference between the mean online dating profile height and mean actual height for female online daters. c. Use the two-sample \(t\) test of Section 11.1 to test \(H_{0}: \mu_{m}-\mu_{f}=0\) versus \(H_{a}: \mu_{m}-\mu_{f}>0,\) where \(\mu_{m}\) is the mean height difference (profile - actual) for male online daters and \(\mu_{f}\) is the mean height difference (profile - actual) for female online daters. d. Explain why a paired \(t\) test was used in Part (a) but a two-sample \(t\) test was used in Part (c).

Consider two populations for which \(\mu_{1}=30\), \(\sigma_{1}=2, \mu_{2}=25,\) and \(\sigma_{2}=3 .\) Suppose that two independent random samples of sizes \(n_{1}=40\) and \(n_{2}=50\) are selected. Describe the approximate sampling distribution of \(\bar{x}_{1}-\bar{x}_{2}\) (center, spread, and shape).

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