Summary Lyman Ott Michael Longnecker

for conducting surveys or scientific studies, you can address how to collect data on the variables of interest in order to address the stated objectives of the data- gathering exercise. We also drew a distinction between observational and experimental studies in terms of the inferences conclusions that can be drawn from the sample data. Differences found between treatment groups from an observational study are said to be associated with the use of the treatments; on the other hand, differences found between treatments in a scientific study are said to be due to the treatments. In the next chapter, we will examine the methods for summarizing the data we collect.

2.8 Exercises

2.2 Observational Studies 2.1 In the following descriptions of a study, confounding is present. Describe the explanatory and confounding variable in the study and how the confounding may invalidate the conclusions of the study. Furthermore, suggest how you would change the study to eliminate the effect of the confounding variable.

a. A prospective study is conducted to study the relationship between incidence of

lung cancer and level of alcohol drinking. The drinking status of 5,000 subjects is determined and the health of the subjects is then followed for 10 years. The results are given below. Lung Cancer Drinking Status Yes No Total Heavy Drinker 50 2150 2200 Light Drinker 30 2770 2800 Total 80 4920 5000

b. A study was conducted to examine the possible relationship between coronary disease

and obesity. The study found that the proportion of obese persons having developed coronary disease was much higher than the proportion of nonobese persons. A medical researcher states that the population of obese persons generally have higher incidences of hypertension and diabetes than the population of nonobese persons. 2.2 In the following descriptions of a study, confounding is present. Describe the explanatory and confounding variable in the study and how the confounding may invalidate the conclusions of the study. Furthermore, suggest how you would change the study to eliminate the effect of the confounding variable.

a. A hospital introduces a new screening procedure to identify patients suffering from

a stroke so that a new blood clot medication can be given to the patient during the crucial period of 12 hours after stroke begins. The procedure appears to be very suc- cessful because in the first year of its implementation there is a higher rate of total recovery by the patients in comparison to the rate in the previous year for patients admitted to the hospital.

b. A high school mathematics teacher is convinced that a new software program will

improve math scores for students taking the SAT. As a method of evaluating her theory, she offers the students an opportunity to use the software on the school’s computers during a 1-hour period after school. The teacher concludes the software is effective because the students using the software had significantly higher scores on the SAT than did the students who did not use the software. 2.3 A news report states that minority children who take advanced mathematics courses in high school have a first-year GPA in college that is equivalent to white students. The newspaper columnist suggested that the lack of advanced mathematics courses in high school curriculums in inner city schools was a major cause of inner city schools having a low success rate in college. What confounding variables may be present that invalidate the columnist’s conclusion? 2.4 A study was conducted to determine if the inclusion of a foreign language requirement in high schools may have a positive effect on a students’ performance on standardized English exams. From a sample of 100 high schools, 50 of which had a foreign language requirement and 50 that did not, it was found that the average score on the English proficiency exam was 25 higher for the students having a foreign language requirement. What confounding variables may be present that would invalidate the conclusion that requiring a foreign language in high school increases English language proficiency? 2.3 Sampling Designs for Surveys Soc. 2.5 An experimenter wants to estimate the average water consumption per family in a city. Discuss the relative merits of choosing individual families, dwelling units single-family houses, apartment buildings, etc., and city blocks as sampling units. H.R. 2.6 An industry consists of many small plants located throughout the United States. An execu- tive wants to survey the opinions of employees on the industry vacation policy. What would you suggest she sample? Pol. Sci. 2.7 A political scientist wants to estimate the proportion of adult residents of a state who favor a unicameral legislature. What could be sampled? Also, discuss the relative merits of personal interviews, telephone interviews, and mailed questionnaires as methods of data collection. Bus. 2.8 Two surveys were conducted to measure the effectiveness of an advertising campaign for a low-fat brand of peanut butter. In one of the surveys, the interviewers visited the home and asked whether the low-fat brand was purchased. In the other survey, the interviewers asked the person to show them the peanut butter container when the interviewee stated he or she had purchased low-fat peanut butter.

a. Do you think the two types of surveys will yield similar results on the percentage of

households using the product? b. What types of biases may be introduced into each of the surveys? Edu. 2.9 Time magazine, in an article in the late 1950s, stated that “the average Yaleman, class of 1924, makes 25,111 a year,” which, in today’s dollars, would be over 150,000. Time’s estimate was based on replies to a sample survey questionnaire mailed to those members of the Yale class of 1924 whose addresses were on file with the Yale administration in the late 1950s. a. What is the survey’s population of interest? b. Were the techniques used in selecting the sample likely to produce a sample that was representative of the population of interest? c. What are the possible sources of bias in the procedures used to obtain the sample? d. Based on the sources of bias, do you believe that Time’s estimate of the salary of a 1924 Yale graduate in the late 1950s is too high, too low, or nearly the correct value? 2.10 The New York City school district is planning a survey of 1,000 of its 250,000 parents or guardians who have students currently enrolled. They want to assess the parents’ opinion about mandatory drug testing of all students participating in any extracurricular activities, not just sports. An alphabetical listing of all parents or guardians is available for selecting the sample. In each of the following descriptions of the method of selecting the 1,000 participants in the survey, identify the type of sampling method used simple random sampling, stratified sampling, or clus- ter sampling.

a. Each name is randomly assigned a number. The names with numbers 1 through 1,000

are selected for the survey.