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Statistical Reasoning in Public Health: Homework #1 Due 9/15/16, 11:59 pm via Courseplus Submit your final answers electronically, via the “Homework 1” quiz files on the Courseplus page. (there are 3 separate quizzes for each section, A-C) Homework 1, Section A 1. 2. 3. 4. 5. 6. 7. 8. 9. How many homeworks are given in Statistical Reasoning 1? What percentage of the course grade is each homework worth? What is the class policy on submitting homeworks after the due date /time? Are you allowed to work together on homework assignments? How many quizzes are given in Statistical Reasoning 1? What percentage of the course grade is each quiz worth? What percentage of the course grade is the final exam worth? Are you allowed to work together on quizzes and exams? Do the quizzes and exams require a proctor? Homework 1, Section B (these questions will appear as multiple choice items in the quiz generator) 1. The duration of time from first exposure to HIV infection to AIDS diagnosis is called the incubation period. The incubation periods of a random sample of 7 HIV infected individuals is given below (in years): 12.0 9.5 a. b. c. d. 10.5 6.3 13.5 7.2 12.5 Report the sample mean. Report the sample median. Report the sample standard deviation If the number 6.3 above were changed to 1.5, what would happen (increase, decrease, or remain the same) to the 1. sample mean? 2. sample median? e. Assume that these data are seven random observations taken from a larger population whose values are normally distributed. (even if this assumption makes little sense) Using this assumption, coupled with prior computations, estimate an interval that contains 95% of incubation time values in the population of HIV patients from which the sample was taken. f. Suppose another random sample of 100 persons is taken from the same population, Statistical Reasoning in Public Health I—Homework 1 2016 Page 1 of 8 and added to the sample of 7, for a total sample of 107 HIV infected individuals. How will the following sample statistics based on the sample of 107 compare in value to the estimates based on the sample statistics from the sample of n=7? 1. sample mean 2. sample median 3. standard deviation values g. Suppose the distribution of these incubation period values is left-skewed in the population of persons with HIV. If you were take single random samples of each of the following size from this population, what will likely be the shape of the distribution of sample values? a. n=75 b. n=200 c. n=3,200 2. The CDC collects anthropometric (weight, height etc..) data on large samples of US youth, both male and female, and uses these data to create growth charts, which essentially characterize the distributions of these measures by age and sex. For example, for 18 years old males, the mean body mass index (BMI) is 21.9 (kg/m2) with a standard deviation (SD) of 3.2 (kg/m2). Physicians (and patients) can use these data to figure out how individual BMI values compare relative to the age and sex specific distribution. Suppose you are a physician and you are screening patients at a health fair. The following describes some of the men you have screened. You may assume the distribution of BMI values for 18 year old males is a normal distribution. a. Male 1 had a BMI of 26.7. His BMI was above average by how many SDs? b. Male 2 had a BMI of 23.5. He His BMI was above average by how many SDs? c. Male 3 had a BMI of that was .75 SDs below the average. What was his BMI measure? d. Estimate a range of “normal” BMI values, ie: a range that contains the middle 95% of the values in the population of 18 year old males. e. Not surprisingly, perhaps, the actual distribution of BMI values among 18 year old males is right skewed (slightly, not heavily so). Given this fact, what additional summary statistics would be necessary to properly estimate the interval in part d? Statistical Reasoning in Public Health I—Homework 1 2016 Page 2 of 8 3. Assume blood-glucose levels in a population of adult women are approximately normally distributed with mean 90 mg/dL and standard deviation 13 mg/dL. For parts a-c, answer each of the following: 1. 2. What percentage of individuals would be called “abnormal” and need to be retested? What is the normal range of glucose levels in units of mg/dL? a. Suppose the “abnormal range” were defined to be glucose levels outside of 1 standard deviation of the mean (i.e., either at least 1 standard deviation above the mean, or at least 1 standard deviation below mean). Individuals with abnormal levels will be retested. b. Suppose the “abnormal range” were defined to be glucose levels outside of 1.5 standard deviations of the mean. c. Suppose the “abnormal range” were defined to be glucose levels outside of 2 standard deviations of the mean. Statistical Reasoning in Public Health I—Homework 1 2016 Page 3 of 8 4. A 2011 article published in the American Journal of Public Health1 reports on the association between neighborhood socioeconomic status and cognitive function in women. 1 As per the authors, the study sample was obtained as follows “We assessed women aged 65 to 81 years (n = 7479) who were free of dementia and took part in the Women’s Health Initiative Memory Study.” The following graphic is included in the manuscript: The 3MSE score is a standardized measure of cognitive functioning (higher values indicate higher cognitive function), and the NSES quartiles are ordinal categories of neighborhood socioeconomic status (SES) scores for the subjects in the study. (Higher scores indicate higher neighborhood SES). Both measures (3MSE scores and NSES scores) were based on information collected from each woman via a survey administered at one time. a. b. c. d. e. f. g. What is the range of 3MSE scores across all women included in the study? Which of the NSES quartiles includes the woman with the lowest 3MSE score? Approximately, what is the median 3MSE score for NSES Q1? Approximately, what is the median 3MSE score for NSES Q4? What is the difference in 3MSE medians for Q4 compared to Q1? What type of distribution do the 3MES scores have in the four NSES quartiles? How do you expect the mean 3MSE score to compare to the median MSE score for NSES Q3? h. Generally, what is the nature of the relationship between 3MSE scores and NSES quartiles? i. Is neighborhood SES definitely the cause of the observed difference in 3MSE score distribution differences between the 4 SES quartiles? 1 Shih R, et al. Neighborhood Socioeconomic Status and Cognitive Function in Women. American Journal of Public Health . September 2011, Vol 101, No. 9 | Statistical Reasoning in Public Health I—Homework 1 2016 Page 4 of 8 5. A 2011 article published in the Journal of Substance Abuse Treatment2 reports the results of a clinical trial designed to assess the effects of acupuncture on anxiety related to withdrawal from psychoactive drugs. As per the abstract: “Auricular acupuncture (AA) is a widely accepted treatment option for substance abuse that is used in more than 700 treatment centers worldwide. Despite claims of perceived clinical benefits by patients and treatment staff, research efforts have failed to substantiate purported benefits, and the mechanism(s) by which AA serves in the treatment of addiction remain inconclusive. Numerous studies have shown AA to be an effective treatment for perioperative anxiety. In this study, we hypothesize that AA reduces the anxiety associated with withdrawal from psychoactive drugs. The study used a randomized, controlled design and included a sample of 101 patients recruited from an addiction treatment service. Subjects were assigned to one of three treatment groups (National Acupuncture Detoxification Association [NADA] AA, AA at sham points, or treatment setting control) and were instructed to attend treatment sessions for 3 days. The primary outcome measure state anxiety was assessed using a pretest–posttest treatment design.” The following boxplots (Figure 4 in the article) show the main results from this study: (higher anxiety scores indicate higher anxiety) 2 Black S, et al. Determining the efficacy of auricular acupuncture for reducing anxiety in patients withdrawing from psychoactive drugs. Journal of Substance Abuse Treatment, 41 (2011) 279–287. Statistical Reasoning in Public Health I—Homework 1 2016 Page 5 of 8 a. (Approximately ) What is the median anxiety score before the session started among participants randomized to receive acupuncture (NADA)? b. (Approximately ) What is the median anxiety score after the session finished among participants randomized to receive acupuncture (NADA)? c. (Approximately) What is the median anxiety score before the session started among participant randomized to receive Relaxation? d. (Approximately) What is the median anxiety score after the session finished among participants randomized to receive Relaxation? e. Based on these boxplot presentations, what sign would the mean anxiety score difference take on (+,-) for after the session compared to before the session for each of the three randomization groups? f. Likely, how will the mean differences (after session – before session) in anxiety scores compare in value across the three randomization groups? (Don’t overthink this one) g. Based on the boxplots, what conclusion can you make about the efficacy of acupuncture on anxiety reduced as compared to the other two groups? h. The authors used the graphic alone to demonstrate the study findings. Why did they not need to first adjust for potential confounders? Homework 1, Part C (your answers to these questions will be entered into text fields in the Quiz Generator) 6. The following abstract is taken from a 2010 article about a randomized experiment to evaluate the efficacy of an intervention on reducing the stigma of HIV among market workers in China.3 Intervention status was randomized at the community level (in other words, each community enrolled in the study was randomly assigned to receive the intervention, or not to receive the intervention) 3 Li L, et al. HIV prevention intervention to reduce HIV-related stigma: evidence from China. AIDS 2010, 24:115– 122 Statistical Reasoning in Public Health I—Homework 1 2016 Page 6 of 8 1. How for the distributions of the HIV stigma scores compare between the control and intervention groups at baseline? Statistical Reasoning in Public Health I—Homework 1 2016 Page 7 of 8 2. What type of “shape” does the distribution of stigma scores for the intervention group at baseline have? 3. How do the distributions of stigma scores change (or not change) over time in the control group? 4. How do the distributions of stigma scores change (or not change) over time in the intervention group? Statistical Reasoning in Public Health I—Homework 1 2016 Page 8 of 8
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