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Problem Set 4 The Moving to Opportunity (MTO) housing voucher experiment was commissioned to study the impact of neighborhoods on child and family outcomes for families residing in public housing projects. MTO was conducted in Baltimore, Boston, Chicago, Los Angeles, and New York, and randomly assigned a voucher to move to a Section 8 private rental unit to families in the projects. Within the treatment group, the offer was further randomly split into two separate treatments: the first was a voucher that could only be used for lease-up of a unit in a low poverty area; the second was a voucher that was unrestricted geographically. A total of 4,498 families were enrolled in the study at baseline, of which 1,398 were assigned to the control group, and 2,900 to the treatment group. An important domain of the study was to examine the impact of neighborhoods on health outcomes. There were two focal outcomes: the prevalence of obesity and diabetes, respectively. Subjects were followed up roughly 12 years after randomization, at which point height and weight were measured, as well as blood samples taken to calculate the level of glycated hemoglobin. The American Diabetes Association's clinical definition of diabetes is a glycated hemoglobin level of 0.065 or higher, i.e., 6.5% or higher. The body-mass index (BMI) of 30 or more was used to measure clinical obesity, where BMI is weight in kilograms divided by the square of height in meters. For the BMI analysis, there were 2,071 members of the treatment group (1,416 got the low-poverty offer; 655 got the unrestricted offer) and 1,092 members of the control group. For the diabetes analysis, there were 1,760 members of the treatment group (1,168 got the low-poverty offer; 592 got the unrestricted offer), and 924 members of the control group. First, analyze the impact of the general offer of a housing voucher. To do so, consider members of both treatment sub-groups in sum as one single "treatment" group and answer the following: a 1. (5 pts) From other health studies, the mean prevalence of clinical obesity for the MTO population was 0.586 (or 58.6%), with a standard deviation of 0.493. For a 5% level of significance, 80% power, a one-tailed test, what is the minimum detectable ITT effect on obesity from the general offer of a housing voucher in the MTO design?

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Final answer:

To determine the minimum detectable effect on obesity from the offer of a housing voucher in the MTO experiment, an ITT analysis would be used with known population mean, standard deviation, power, and significance level, applying a formula involving Z-scores which require statistical software or tables to find exact values.

Step-by-step explanation:

To analyze the impact of providing a housing voucher on the prevalence of clinical obesity in the Moving to Opportunity (MTO) experiment, we use statistical hypothesis testing. Given the population mean prevalence of obesity (μ) is 0.586 with a standard deviation (σ) of 0.493, we want to detect the minimum intervention effect (d) for a power of 80% (1-β), at a 5% significance level (α), for a one-tailed test. To calculate this, we use the formula for the minimum detectable effect (MDE) in an intention-to-treat (ITT) analysis: MDE = (Z₁-β + Zα) * (σ / √n), where Z₁-β and Zα are the Z-scores corresponding to the power and significance level respectively, and n is the sample size of the combined treatment group. Unfortunately, without the exact Z-scores or a statistical software or table to find these values, the exact minimum detectable ITT effect cannot be determined here.

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User Droussel
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How is that so?

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User ToooooLong
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