Posted: December 1st, 2022

Research Methods & Statistics essay

INSTRUCTIONS:
This is a homework assignment, not an exam. Do the work individually, but you are free to ask for assistance. The goal is for you to learn and understand the material.
Unless otherwise specified, all calculations are to be typed. The use of a calculator is permitted, but do not use a statistical software package (e.g., Excel, SPSS, etc.). The purpose of this homework, using small data sets, is to give you a familiarity with the steps involved in calculating statistical parameters, so that you understand what’s going on “behind the scenes” when you do use statistical software packages on data from large data sets.
If a problem says “Show all work!”, show all work needed to arrive at the answer. That includes the formula (or a description of how to find the solution), entering the numbers into the formula, each step in the calculations, and your final answer.
Do your work on this sheet.
Do put your name on the paper
Do remember to follow the formatting instructions in the syllabus:
Use commas in numbers having four or more digits; 1,875, not 1875
Use a leading zero in decimals that lack a whole number component; 0.352, not .362
Separate binary numbers into groups of 4 (e.g., 1101 0111 1001, not 110101111001
Do round your final numerical answers to two decimal places: e.g., 0.1873 would round to 0.19,
0.1848 would round to 0.18

Do remember to use parentheses, brackets, and braces correctly when needed.
e.g., TN / (TN + FP), not TN / TN + FP
The reason for this is that there is a standard “Order of Operations” in algebra (Google it):

Compare:
2 / (2 + 4) = 2 / 6 = 0.333, but
2 / 2 + 4 = 1 + 4 = 5

Do your calculations on the exam paper, not on a separate sheet.

Do *not* change the wording of questions on the exam paper.
Do *not* just submit a document with answers on it.
Do *not* do your work or have your answers in red font. I use red font for markups.
Do *not* create isolated text boxes on the exam paper for your calculations or answers. It makes it difficult to enter feedback comments.

If the problem involves setting up a table, use the “Insert table” function in Word (“Insert” tab > “Table” (select the number of cells in rows and columns from the pull-down menu and click “Insert Table”)
Do put your final answers in bold font and your bold font answer may, or may not, be highlighted in yellow.
Do title your submission as follows
LastName FirstInitial course# Assignment#
No commas, no underscores.

E.g.,
Smith J 5309 HW 3

I save homeworks, and that format saves them alphabetically by last name, tells me what course it’s from; and what the assignment was. Titles such as “Homework”, “HW 3”, “Stats”; “J Smith”; etc., mean that I have to re-label each of those assignments when I save them, and considering the number of students in all of my courses, that takes a considerable amount of time. So, the watchword is, “Help the professor”. It’s greatly appreciated!!

Point values for each question are indicated in parentheses following the question. Partial credit may be given for solutions that are partially correct; conversely, partial credit will be deducted for solutions that are partially incorrect, do not show all work, or are not formatted as specified.
Use additional space/pages as needed.

Do submit your homework to the Assignments Tool as an MS Word document *only* (no pdfs, no scanned sheets).
Failure to follow these rules will result in point deductions.
Let me know if you have any questions.
Do well!

1. A blood test to diagnose a disease was performed on a number of patients. Given the following data:

Number of patients = 1,561
Number of patients who had a positive test result and had the disease = 1,193
Number of patients who had a negative test, and did not have the disease = 253
Number of patients who had a positive test result, but did not have the disease = 58
Number of patients who had a negative test result, but who had the disease = 57

a. Construct, label, and completely fill in a 2 x 2 decision table that accurately reflects the data (10 points)
b. Calculate the sensitivity of the test. Show all work! (5 points)
c. Calculate the specificity of the test. Show all work! (5 points)
d. Calculate the false positive rate. Show all work! (5 points)
e. Calculate the false negative rate. Show all work! (5 points)

2. A blood test to diagnose a disease was performed on a number of patients. Given the following information:
Number of patients who have a positive test result and have the disease = 1,491
Number of patients who have a negative test result = 3,149
Number of patients who have a positive test result but don’t have the disease = 89
Number of patients who do not have the disease = 3,017

a. Construct, label, and completely fill in a 2 x 2 decision table that accurately reflects the data (10 points)
b. Calculate the sensitivity of the test. Show all work! (5 points)
c. Calculate the specificity of the test. Show all work! (5 points)
d. Calculate the False Positive Rate. Show all work! (5 points)
e. Calculate the False Negative Rate. Show all work! (5 points)

3. Two groups of patients were chosen in order to compare a new treatment with a standard treatment. One group of patients received the new treatment and one group received the standard treatment. Some patients in each group had an adverse outcome and some patients in each group had a good outcome. Given the following data:
Number of patients (total) = 4,697
Number of patients who had an adverse outcome with the new treatment = 168
Number of patients who had an adverse outcome with the standard treatment = 205
Number of patients who had a good outcome with the new treatment = 2,257
Number of patients who had a good outcome with the standard treatment = 2,067

a. Construct, label, and completely fill in a 2 x 2 decision table that accurately reflects the data (10 points)
b. Calculate the relative risk of an adverse outcome for the new treatment. Show all work! (5 points)
c. Calculate the relative risk reduction for the new treatment. Show all work! (5 points)
d. Calculate the risk difference. Show all work! (5 points)
e. Calculate the number needed to treat for the new treatment. Show all work! (5 points)

4. A restaurant in your town had 163 diners on Friday night. By Monday evening, 24 of those diners had reported to the Emergency Department, outpatient clinics, or saw their physicians with symptoms of gastrointestinal distress, suggesting food poisoning. Stool cultures for Salmonella were positive in all 24 diners.

a. What is the estimated* probability of a diner having contracted food poisoning at that restaurant on that Friday night? Show all work! (5 pts)

[*Note: This is an estimated probability because it doesn’t include persons whose symptoms may not have been severe enough for them to have sought medical attention (the actual probability could be higher); nor does it exclude the possibility that some of those symptomatic people may have contracted food poisoning from some other source (the actual probability could be lower); but the estimated probability would give epidemiologists a base line figure to work from.]

5. In 2015, Texas led the nation in the percentage of people who lacked health insurance (21.6% of the population) [Ref: https://www.texmed.org/Template.aspx?id=42282]. It is known that, nationally, 5% of patients account for 50% of the costs of healthcare. These are the “high cost” patients

Assume* that:
Being a high cost patient and being uninsured are independent characteristics
Insured and uninsured people become “patients” at the same rate
The uninsured and high cost patients in Texas are evenly distributed across the state, and that high cost patients are evenly distributed across insured and uninsured patient populations
a. What is the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured? Show all work! (5 pts)

*[These are huge and unrealistic assumptions, but let’s assume them just for the purpose of this problem].

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