HPHA 5309
Homework #3 (material from Lectures 11, 12, 13, 14)
Name _____________________________________________
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.
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.
For problems #7 and 8, do the calculations by hand and show *all* work. That is, include the formulas, substitution of the data into the formulas, the calculations, and your final answer).
For problems #9 and #10, use Excel or other statistics software application. Your answer will be a copy and paste of your Excel (or other) page. Just copy and paste the portion of the page where your data and answer are; do not copy and paste the entire page (they’re huge!).
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 ________________________________ is a range of values within which it is probable that the true value of a parameter (e.g., a mean) lies. It can also be thought of as a measure of how closely the measured values from a sample cluster around the true value for the population as a whole. (5)
2. The formula for converting odds to probability is ________. (10)
a. Odds = probability / (1 – probability)
b. Probability = odds / (1 + odds)
c. Probability = odds / (1 – odds)
d. Probability = (1 + odds) / odds
e. Probability = (1 – odds) / odds
3. True or False: Any distribution of data can be converted into a Z-distribution. (5)
a. True
b. False
4. The Z-distribution has a mean of ____________ and a standard deviation of ________. (10)
a. 1, 0
b. 50, 10
c. 50, 100
d. 0, 1
e. 0, 3
5. True or False: In a research study, the alpha (α) and the p-value are two names for the same thing. (5)
a. True
b. False
6. True or False: If your level of statistical significance (alpha) is 0.05, and the p-value calculated from your data is p = 0.07, you accept the null hypothesis. (5)
a. True
b. False
7. A researcher asked 933 people what their favorite type of TV program was: news, documentary, soap or sports. They could only choose one answer. As such, the researcher had the number of people who chose each category of program. How should she analyze these data? (5)
a. t-test
b. One-way analysis of variance
c. Chi-square test
d. Regression
8. On which of the following does the critical value for a chi-square statistic rely? (5)
a. The degrees of freedom
b. The sum of the frequencies
c. The row totals
d. The number of variables
9. The ____ the P-value, the stronger the evidence against the null hypothesis provided by the data (5)
a. Larger
b. Smaller
10. Given the following data:
Number of patients = 3,590
Number of patients who had a positive test result and had the disease = 2,181
Number of patients who had a negative test, and did not have the disease = 1097
Number of patients who had a positive test result, but did not have the disease = 155
Number of patients who had a negative test result, but who had the disease = 157
1. Create a complete and fully labelled 2×2 table (10)
1. Calculate the positive predictive value. Show all work! (5)
1. Calculate the likelihood ratio for a positive test result (5)
11. A random sample of 20 observations produced a sample mean of 𝑥̅= 92.4 and s = 25.8. What is the value of the standard error of 𝑥̅? (10)
a. 4.6
b. 15.9
c. 1.3
d. 5.8
e. 2.6
12. (15 points)
Go the website: https://www.graphpad.com/quickcalcs/ttest1.cfm
Select Piared T test.
Add the following values in Box 3 Enter data under Group 1 and Group 2
| Physician number |
Survey #1 average score (out of 10) |
Survey #2 average score (out of 10) |
| |
|
|
| 01 |
7.2 |
4.5 |
| 02 |
6.5 |
4 |
| 03 |
5.5 |
4.8 |
| 04 |
7.5 |
6.4 |
| 05 |
6.8 |
7.4 |
| 06 |
8.0 |
9.0 |
| 07 |
8.3 |
3 |
| 08 |
4.3 |
5.5 |
| 09 |
7.1 |
8.0 |
| 10 |
6.6 |
7.1 |
| 11 |
4.5 |
5.0 |
| 12 |
7.9 |
3.4 |
| 13 |
4.6 |
4.3 |
| 14 |
6.5 |
6.0 |
| 15 |
5.8 |
3.5 |
Click on Calculate now and read the results of paired t test.
The above data is from a physician burnout survey at a local hospital. More context about your research survey is below:
Physician burnout is a serious problem and you have the impression that morale among the physicians at your facility is at a low point. You administer a survey to get some quantitative data, as well as some suggestions for improvement. One of the most common suggestions is that hiring physician extenders (PAs, scribes, or other extenders) would improve things. Your supervisor gives you permission to hire some physician extenders, but wants to know if the investment achieves significant results. You decide to administer a second survey six months following the hiring of physician extenders and will do a t-test to see if there’s a significant change in the survey results compared to the results from the survey prior to the hiring
a. Report the p value (5)
b. What is the null hypothesis? (3)
c. Do you reject the null hypothesis? (2)
d. What is your conclusion about the effect of hiring physician extenders? (5)
13. Bonus question (out of book/out of syllabus question) Would the findings be different if linear regression was used instead of t test in question 12? (5)
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