Homework 1

BSTA 513/613

Due: Thursday April 11, 2024 at 11pm

Author

Your name here - update this!!!!

Published

April 11, 2024

Modified

April 12, 2024

Caution

I took out likelihood ratio tests in Question 5. We did not cover them!

Purpose

This homework is designed to help you practice the following important skills and knowledge that we covered in Lessons 1-2:

Practicing and outlining your decision process to analyze the relationship between two categorical variables
Interpreting research aims into questions/tests that can be answered with statistics
Using R to calculate sample proportions
Using R to calculate test statistic values for inference tests
Interpreting new phrasing of questions that were introduced in class

Directions

Download the .qmd file here.
You will not need to download datasets for this homework.
Please upload your homework to Sakai. Upload both your .qmd code file and the rendered .html file
- Please rename you homework as Lastname_Firstinitial_HW1.qmd. This will help organize the homeworks when the TAs grade them.
- Please also add the following line under subtitle: “BSTA 513/613”: author: First-name Last-name with your first and last name so it is attached to the viewable document.
For each question, make sure to include all code and resulting output in the html file to support your answers
Show the work of your calculations using R code within a code chunk. Make sure that both your code and output are visible in the rendered html file. This is the default setting.
Write all answers in complete sentences as if communicating the results to a collaborator.

Tip

It is a good idea to try rendering your document from time to time as you go along! Note that rendering automatically saves your .qmd file and rendering frequently helps you catch your errors more quickly.

Questons Part 1

The following questions are intended to give you practice in understanding concepts and completing calculations.

Question 1

If the probability that one white blood cell is a lymphocyte is 0.3, compute the probability of 2 lymphocytes out of 10 white blood cells. Also, compute the probability that at least 3 lymphocytes out of 10 white blood cells. You may calculate by hand, using a web app, or using R.

Question 2

Consider a 2 x 2 table from a prospective cohort study:

	Favorable	Unfavorable
Treatment	30	20
Placebo	10	60

Part a

Estimate the probability of having favorable results for subjects in the treatment group. Include an interpretation and report with the 95% confidence interval.

Part b

Repeat part a for the placebo group.

Part c

Conduct a statistical test to evaluate whether there is an association between group and outcome. What is the name of the test? Make sure to follow the entire test process demonstrated in the slides.

Question 3

Consider a cohort study with results shown as in following table:

	Favorable	Unfavorable
Treatment	6	1
Placebo	2	5

Conduct a statistical test to evaluate whether there is an association between group and outcome. What is the name of the test? Make sure to follow the entire test process demonstrated in the slides.

Question 4

Table 4 shows the information of a selected group of adolescents on whether they use smokeless tobacco and their perception of risk for using smokeless tobacco.

Table 4:

	YES	NO
Minimal	25	60
Moderate	35	172
Substantial	10	200

Part a

Conduct a statistical test to examine general association between adolescent smokeless tobacco users and risk perception. What is the name of the test? Make sure to follow the entire test process demonstrated in the slides.

Part b

Is there a trend of increased risk perception for smokeless tobacco users? What test would you use? Make sure to follow the entire test process demonstrated in the slides.

Questions Part 2

The following questions are intended to give you practice in connecting concepts that will help you make decisions in real world applications.

Question 5

Start making a comprehensive table or outline for the inference tests that we have covered. Here is a list of the tests we have covered:

Single proportion
Chi-squared test for general association
Fisher’s Exact test for general association
Cochran-Armitage test for trend
Mantel-Haenszel test for linear trend

And here is a list of attributes to include:

Number of variables testing
Types of variables
Criteria (if any)
Hypothesis test
Test statistic (if we went over it)
R code for test
Sample size / Power calculation (optional, not discussed in class)
Special notes (optional)

For example, I could make a table with different rows corresponding to different tests and different columns for each attribute.

Question 6

I want you to gain experience exploring a package and function. This is an important skill in coding that can help you grow as an applied statistician.

In your previous course, the function lm() was introduced to perform linear regression. In this class, we will heavily use the function glm(). By typing “?glm” in the R console, we can open the Help page for glm(). The following questions ask about the glm() function. You can Google or use R documentation to answer the questions.

Feel free to read more about the differences between lm() and glm().

Part a

What does the input “family” mean? If I wanted to perform regression using a Poisson distribution, what would I input into family?

Part b

What is the default action for the “na.action” input?

Part c

How does the glm() function fit our model? (Hint: see “method”)

Part d

Do you think the output of summary() will be the same for lm() and glm()?

Question 7

OPTIONAL

Let’s make a decision tree on the different tests we learned! I would like you to make a flow chart for the different tests we learned in Classes 1 and 2. You’ll need to include characteristics for:

Number of variables (1, 2, or 3 - we will go over 3 variables in Class 4)
Number of categories in each variable
Sample size is small
Ordinal/nominal independent variable
Ordinal/nominal response variable(s)

For example, if I make a decision tree that includes end nodes for different animals (cat, dog, snake, turtle, and hawk) using yes/no characteristics (has a shell, woof/meows, has fur, or flies), then my flow chart would look like: See my example under Sakai Resources. You are welcome to draw this chart. I used SmartArt under the Insert tab in Word to create mine.