Station 3: Inference with R
Introduction
You should remember the basics of hypothesis testing from your introductory statistics class, whether it was MAT 125, AP statistics, or a course through a different school or department. You can find the R code to perform all the necessary inference procedures on the “Inference Summary Sheet” page under the Computing tab on the course website.
At this station, you will pose and answer research questions from beginning to end, using the US States data (from Station 2). You will have the opportunity to ask and answer 3 different research questions: one using only one variable, and two exploring the relationship between two variables. Although not required, you may re-use your work from Station 2.
Please reference the data codebook (available on the Data sets tab on Canvas) to decide which variables you’d like to use when forming your research question.
A. Univariate: Quantitative
TASK 1.1.1–Choose a quantitative variable from the US States dataset you’d like to explore. What is the variable?
Pose a research question
TASK 1.1.2–What would be a reasonable research question to ask about this parameter? Your answer should make sense practically.
TASK 1.1.3–Write the null and alternative hypotheses in terms of the population parameter. If your research question is better suited for a confidence interval, you do not need to state hypotheses.
Perform EDA
A good EDA should attempt to preliminarily answer the research question and also identify any issues that might impact eventual inference.
TASK 1.1.4–Generate a relevant plot for your research question.
TASK 1.1.5– Calculate the summary statistic that is most relevant to your CI/test.
TASK 1.1.6–Write a few sentences summarizing what you learned from your EDA
Answer the question using inference
To answer your research question, you’ll need to test the hypotheses you defined earlier, or construct the relevant confidence interval.
TASK 1.1.7–What is the name of the statistical test or interval you will perform/construct (e.g., 1-sample t-test for the mean, CI for the difference in means, 1-sample proportion test)?
TASK 1.1.8–Did your EDA indicate any problems with performing this test/CI? That is, are the conditions for inference met?
TASK 1.1.9–Use R to generate the test statistic and p-value, or build the confidence interval.
TASK 1.1.10–Make a conclusion about the null and alternative hypotheses, being sure to answer your research question in context. OR Provide an interpretation of the confidence interval in context.
B. Relationship between two variables 1: Numerical/Binary
Choose two variables from the Codebook: one numerical, one binary. In this section you will investigate the relationship between these two variables.
TASK 2.1.1–What are the two variables? Your answer should include a brief description and be more than simply the variable name.
Pose a research question
TASK 2.1.2–What would be a reasonable research question to ask about this parameter? Your answer should make sense practically.
TASK 2.1.3–Write the null and alternative hypotheses in terms of the population parameter. In this case, I want you to perform a hypothesis test. Later, I’ll also have you build the CI.
Perform EDA
Remember, a good EDA should attempt to answer the research questions and also identify any issues that might impact eventual inference.
TASK 2.1.4–Generate a relevant plot for your research question.
TASK 2.1.5–Calculate the summary statistics that are most relevant to your test.
TASK 2.1.6–Write a few sentences summarizing what you learned from your EDA
Answer the question using inference
To answer your research question, you’ll need to test the hypotheses you defined earlier.
TASK 2.1.7–What is the name of the statistical test you will perform?
TASK 2.1.8–Did your EDA indicate any problems with performing this test? That is, are the conditions for inference met?
TASK 2.1.9–Use R to generate the test statistic and p-value.
TASK 2.1.10–Make a conclusion about the null and alternative hypotheses, being sure to answer your research question in context.
TASK 2.1.11–Now use R to calculate a 95% confidence interval for the parameter of interest, and provide an interpretation in context. First, you must ask yourself, “What is the parameter of interest?”
C. Relationship between two variables 2: Binary/Binary
Choose two binary variables from the Codebook. In this section you will investigate the relationship between these two variables.
TASK 2.2.1–What are the two variables? Your answer should include a brief description and be more than simply the variable name.
Pose a research question
TASK 2.2.2–What would be a reasonable research question to ask about this parameter? Your answer should make sense practically.
TASK 2.2.3–Write the null and alternative hypotheses in terms of the population parameter. In this case, I want you to perform a hypothesis test. Later, I’ll also have you build the CI.
Perform EDA
Remember, a good EDA should attempt to answer the research questions and also identify any issues that might impact eventual inference.
TASK 2.2.4–Generate a relevant plot for your research question.
TASK 2.2.5–Calculate the summary statistics that are most relevant to your hypothesis test.
TASK 2.2.6–Write a few sentences summarizing what you learned from your EDA
Answer the question using inference
To answer your research question, you’ll need to test the hypotheses you defined earlier.
TASK 2.2.7–What is the name of the statistical test will you perform to test the hypotheses?
TASK 2.2.8–Did your EDA indicate any problems with performing this test? That is, are the conditions for inference met?
TASK 2.2.9–Use R to generate the test statistic and p-value.
TASK 2.2.10–Make a conclusion about the null and alternative hypotheses, being sure to answer your research question in context.
TASK 2.2.11–Now use R to calculate a 95% confidence interval for the parameter of interest, and provide an interpretation in context. First, you must ask yourself, “What is the parameter of interest?”