Question

12 Points For the four following questions, your task is to evaluate the assumptions for the given test. It is not enough to simply stated that an assumption "is met" or "is not met". Instead, present your evidence in the form of background knowledge, visualizations, and numerical summaries to make an argument for your determination. Take care to ensure that the content that you present is as communicative as possible -- label your plots and figures, and ensure that a reader can learn your entire intent. The statistical test that we ask you to evaluate may or may not be the most appropriate test for the scenario. Because the goal of this task is to evaluate whether the data satisfies the assumptions necessary for the test to provide meaningful results, you do not need perform the test (you may perform the test, but we will not be marking for the test results). For each of these questions, upload a pdf that is at most one page in length with standard formatting. Your answers should be in paragraph form, with full sentences. Bulleted, or list-only answers will not score full marks. Starter code is located in the folder of this lab repo. Q3.2 Legislators 3 Points The file is taken from the congress-legislators project on Github. You would like to test whether Democratic or Republican senators are older. List all assumptions for a Wilcoxon rank-sum test (using the Hypothesis of Comparisons). Then evaluate each assumption, presenting evidence based on your background knowledge, visualizations, and numerical summaries.

Answer 1

To evaluate the assumptions for a Wilcoxon rank-sum test to compare the age of Democratic and Republican senators, we need to consider the following assumptions:

1. Independent observations:

One assumption of the Wilcoxon rank-sum test is that the observations are independent. In this case, we assume that the age of one senator does not affect the age of another senator. This assumption can be reasonably met as each senator's age is independent of the others.

2. Identically distributed populations:

Another assumption is that the age distributions of Democratic and Republican senators have the same shape and spread. To evaluate this assumption, we can create visualizations and numerical summaries of the age distributions for each group.

a. Visualization:

We can plot histograms or density plots of the age distributions for Democratic and Republican senators. By visually comparing the shapes and spreads of the distributions, we can assess whether they appear to be similar.

b. Numerical summaries:

We can calculate summary statistics such as the mean, median, standard deviation, and interquartile range for each group. By comparing these statistics, we can evaluate whether the distributions have similar central tendencies and variabilities.

If the visualizations and numerical summaries suggest that the age distributions of Democratic and Republican senators are similar, then the assumption of identically distributed populations is reasonably met.

3. Ordinal data:

The Wilcoxon rank-sum test assumes that the data being compared is at least ordinal. In this case, we are comparing the ages of senators, which can be considered at least ordinal as they can be ranked from youngest to oldest.

Based on the background knowledge and evidence provided through visualizations and numerical summaries, we can assess whether the assumptions for the Wilcoxon rank-sum test are reasonably met. If the assumptions are met, we can proceed with the test to evaluate whether there is a significant difference in the ages of Democratic and Republican senators.