Getting Started

The data

Every two years, the Centers for Disease Control and Prevention conduct the Youth Risk Behavior Surveillance System (YRBSS) survey, where it takes data from high schoolers (9th through 12th grade), to analyze health patterns. You will work with a selected group of variables from a random sample of observations during one of the years the YRBSS was conducted. We have already seen this dataset in the previous lab and it should already be imported to your Data toolbox.

There are observations on 13 different variables, some categorical and some numerical. Recall that you can find the meaning of each variable by locating the yrbss dataset in the Rguroo’s OpenIntro Dataset Repository and clicking on the information icon info. Also, recall that you can obtain a summary of the data by right-clicking the yrbss dataset name in the Data toolbox and selecting Dataset Summary.

  1. What are the cases in this data set? How many cases are there in our sample?

Exploratory data analysis

You will first start with analyzing the weight of the participants in kilograms: weight.

  1. How many observations are we missing weights from?

  2. Using the Histogram function in Rguroo, visualize the distribution of weights. Include the plot you create and write 1-2 sentences to describe the distribution in words.

Next, consider the possible relationship between a high schooler’s weight and their physical activity. Plotting the data is a useful first step because it helps us quickly visualize trends, identify strong associations, and develop research questions.

First, let’s create a new variable physical_3plus, which will be coded as either “yes” if they are physically active for at least 3 days a week, and “no” if not. Remember that we do this in the Transform function. The code is:

ifelse(physically_active_7d >= 3, "yes", "no")
*Creating the catgorical variable physical_3plus*

Creating the catgorical variable physical_3plus

Let’s Save the dataset with the added variable physical_3plus as yrbss_transformed.

To create a boxplot, open the Plots toolbox and select Create Plots \(\rightarrow\) Boxplot. Move the variable weight in the Numerical Variables section to the Selected column, and move the variable physical_3plus in the Factor Variables column to the Selected column. Rguroo considers the missing values for a categorical variable as a level of a categorical variable. In order not to include the missing cases in the physical_3plus variable, click on the Level Editor button, and in the Factor Level Editor dialog, select physical_3plus and move the level NA (standing for missing data) from the Level column to the Dropped Level column. Click the Preview icon eye to see the new set of boxplots.

*Creating a boxplot of weights by the categorical variable physical_3plus*

Creating a boxplot of weights by the categorical variable physical_3plus

  1. Look at the side-by-side boxplot of physical_3plus and weight that you created in Rguroo. Is there a relationship between these two variables? What did you expect and why?

The box plots show how the medians of the two distributions compare, but we can also compare the means of the distributions. You can check the box Show Mean on the top right of the Boxplot dialog to add two red diamonds to the plot that indicate the mean weight for each group. You can also use the Summary Statistic function in the Data toolbox to find the values for the mean weight in each group.

There is an observed difference, but is this difference statistically significant? In order to answer this question we will conduct a hypothesis test.

Hypothesis Test Step-by-Step

Step 0: Ensure all necessary conditions for performing inference are met

Before doing the hypothesis test, we need to look at our graphical and numerical summaries to determine which conditions for performing our desired inference are satisfied. If all conditions are satisfied, then we can proceed. If not, then we need to find a different type of hypothesis test that only requires the conditions that are satisfied.

  1. Are all conditions necessary for inference satisfied? Comment on each. You can see the group sizes in the Summary Statistic output that you created above.

Step 1: Specify the null hypothesis, alternative hypothesis, and significance level

We write each hypothesis as a complete sentence and also, if possible, as a “mathematical sentence” (equation or inequality) about the parameter(s) of interest.

  1. Write the (null and alternative) hypotheses for testing if the average weights are different between those who exercise at least three times a week and those who don’t.

We also specify our significance level \(\alpha\) in this step. This removes the temptation to define our \(\alpha\) level after seeing the results of the test. For this lab example, we will use \(\alpha = 0.05\), a typical default significance level.

Step 2: Choose the appropriate procedure in your statistical software

Since our null and alternative hypothesis concern population means, we use Rguroo’s Mean Inference dialog from the Analytics toolbox to conduct this hypothesis test. Since our null and alternative hypothesis discuss a difference between two groups, we select the One and Two Population option under Mean Inference.

Step 3: Set up the test in your statistical software

To fill out the One & Two Population Mean Inference dialog for this test, select the yrbss_transformed Dataset. We want to look at the values of a numerical Variable, weight, grouped By Factor, physical_3plus. Select either “yes” or “no” as the Level in the Population 1 section and the other value as the Level in the Population 2 section. In the screenshot below, Population 1 represents the people who are physically active at least 3 days a week (“yes”) and Population 2 represents the people who are not (“no”).

*Testing a hypothesis about difference of two population means*

Testing a hypothesis about difference of two population means

In the tabs below, click Population 1-2 to indicate that we are comparing two populations, then click the Test of Hypothesis tab. The default option in Rguroo is to do a test using a z-statistic; uncheck that box and instead check the Permutation Unscaled box to do a simulation-based test for the difference of means. Fill in the appropriate alternative hypothesis.

*Specifying the method and the alternative hypothesis*

Specifying the method and the alternative hypothesis

Step 4: Run the test and identify the p-value in the output

Now, we can Preview eye the Rguroo output for our hypothesis test. We can visualize the null distribution (the sampling distribution of the test statistic, assuming the null hypothesis is true) by finding in the output the graph labeled “Distribution of Permutation Replicates.”

  1. According to the graph, what is the p-value? How many replicates were generated, and how many of them produced a difference at least as great as the observed difference in sample means?

Step 5: Make a conclusion in context

A conclusion requires two steps. First, we must decide whether to reject the null hypothesis. Second, we must explain what that decision means in the context of our original question.

  1. Using our \(\alpha = 0.05\) significance level, do we have enough statistical evidence to reject the null hypothesis? What does this suggest about the difference in average weight between those who exercise at least three times a week and those who don’t?

This process is the standard workflow for performing hypothesis tests.

More Practice

  1. Construct and record a 95% confidence interval for the difference between the average weights of those who exercise at least three times a week and those who don’t, and interpret this interval in context of the data. This exercise uses the same data as in the previous section. To construct a bootstrap confidence interval using this data, click the Basics button to reopen the dialog box, select the Confidence Interval tab, and select the option Bootstrap Percentile.

  2. Calculate a 95% confidence interval for the average height in meters (height) and interpret it in context.

  3. Click on Basics, change the Confidence Level to 0.90, and obtain a new confidence interval for the same parameter at the 90% confidence level. Comment on the width of this interval versus the one obtained in the previous exercise.

  4. Conduct a hypothesis test evaluating whether the average height is different for those who exercise at least three times a week and those who don’t. Follow all steps in the workflow.

  5. Now, a non-inference task: Determine the number of different options there are in the dataset for the variable hours_tv_per_school_day.

  6. Come up with a research question evaluating the relationship between height or weight and sleep. Formulate the question in a way that it can be answered using a hypothesis test and/or a confidence interval for a difference of means. Report the statistical results, and also provide an explanation in plain language. Be sure to check all assumptions, state your \(\alpha\) level, and conclude in context.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Rguroo.com, the Rguroo.com logo, and all other trademarks, service marks, graphics and logos used in connection with Rguroo.com or the Website are trademarks or registered trademarks of Soflytics Corp. or Soflytics Corp. licensors and are not included under the CC-BY-SA license.