Getting Started

Load packages

In this lab we will explore the data using the dplyr package and visualize it using the ggplot2 package for data visualization. The data can be found in the companion package for OpenIntro labs, oilabs.

Let’s load the packages.


Creating a reproducible lab report

To create your new lab report, start by opening a new R Markdown document… From Template… then select Lab Report from the oilabs package.

The data

In 2004, the state of North Carolina released a large data set containing information on births recorded in this state. This data set is useful to researchers studying the relation between habits and practices of expectant mothers and the birth of their children. We will work with a random sample of observations from this data set.

Load the nc data set into our workspace.


We have observations on 13 different variables, some categorical and some numerical. The meaning of each variable can be found by bringing up the help file:

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

Remember that you can answer this question by viewing the data in the data viewer or by using the following command:


Exploratory data analysis

We will first start with analyzing the weight gained by mothers throughout the pregnancy: gained.

Using visualization and summary statistics, describe the distribution of weight gained by mothers during pregnancy. The favstats function from mosaic can be useful.

favstats(~gained, data = nc)
  1. How many mothers are we missing weight gain data from?

Next, consider the possible relationship between a mother’s smoking habit and the weight of her baby. Plotting the data is a useful first step because it helps us quickly visualize trends, identify strong associations, and develop research questions.

  1. Make a side-by-side boxplot of habit and weight. What does the plot highlight about the relationship between these two variables?

The box plots show how the medians of the two distributions compare, but we can also compare the means of the distributions using the following to first group the data by the habit variable, and then calculate the mean weight in these groups using the mean function.

nc %>%
  group_by(habit) %>%
  summarise(mean_weight = mean(weight))

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


  1. Are all conditions necessary for inference satisfied? Comment on each. You can compute the group sizes with the summarize command above by defining a new variable with the definition n().

  2. Write the hypotheses for testing if the average weights of babies born to smoking and non-smoking mothers are different.

Next, we introduce a new function, inference, that we will use for conducting hypothesis tests and constructing confidence intervals.

inference(y = weight, x = habit, data = nc, statistic = "mean", type = "ht", null = 0, 
          alternative = "twosided", method = "theoretical")

Let’s pause for a moment to go through the arguments of this custom function. The first argument is y, which is the response variable that we are interested in: weight. The second argument is the explanatory variable, x, which is the variable that splits the data into two groups, smokers and non-smokers: habit. The third argument, data, is the data frame these variables are stored in. Next is statistic, which is the sample statistic we’re using, or similarly, the population parameter we’re estimating. In future labs we’ll also work with “median” and “proportion”. Next we decide on the type of inference we want: a hypothesis test ("ht") or a confidence interval ("ci"). When performing a hypothesis test, we also need to supply the null value, which in this case is 0, since the null hypothesis sets the two population means equal to each other. The alternative hypothesis can be "less", "greater", or "twosided". Lastly, the method of inference can be "theoretical" or "simulation" based.

For more information on the inference function see the help file with ?inference.

  1. Change the type argument to "ci" to construct and record a confidence interval for the difference between the weights of babies born to nonsmoking and smoking mothers, and interpret this interval in context of the data. Note that by default you’ll get a 95% confidence interval. If you want to change the confidence level, add a new argument (conf_level) which takes on a value between 0 and 1. Also note that when doing a confidence interval arguments like null and alternative are not useful, so make sure to remove them.

By default the function reports an interval for (\(\mu_{nonsmoker} - \mu_{smoker}\)) . We can easily change this order by using the order argument:

inference(y = weight, x = habit, data = nc, statistic = "mean", type = "ci", 
          method = "theoretical", order = c("smoker","nonsmoker"))

More Practice

  1. Calculate a 95% confidence interval for the average length of pregnancies (weeks) and interpret it in context. Note that since you’re doing inference on a single population parameter, there is no explanatory variable, so you can omit the x variable from the function.

  2. Calculate a new confidence interval for the same parameter at the 90% confidence level. You can change the confidence level by adding a new argument to the function: conf_level = 0.90. Comment on the width of this interval versus the one obtained in the previous exercise.

  3. Conduct a hypothesis test evaluating whether the average weight gained by younger mothers is different than the average weight gained by mature mothers.

  4. Now, a non-inference task: Determine the age cutoff for younger and mature mothers. Use a method of your choice, and explain how your method works.

  5. Pick a pair of variables: one numerical (response) and one categorical (explanatory). Come up with a research question evaluating the relationship between these variables. Formulate the question in a way that it can be answered using a hypothesis test and/or a confidence interval. Answer your question using the inference function, 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. (Note: Picking your own variables, coming up with a research question, and analyzing the data to answer this question is basically what you’ll need to do for your project as well.)

This is a product of OpenIntro that is released under a Creative Commons Attribution-ShareAlike 3.0 Unported. This lab was adapted for OpenIntro by Mine Çetinkaya-Rundel from a lab written by the faculty and TAs of UCLA Statistics.