## Getting Started

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.

library(dplyr)
library(ggplot2)
library(oilabs)

### 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.

data(nc)

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:

?nc
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:

glimpse(nc)

## 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.

library(mosaic)
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.

We can remove the missing habit and weight data with the following code. This step will make some analyses easier, but we should keep in mind that we have removed missing data. There might be important information in the missingness.

nc <- nc %>%
filter(!is.na(habit), !is.na(weight))
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.

## Inference

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 that equals 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, t.test, that we will use for conducting hypothesis tests and constructing confidence intervals.

t.test(weight ~ habit, data = nc)

Let’s pause for a moment to go through the arguments of this function. The first argument is a formula weight ~ habit, which is a formula where the response variable and explanatory variable are separated by the ~ symbol. The second argument, data, is the data frame these variables are stored in.

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

t.test has a series of default arguments. It is helpful to know the defaults such that you can change them if you want to. The code below gives us the same output on the much simpler code above, because all of the argunents in the code below are defaults of t.test.

t.test(weight ~ habit, data = nc, alternative = "two.sided",
mu = 0, paired = FALSE, var.equal = FALSE,
conf.level = 0.95)

First, we can ask for a one tailed test by changing the alternative = argument to "less" or "greater". The alternative hypothesis can be "less", "greater", or "two.sided". When performing a hypothesis test, we also need to supply the mu value, the null hypothesized value, which in this case defaults to 0, since the null hypothesis sets the two population means equal to each other. Next, we can change paired = to TRUE for a paired samples t-test, and we can change var.equal = to TRUE if we are assuming equal variances. Lastly, we can change the confidence level.

1. Using the t.test, 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.

## 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.

1. 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 t.test function, report the statistical results, and also provide an explanation in plain language. Be sure to check all assumptions 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.