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.
Each member of the team should:
lab-08-inference-smoking-YOUR_TEAM_NAME.lab-08.Rmd and Knit it.
Make sure it compiles without errors. The output will be in the file
markdown .md file with the same name.Let’s warm up with some simple exercises.
We’ll use the tidyverse package for much of the data wrangling and visualization, and the data lives in the openintro package. You can load them by running the following in your Console:
library(tidyverse)
library(openintro)The data can be found in the openintro package, and
it’s called ncbirths. Since the dataset is distributed with
the package, we don’t need to load it separately; it becomes available
to us when we load the package. You can find out more about the dataset
by inspecting its documentation, which you can access by running
?ncbirths in the Console or using the Help menu in RStudio
to search for ncbirths. You can also find this information
here.
In this lab we’ll be generating random samples. The last thing you want is those samples to change every time you knit your document. So, you should set a seed. There’s an R chunk in your R Markdown file set aside for this. Locate it and add a seed. Make sure all members in a team are using the same seed so that you don’t get merge conflicts and your results match up for the narratives.
The first step in the analysis of a new dataset is getting acquainted with the data. Make summaries of the variables in your dataset, determine which variables are categorical and which are numerical. For numerical variables, are there outliers? If you aren’t sure or want to take a closer look at the data, make a graph.
A 1995 study suggests that average weight of Caucasian babies born in
the US is 3,369 grams (7.43 pounds).1 Wen, Shi Wu, Michael S. Kramer, and Robert H. Usher.
“Comparison of birth weight distributions between Chinese and Caucasian
infants.” American Journal of Epidemiology 141.12 (1995): 1177-1187. In this dataset we only have information on
mother’s race, so we will make the simplifying assumption that babies of
Caucasian mothers are also Caucasian,
i.e. whitemom = "white".
We want to evaluate whether the average weight of Caucasian babies has changed since 1995.
Our null hypothesis should state “there is nothing going on”, i.e., no change since 1995: \(H_0: \mu = 7.43\) pounds.
Our alternative hypothesis should reflect the research question, i.e., some change since 1995. Since the research question doesn’t state a direction for the change, we use a two sided alternative hypothesis: \(H_A: \mu \ne 7.43\) pounds.
Create a filtered data frame called ncbirths_white
that contain data only from white mothers. Then, calculate the mean of
the weights of their babies.
Are the conditions necessary for conducting simulation-based inference satisfied? Explain your reasoning.
We will use simulation-based methods to calculate a confidence interval for the true mean weight of Caucasian babies in North Carolina in 2004, as well as test the hypotheses stated above.
ncbirths_white data set. Then:The above exercise will take a while — make sure every team member is contributing to the solution. That may mean getting up and all looking at the same computer!
Let’s first discuss how a hypothesis test using simulation would work. Our goal is to simulate a null distribution of sample means that is centered at the null value of 7.43 pounds. In order to do so, we
Note, we already did the first three steps in the previous section!
Every team member should be contributing to the solution for the above exercise!
This lab is adapted from material in the Data Science in a Box course by Mine Çetinkaya-Rundel licensed under a Creative Commons Attribution Share Alike 4.0 International. Visit here for more information about the license.