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.
use "nc.dta"We have observations on 13 different variables, some categorical and some numerical. Each observation is a birth recorded in North Carolina.
Remember that you can answer this question by viewing the data in the Data Editor or by looking at the bottom right in the Properties window.
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 summarize function can be useful.
summarize gainedcodebook command is useful for finding missing values.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.
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 sort the data by the habit variable, and then calculate the mean weight separately for these groups using the summarize function.
bysort weight: summarize weightThere is an observed difference, but is this difference statistically significant? In order to answer this question we will conduct a hypothesis test.
Are all conditions necessary for inference satisfied? Comment on each. You can compute the group sizes with the summarize command above.
Write the hypotheses for testing if the average weights of babies born to smoking and non-smoking mothers are different.
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 the option (level(X)) where X is a value between 0 and 100.
By default the function reports an interval for the difference diff specified as (\(\mu_{nonsmoker} - \mu_{smoker}\)) .
ttest weight, by(habit)We can change this order by creating a new indicator variable, nonsmoker that is 0 for smokers and 1 for non-smokers. Then, we can use ttest with the new indicator variable.
generate nonsmoker = 1 if habit == 1
replace nonsmoker = 0 if habit == 2
ttest weight, by(nonsmoker)Calculate a 95% confidence interval for the average length of pregnancies (weeks) and interpret it in context. Hint: Try using the function mean.
Calculate a new confidence interval for the same parameter at the 90% confidence level. You can change the confidence level using the same level option discussed above. Comment on the width of this interval versus the one obtained in the previous exercise.
Conduct a hypothesis test evaluating whether the average weight gained by younger mothers is different than the average weight gained by mature mothers.
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.
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 Stata, 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.
This is a product of OpenIntro that is released under a Creative Commons Attribution-ShareAlike 3.0 Unported. This lab was adapted for Stata by Jenna R Krall and OpenIntro by Mine Çetinkaya-Rundel from a lab written by the faculty and TAs of UCLA Statistics.