Introduction

Welcome to the first problem set. There is not a great deal of material here, but since this may be your first time using R and R Markdown, there are many potential pitfalls, so leave yourself plenty of time to complete it. The idea here is not that you can sit down and answer these questions straight away, but that you have a week to figure it out, and this is a key part of the learning process.

If you are looking at the HTML version of the problem set (pset1.html) that may have opened in your web browser, you are seeing the ouput produced by running the “script”” or code called in the file pset1.rmd, also available on the course website. Go ahead and open the file called pset1.rmd. If it does not open automatically within R Studio, you can open R Studio first and then use the File menu to open up pset1.rmd. Once you open pset1.rmd, you can continue reading the text easily in that file.

It will be easiest for you to open the .rmd file posted for each pset, and start writing your solutions in by learning from the code you see in the questions.

Before you start: The R Markdown Introduction

The text, output and graphics in this section are provided as an example whenever you create a new R markdown (.rmd) file in R Studio. It’s a good quick introduction so I replicate it here with minor modification. At this point, you may not understand all of the R code being used here, but the goal is to understand how the .rmd file works and how it relates to the .html file that gets outputted.

Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com. (Here we have set the code to produce an HTML output, which is what you need to upload for this class).

When you click the Knit button a document will be generated that includes both the content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:

summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

You can also embed plots, for example:

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot. In general, you will not include the echo = FALSE, because we will want to see your code.

Submission Instructions

Please submit your problem set via Canvas. Submit both the .rmd file, and the HTML file it creates. This assignment is due by 11:59 PM on Friday October 11, 2024. Late problem sets will receive a penalty for each day of delay. Please list any students you collaborated with. Please disclose whether you employed ChatGPT to complete this assignment.

Example Problem

Here is an example problem, with an example solution.

Question 0. In this question, we’ll provide the answer for you, as an example. You need to be looking at the .rmd file right now for this to make much sense.

Showing your code and the result, execute the code getwd(). Describe what this command does. You may want to execute the command directly in the console first (ask your TA if you dont know how to run a command–this is essential) to see what it does, but be sure to write it into your .rmd file so that it runs when you click knit.

Solution: Question 0 

getwd()
## [1] "/home/jovyan"

This command, when executed (either in the console or through the .rmd file once you click ``knit’’), tells the user what directory is set as the working directory. This is the directory where output will be saved, or where R will look first when searching for a file, for example a dataset. You need to always set your working directory first so R knows where to pull the data from.

Make sure to try executing your .rmd file now by clicking knit. Then take a look at the HTML that it created and see what you get.

Okay, your turn to answer the remaining questions!

Part 1. Theory. Short answer questions (1 point each; 5 points total)

Start by reading Chapter 1 of the textbook, Real Stats. You can also review your lecture notes.

Q1. A researcher observes that countries with parliamentary systems have higher levels of income. She decides to publish a research article that says having this form of government causes countries to become richer. Would you like to be a co-author on this paper? Why or why not? (100 words max) I would not because while with observation you can claim an association between parliamentary systems and higher levels of income, you can’t claim a causation. The reason why is due to endogenous factors like how parliamentary systems are usually democracies which typically have higher GDP and income then regular countries. Q2. Explain what this sentence means: “Experiments create exogeneity via randomization.” (75 words max) This sentence mean that through randomly assigning a control and treatment group, your experiment break the relationship between the independent variable and error term allowing for exogenous experiments, i.e. the independent variable is associated wit the error term. Q3. What do we refer when we talk about the “internal validity” and “external validity” of experiments? (100 words max) When talking about “internal validity” of experiment we refer to how the experiment was well designed like we should be confidently be able say without hints of endogenous that X caused Y, is it free from confounding factors or bias. In terms of external validity we trying find if the results are generalizable and can you get the result outside of the situation of the experiment. Q4. You decide to run an experiment to see whether working in groups helps students learn. You randomly assign half of the class to form study groups to work on their problem sets. For the other half of the class, you assign them to work individually. At the end of the semester, you give the entire class a test. You find that the students in the first group did much better than those in the second group, who worked individually. (120 words max)

4a. What could you call each group? I’ll call the first group the Study Buddies and the second group The Loners 4b. What is your independent variable and what is your dependent variable? The independent variable is the way people study, individual vs study while the dependent variable is the outcome of student grades, to see whether working in groups helps student learn
4c. Given this set up, list some factors you are controlling for. I am controlling who gets to work together and who does not, I am controlling my selection which happen to be this specific class. 4d. Can you say that working in groups caused the students to do better on the test? Why or why not? Explain using the technical terms in the textbook. No we can not that working in groups caused the students to do better on the test due to not knowing the internal validity i.e. is there any confounders/bias and if the experiment has external validity i.e. can you get the same result or was it due to the specific situation. There also could be endogenity like study groups having overall better way of studying then individuals. 4e. Can you say that this finding would also apply in other types of courses (for example, writing-intensive classes)? Why or why not? Explain using the technical terms in the textbook. No because we don’t know the external validity of the result like writing-intensive classes. We need to run multiple randomized experiments to have exogenous i.e. help eliminate factors associate with the error term, and do them in different population or context to see if these result are generalizable . Q5. Imagine you are looking at the relationship between income and level of education. List some of the factors that could lead to endogeneity. (50 words max) There could be confounding factors with the more income you have the more likely you have enough money to go to college because tuition are expensive. There also the factor if someone has a successful family business they have no good reason to for higher education. ***** Part 2. Data Analysis (1/2 point each; 5 points total)

The decrease in infant mortality in the second half of the 20th century is one of the most relevant global development trends. What is the relationship between income and health outcomes?

We will use a dataset from “Our World in Data” (Saloni Dattani and Fiona Spooner and Hannah Ritchie and Max Roser, 2023) to explore this question.

Download the dataset, hdi_health.RData, which you’ll find on the course website. You may want to put it in your working directory to make it easy to find (use getwd() to see what your current working directory is; you can use the Session menu in Rstudio or the setwd() command to change your working directory.)

Here is a brief description of the variables:

As will often be the case when using R, you will need to use the $ operator to access these variables within the object. Specifically, once you have loaded hdi_health.RData, the result will be available in the data hdi_health. To get at the variable Entity, for example, you would use hdi_health$Entity. Remember, the end of each chapter in the textbook includes R code that can be helpful. We also posted R resources on Gauchospace.

Q1. Load the data into R. The data are stored as an Rdata file, so you can use the load() function to load it.

setwd("/home/jovyan")
load("hdi_health.Rdata")

Q2. Check the dimensions of the data (i.e. the number of rows and columns). How many observations are there? How many variables are there? There are 175 observation and 3 variables in the data. Q3. How many countries and territories are covered in this data set? There is 175 countries and territories covered in the data set Q4. Calculate the average of avg_hdi, which is mean Human Development Index for each country, across all points in the sample. Do you think this average is large or small? What is the minimum and the maximum avg_hdi?

mean(hdi_health$avg_hdi)
## [1] 0.6644084
min(hdi_health$avg_hdi)
## [1] 0.3097097
max((hdi_health$avg_hdi))
## [1] 0.9214194

The minimum is 0.3097097 of the avg hdi,the maximum is 0.9214194 in avg hdi and the “average” or mean is 0.6644084. The average is moderately large because when compared to the midrange of 0.6155623 it is greater than it meaning the average is skewed high and is closer to the maximum. Q5. Calculate the average infant mortality rate across all points in the sample. What does this tell you about the prevalence of infant mortality?

mean(hdi_health$avg_infant_mortality)
## [1] 5.062867

This tell me the prevalence of infant mortality is relatively low because lower income countries have more infant mortality rates and outnumber higher income countries on the chart, who have less kids and infant mortality.

Q6. Produce a simple scatterplot with Human Development Index on the horizontal axis and the average Infant Mortality Rate on the vertical axis.

plot(hdi_health$avg_hdi,hdi_health$avg_infant_mortality)

Q7. Make the plot again, but this time add a trend line (also known as a line of best fit or a regression line) using the abline() command.

plot(hdi_health$avg_hdi, hdi_health$avg_infant_mortality)
abline(lm(hdi_health$avg_infant_mortality~hdi_health$avg_hdi))

Q8. What does this line tell you about development and health outcomes? That there is an association that the more developed the country is the better the health outcomes for the babies. Q9. What could you call this relationship? I would say this chart has a negative correlation or a reverse relationship where the greater the development the less infant moralities.