hw02-sol

Problem Set 2: Summarize global cesarean delivery rates and GDP across 137 countries Your name and student ID January 29, 2024 Instructions • Solutions will be released by Sunday, January 28th. • This semester, problem sets are for practice only and will not be turned in for marks. Helpful hints: • Every function you need to use was taught during lecture! You may need to revisit the lecture code to help you along by opening the relevant files on Datahub. Alternatively, you may wish to view the code in the condensed PDFs posted on the course website. Good luck! • Knit your file early and often to minimize knitting errors! If you copy and paste code for the slides, you are bound to get an error that is hard to diagnose. Typing out the code is the way to smooth knitting! We recommend knitting your file each time after you write a few sentences/add a new code chunk, so you can detect the source of knitting errors more easily. This will save you and the GSIs from frustration! • If your code runs off the page of the knitted PDF, be sure to fix this! If it doesn’t look right, go back to your .Rmd file and add spaces (new lines) using the return or enter key so that the code runs onto the next line. 1

Summarizing global cesarean delivery rates and GDP across 137 countries Introduction Recall from this week’s lab that we constructed bar charts and histograms to explore a data set that looked at global rates of cesarean delivery and GDP. If you need a refresher, you can view your knitted file from lab and remind yourself about what you found. In this week’s problem set, you will describe these distributions using numbers. You will investigate the mean and median of the distribution of GDP. You will also examine the distribution of cesarean delivery separately for countries of varying income levels. Lastly, you will describe the spread of the distributions using quartiles and make a box plot . Execute this code chunk to load the required libraries: library (readr) ## ## Attaching package: ' readr ' ## The following objects are masked from ' package:testthat ' : ## ## edition_get, local_edition library (dplyr) ## ## Attaching package: ' dplyr ' ## The following object is masked from ' package:testthat ' : ## ## matches ## The following objects are masked from ' package:stats ' : ## ## filter, lag ## The following objects are masked from ' package:base ' : ## ## intersect, setdiff, setequal, union library (ggplot2) Just like in lab, read in the data that is stored as a .csv file and assign it to an object called CS_data . We will also use dplyr’s mutate() to create the new cesarean delivery variable that ranges between 0 and 100: CS_data <- read_csv ( "data/cesarean.csv" ) ## Rows: 137 Columns: 7 ## -- Column specification -------------------------------------------------------- ## Delimiter: "," ## chr (4): Country_Name, CountryCode, Income_Group, Region ## dbl (3): Births_Per_1000, GDP_2006, CS_rate ## ## i Use ` spec() ` to retrieve the full column specification for this data. ## i Specify the column types or set ` show_col_types = FALSE ` to quiet this message. 2

1. [1 point] Fill in the blanks indicated by “—-” by saving the answer to each blank in the code chunk below. Make sure you capitalize correctly, as R is case-sensitive. The function mutate() takes the old variable called –(aa)– and multiplies it by –(bb)– to make a new variable called –(cc)– . aa <- "CS_rate" bb <- 100 cc <- "CS_rate_100" . = ottr :: check ( "tests/p1.R" ) ## ## All tests passed! 4

Investigate what would have happened had we not assigned the data using <- to CS_data . Re-run the code without the assignment operator and see what happens. # First, let ' s re-read in the data as we did in the previous chunk CS_data <- read_csv ( "data/cesarean.csv" ) ## Rows: 137 Columns: 7 ## -- Column specification -------------------------------------------------------- ## Delimiter: "," ## chr (4): Country_Name, CountryCode, Income_Group, Region ## dbl (3): Births_Per_1000, GDP_2006, CS_rate ## ## i Use ` spec() ` to retrieve the full column specification for this data. ## i Specify the column types or set ` show_col_types = FALSE ` to quiet this message. CS_data $ Income_Group <- forcats :: fct_relevel (CS_data $ Income_Group, "Low income" , "Lower middle income" , "Upper middle income" , "High income: nonOECD" , "High income: OECD" ) # Now, we try mutating again without the re-assignment to CS_data CS_data %>% mutate ( CS_rate_100 = CS_rate * 100 ) ## # A tibble: 137 x 8 ## Country_Name CountryCode Births_Per_1000 Income_Group Region GDP_2006 CS_rate ## <chr> <chr> <dbl> <fct> <chr> <dbl> <dbl> ## 1 Albania ALB 46 Upper middl~ Europ~ 3052. 0.256 ## 2 Andorra AND 1 High income~ Europ~ 42417. 0.237 ## 3 United Arab~ ARE 63 High income~ Middl~ 42950. 0.1 ## 4 Argentina ARG 689 High income~ Latin~ 6649. 0.352 ## 5 Armenia ARM 47 Lower middl~ Europ~ 2127. 0.141 ## 6 Australia AUS 267 High income~ East ~ 36101. 0.303 ## 7 Austria AUT 76 High income~ Europ~ 40431. 0.271 ## 8 Azerbaijan AZE 166 Upper middl~ Europ~ 2473. 0.076 ## 9 Belgium BEL 119 High income~ Europ~ 38936. 0.159 ## 10 Benin BEN 342 Low income Sub-S~ 557. 0.036 ## # i 127 more rows ## # i 1 more variable: CS_rate_100 <dbl> # check the variables in CS_data names (CS_data) ## [1] "Country_Name" "CountryCode" "Births_Per_1000" "Income_Group" ## [5] "Region" "GDP_2006" "CS_rate" Did CS_rate_100 get added to the data set? No. You can tell by using head(CS_data) to view the first few rows and notice that the variable hasn’t been added. This is because when we don’t assign the output to anything, it just prints it out for us to see. Nothing is saved. So, we want to save the output by assigning the result of the code to an object, which is CS_data in this case. In general, you want to use new object names at every significant step in your analysis as you work with your data, so that you have access to the specific data at all of those significant stages. However, if you are performing multiple small operations on the same dataset, you can overwrite the original object since you know you won’t be needing the in-between steps. See the example below. # This overwrites the original CS_data object CS_data <- CS_data %>% mutate ( CS_rate_100 = CS_rate * 100 ) 5

3. [1 point] Based on your answer, will the mean be approximately the “same”, “larger than”, or “smaller than” the median? Uncomment one of the possible choices. p3 <- ' larger than ' . = ottr :: check ( "tests/p3.R" ) ## ## All tests passed! 7

4. [3 points] Describe, in words, how the mean and median are calculated. • [1 point] Mean: add up all the measurement values and divide by their total observation count. • [2 points] Median: First, order the measurements by their value. If the total observation count is an odd number, the middle observation is the median. If an even number, add the two middle measurement values and divide by two to calculate the median. To calculate the mean and median in R, we can use the summarize() function from the dplyr package. The summarize() function is used any time we want to take a variable and use one number to summarize something about it, like with the mean or median. Below is the code to summarize the mean of all countries’ GDP_2006 and to print it to the screen. In the code, we name the mean mean_GDP and output the result: GDP_summary <- CS_data %>% summarize ( mean_GDP = mean (GDP_2006)) GDP_summary ## # A tibble: 1 x 1 ## mean_GDP ## <dbl> ## 1 11791. 8

6. [2 points] geom_vline() can be used to add the mean and the median to the histogram shown above. This geom_vline() adds a vertical line to the graph. You need to specify where to add the line by passing it an “x-intercept” argument. Remove the comments (i.e., the three “#”) from the code below and update the geom_vline() code to plot lines at the mean and median by telling it the mean and median estimates. The argument lty=1 (line type) will plot a solid line and lty=2 will plot a dashed line. For the purposes of this question, please assign the x-intercept to a plain NUMERIC value, not a variable or expression. p6 <- ggplot ( data = CS_data, aes ( x = GDP_2006)) + geom_histogram ( col = ' white ' , fill = ' sienna2 ' ) + xlab ( ' GDP in 2006 ' ) + theme_minimal () + geom_vline ( aes ( xintercept = 11790.67 ), lty= 1 ) + geom_vline ( aes ( xintercept = 3351.305 ), lty= 2 ) p6 ## ` stat_bin() ` using ` bins = 30 ` . Pick better value with ` binwidth ` . 0 10 20 30 40 0 25000 50000 75000 GDP in 2006 count . = ottr :: check ( "tests/p6.R" ) ## ## All tests passed! 10

Summarizing the distribution of cesarean delivery rates Recall the distribution of cesarean delivery rates across countries: ggplot ( data = CS_data, aes ( x = CS_rate_100)) + geom_histogram ( binwidth = 4 , col = "white" , fill = "sienna2" ) + xlab ( "Cesarean delivery rate (%)" ) + theme_minimal () 0 5 10 15 20 25 0 10 20 30 40 Cesarean delivery rate (%) count 11

There appears to be multiple peaks in the cesarean delivery rate histogram which may point to another variable influencing the distribution. We can make a separate histogram for each income group using the facet_wrap() function. 8. [1 point] Extend the ggplot code given below using the facet_wrap() statement to make a separate histogram for each level of the Income_Group variable. p8 <- ggplot ( data = CS_data, aes ( x = CS_rate_100)) + geom_histogram ( binwidth = 6 , col = "white" , fill = "sienna2" ) + xlab ( "Cesarean delivery rate (%)" ) + theme_minimal () + facet_wrap (. ~ Income_Group) p8 High income: nonOECD High income: OECD Low income Lower middle income Upper middle income 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 5 10 15 0 5 10 15 Cesarean delivery rate (%) count . = ottr :: check ( "tests/p8.R" ) ## ## All tests passed! 13

9. [2 points] Based on both this plot and the previous plot, describe why the data had two peaks. Many of the low and lower-middle income countries had CS rates < 10%, while the higher income counties have rates closer to 20%. 14

11. [2 points] Calculate the mean_CS and median_CS of CS_rate_100 using only one summarize() command. Assign this summary to a dataframe called CS_summary and then print the results by typing CS_summary . CS_summary <- CS_data %>% summarize ( mean_CS = mean (CS_rate_100), median_CS = median (CS_rate_100)) CS_summary ## # A tibble: 1 x 2 ## mean_CS median_CS ## <dbl> <dbl> ## 1 15.3 15.6 . = ottr :: check ( "tests/p11.R" ) ## ## All tests passed! 16

Measures of variation 12. [2 points] Use ggplot2 to make a boxplot of the distribution of CS_rate_100 . p12 <- ggplot ( data = CS_data, aes ( y = CS_rate_100)) + geom_boxplot ( col = "black" , fill = "sienna2" ) + theme_minimal () p12 0 10 20 30 40 -0.4 -0.2 0.0 0.2 0.4 CS_rate_100 # YOUR CODE HERE . = ottr :: check ( "tests/p12.R" ) ## ## All tests passed! 17

Double check that geom_boxplot() is making the box plot correctly. You can do this by adding horizontal lines to the plot at each number in your five number summary using geom_hline() . Because horizontal lines intercept the y-axis, geom_hline() requires the yintercept argument that you can set to each number in your summary. 14. [2 points] The code below includes one horizontal line at the minimum value shown in blue. Add the rest of the lines in the order denoted in question 13. p14 <- ggplot ( data = CS_data, aes ( y = CS_rate_100)) + geom_boxplot ( col = "black" , fill = "sienna2" ) + theme_minimal () + geom_hline ( aes ( yintercept = 0.4 ), col = "blue" ) + geom_hline ( aes ( yintercept = 5.1 ), col = "blue" ) + geom_hline ( aes ( yintercept = 15.6 ), col = "blue" ) + geom_hline ( aes ( yintercept = 23.3 ), col = "blue" ) + geom_hline ( aes ( yintercept = 45.9 ), col = "blue" ) p14 0 10 20 30 40 -0.4 -0.2 0.0 0.2 0.4 CS_rate_100 . = ottr :: check ( "tests/p14.R" ) ## ## All tests passed! 19

15. [4 points] Run the following code that adds two points to CS_data , makes a new dataset called CS_data_plus_2 , and redraws the box plot. How did the box plot change? Perform a calculation to justify why it changed. What are the newly-added features on the plot called? out_data <- tibble :: tribble ( ~ Country_Name, ~ CS_rate_100, "Point 1" , 90 , "Point 2" , 60 ) CS_data_plus_2 <- dplyr :: full_join (CS_data, out_data) ## Joining with ` by = join_by(Country_Name, CS_rate_100) ` ggplot ( data = CS_data_plus_2, aes ( y = CS_rate_100)) + geom_boxplot ( col = "black" , fill = "sienna2" ) 0 25 50 75 -0.4 -0.2 0.0 0.2 0.4 CS_rate_100 five_num_summary_new <- CS_data_plus_2 %>% summarize ( min = min (CS_rate_100), Q1 = quantile (CS_rate_100, 0.25 ), median = median (CS_rate_100), Q3 = quantile (CS_rate_100, 0.75 ), max = max (CS_rate_100) ) • [1pt] There are two points above the top whisker on the revised box plot. • [2pts calculation] These points must be larger than Q3 + 1.5*IQR. – The IQR = Q3-Q1 =23.65 - 5.2 = 18.45. – IQR times 1.5 = 27.675 20