1 Climate change and temperature anomalies

If we wanted to study climate change, we can find data on the Combined Land-Surface Air and Sea-Surface Water Temperature Anomalies in the Northern Hemisphere at NASA’s Goddard Institute for Space Studies. The tabular data of temperature anomalies can be found here

To define temperature anomalies you need to have a reference, or base, period which NASA clearly states that it is the period between 1951-1980.

Run the code below to load the file:

weather <- 
  read_csv("https://data.giss.nasa.gov/gistemp/tabledata_v4/NH.Ts+dSST.csv", 
           skip = 1, 
           na = "***")

Notice that, when using this function, we added two options: skip and na.

  1. The skip=1 option is there as the real data table only starts in Row 2, so we need to skip one row.
  2. na = "***" option informs R how missing observations in the spreadsheet are coded. When looking at the spreadsheet, you can see that missing data is coded as "***". It is best to specify this here, as otherwise some of the data is not recognized as numeric data.

Once the data is loaded, notice that there is a object titled weather in the Environment panel. If you cannot see the panel (usually on the top-right), go to Tools > Global Options > Pane Layout and tick the checkbox next to Environment. Click on the weather object, and the dataframe will pop up on a seperate tab. Inspect the dataframe.

For each month and year, the dataframe shows the deviation of temperature from the normal (expected). Further the dataframe is in wide format.

You have two objectives in this section:

  1. Select the year and the twelve month variables from the weather dataset. We do not need the others (J-D, D-N, DJF, etc.) for this assignment. Hint: use select() function.

  2. Convert the dataframe from wide to ‘long’ format. Hint: use gather() or pivot_longer() function. Name the new dataframe as tidyweather, name the variable containing the name of the month as month, and the temperature deviation values as delta.

tidyweather <- weather %>%
  select(1:13) %>% 
  pivot_longer(cols =2:13,
               names_to = "Month",
               values_to = "delta")

Inspect your dataframe. It should have three variables now, one each for

  1. year,
  2. month, and
  3. delta, or temperature deviation.

1.1 Plotting Information

Let us plot the data using a time-series scatter plot, and add a trendline. To do that, we first need to create a new variable called date in order to ensure that the delta values are plot chronologically.

tidyweather <- tidyweather %>%
  mutate(date = ymd(paste(as.character(Year), Month, "1")),
         month = month(date, label=TRUE),
         year = year(date))

ggplot(tidyweather, aes(x=date, y = delta))+
  geom_point()+
  geom_smooth(color="red") +
  theme_bw() +
  labs (
    title = "Weather Anomalies"
  )

Is the effect of increasing temperature more pronounced in some months? Use facet_wrap() to produce a seperate scatter plot for each month, again with a smoothing line. Your chart should human-readable labels; that is, each month should be labeled “Jan”, “Feb”, “Mar” (full or abbreviated month names are fine), not 1, 2, 3.

It is sometimes useful to group data into different time periods to study historical data. For example, we often refer to decades such as 1970s, 1980s, 1990s etc. to refer to a period of time. NASA calcuialtes a temperature anomaly, as difference form the base periof of 1951-1980. The code below creates a new data frame called comparison that groups data in five time periods: 1881-1920, 1921-1950, 1951-1980, 1981-2010 and 2011-present.

We remove data before 1800 and before using filter. Then, we use the mutate function to create a new variable interval which contains information on which period each observation belongs to. We can assign the different periods using case_when().

comparison <- tidyweather %>% 
  filter(Year>= 1881) %>%     #remove years prior to 1881
  #create new variable 'interval', and assign values based on criteria below:
  mutate(interval = case_when(
    Year %in% c(1881:1920) ~ "1881-1920",
    Year %in% c(1921:1950) ~ "1921-1950",
    Year %in% c(1951:1980) ~ "1951-1980",
    Year %in% c(1981:2010) ~ "1981-2010",
    TRUE ~ "2011-present"
  ))

Inspect the comparison dataframe by clicking on it in the Environment pane.

Now that we have the interval variable, we can create a density plot to study the distribution of monthly deviations (delta), grouped by the different time periods we are interested in. Set fill to interval to group and colour the data by different time periods.

ggplot(comparison, aes(x=delta, fill=interval))+
  geom_density(alpha=0.2) +   #density plot with tranparency set to 20%
  theme_bw() +                #theme
  labs (
    title = "Density Plot for Monthly Temperature Anomalies",
    y     = "Density"         #changing y-axis label to sentence case
  )

So far, we have been working with monthly anomalies. However, we might be interested in average annual anomalies. We can do this by using group_by() and summarise(), followed by a scatter plot to display the result.

#creating yearly averages
average_annual_anomaly <- tidyweather %>% 
  group_by(Year) %>%   #grouping data by Year
  
  # creating summaries for mean delta 
  # use `na.rm=TRUE` to eliminate NA (not available) values 
  summarise(annual_average_delta = mean(delta, na.rm=TRUE)) 

#plotting the data:

ggplot(average_annual_anomaly, aes(x=Year, y= annual_average_delta))+
  geom_point()+
  
  #Fit the best fit line, using LOESS method
  geom_smooth() +
  
  #change to theme_bw() to have white background + black frame around plot
  theme_bw() +
  labs (
    title = "Average Yearly Anomaly",
    y     = "Average Annual Delta"
  )

1.2 Confidence Interval for delta

NASA points out on their website that

A one-degree global change is significant because it takes a vast amount of heat to warm all the oceans, atmosphere, and land by that much. In the past, a one- to two-degree drop was all it took to plunge the Earth into the Little Ice Age.

Your task is to construct a confidence interval for the average annual delta since 2011, both using a formula and using a bootstrap simulation with the infer package. Recall that the dataframe comparison has already grouped temperature anomalies according to time intervals; we are only interested in what is happening between 2011-present.

formula_ci <- comparison %>%
  filter(Year>=2011) %>%
  summarise( mean_averag_ann = mean(delta, na.rm = TRUE), 
             sd_averag_ann = sd(delta, na.rm = TRUE), 
             count = n(), 
             
             # get t-critical value with (n-1) degrees of freedom
             t_critical = qt(0.975, count-1),
             se = sd_averag_ann/sqrt(count),
             margin_of_error = t_critical * se,
             ci_low = mean_averag_ann - margin_of_error,
             ci_high = mean_averag_ann + margin_of_error
  )


formula_ci
## # A tibble: 1 x 8
##   mean_averag_ann sd_averag_ann count t_critical     se margin_of_error ci_low
##             <dbl>         <dbl> <int>      <dbl>  <dbl>           <dbl>  <dbl>
## 1            1.06         0.280   132       1.98 0.0244          0.0483   1.02
## # ... with 1 more variable: ci_high <dbl>
  #kable()
# use the infer package to construct a 95% CI for delta

What is the data showing us? Please type your answer after (and outside!) this blockquote. You have to explain what you have done, and the interpretation of the result. One paragraph max, please!

2 General Social Survey (GSS)

The General Social Survey (GSS) gathers data on American society in order to monitor and explain trends in attitudes, behaviours, and attributes. Many trends have been tracked for decades, so one can see the evolution of attitudes, etc in American Society.

In this assignment we analyze data from the 2016 GSS sample data, using it to estimate values of population parameters of interest about US adults. The GSS sample data file has 2867 observations of 935 variables, but we are only interested in very few of these variables and you are using a smaller file.

gss <- read_csv(here::here("data", "smallgss2016.csv"), 
                na = c("", "Don't know",
                       "No answer", "Not applicable"))

You will also notice that many responses should not be taken into consideration, like “No Answer”, “Don’t Know”, “Not applicable”, “Refused to Answer”.

We will be creating 95% confidence intervals for population parameters. The variables we have are the following:

  • hours and minutes spent on email weekly. The responses to these questions are recorded in the emailhr and emailmin variables. For example, if the response is 2.50 hours, this would be recorded as emailhr = 2 and emailmin = 30.
  • snapchat, instagrm, twitter: whether respondents used these social media in 2016
  • sex: Female - Male
  • degree: highest education level attained

2.1 Instagram and Snapchat, by sex

Can we estimate the population proportion of Snapchat or Instagram users in 2016?

  1. Create a new variable, snap_insta that is Yes if the respondent reported using any of Snapchat (snapchat) or Instagram (instagrm), and No if not. If the recorded value was NA for both of these questions, the value in your new variable should also be NA.
gss_add <- gss %>% 
  mutate(snap_insta = case_when(
    instagrm =="Yes" | snapchat =="Yes" ~ "Yes",
    instagrm =="No" & snapchat =="No" ~ "No",
  ))
  1. Calculate the proportion of Yes’s for snap_insta among those who answered the question, i.e. excluding NAs.
gss_add <- gss %>% 
  mutate(snap_insta = case_when(
    instagrm =="Yes" | snapchat =="Yes" ~ "Yes",
    instagrm =="No" & snapchat =="No" ~ "No",
  )) %>% 
summarise(count_yes= count(snap_insta=="Yes"),
          count_snap_insta = count(snap_insta),
          yes_prop = count_yes/count_snap_insta)
  1. Using the CI formula for proportions, please construct 95% CIs for men and women who used either Snapchat or Instagram
gss_add2 <- gss %>% 
   mutate(snap_insta = case_when(
    instagrm =="Yes" | snapchat =="Yes" ~ "Yes",
    instagrm =="No" & snapchat =="No" ~ "No",
  )) %>% 
  filter(snap_insta=="Yes") %>% 
  summarise(count_yes=n(),
          count_snap_insta_male = count(sex=="Male"),
          count_snap_insta_female = count(sex=="Female"),
          male_prop = count_snap_insta_male/count_yes,
          female_prop=count_snap_insta_female/count_yes
          )

2.2 Twitter, by education level

Can we estimate the population proportion of Twitter users by education level in 2016?.

There are 5 education levels in variable degree which, in ascneding order of years of education, are Lt high school, High School, Junior college, Bachelor, Graduate.

  1. Turn degree from a character variable into a factor variable. Make sure the order is the correct one and that levels are not sorted alphabetically which is what R by default does.
facto <- c("Lt high school", "High School", "Junior college", "Bachelor", "Graduate")
bach_degree <- gss %>% 
  arrange(factor(degree , levels = facto))
  1. Create a new variable, bachelor_graduate that is Yes if the respondent has either a Bachelor or Graduate degree. As before, if the recorded value for either was NA, the value in your new variable should also be NA.
facto1 <- c("Lt high school", "High School", "Junior college")
bach_degree1 <- bach_degree %>% 
  mutate(bachelor_graduate = case_when(
    degree== "Bachelor" | degree =="Graduate" ~ "Yes",
    #degree == facto1 ~ "No"
    degree %in% facto1 ~ "No"
  ))
  1. Calculate the proportion of bachelor_graduate who do (Yes) and who don’t (No) use twitter.
bach_degree2 <- bach_degree1 %>% 
  summarise(nomber =n(),
            count_bach_yes = count(bachelor_graduate=="Yes"),
            count_bach_no = count(bachelor_graduate=="No"),
            bach_yes_prop = count_bach_yes/nomber,
            bach_no_prop = count_bach_no/nomber,
            
            )
  1. Using the CI formula for proportions, please construct two 95% CIs for bachelor_graduate vs whether they use (Yes) and don’t (No) use twitter.
bach_degree3 <- bach_degree1 %>% 
  # filter(bachelor_graduate =="Yes") %>%  
  summarise(nomber =n(),
            count_bach_yes = count(bachelor_graduate =="Yes"),
            #count_bach_no = count(bachelor_graduate =="No"),
            bach_yes_prop = count_bach_yes/nomber,
            #bach_no_prop = count_bach_no/nomber,
            sd_yes = 2*bach_yes_prop,
            se_yes = sd_yes/sqrt(nomber),
            upper_ci_yes = bach_yes_prop + qt(0.975, nomber-1)*sd_yes
            )
bach_degree4 <- bach_degree1 %>% 
  # filter(bachelor_graduate =="Yes") %>%  
  summarise(nomber =n(),
            #count_bach_yes = count(bachelor_graduate =="Yes"),
            count_bach_no = count(bachelor_graduate =="No"),
            #bach_yes_prop = count_bach_yes/nomber,
            bach_no_prop = count_bach_no/nomber,
            sd_no = 2*bach_no_prop,
            se_no = sd_no/sqrt(nomber),
            lower_ci_no = bach_no_prop - qt(0.975, nomber-1)*sd_no
            )
  1. Do these two Confidence Intervals overlap?

2.3 Email usage

Can we estimate the population parameter on time spent on email weekly?

  1. Create a new variable called email that combines emailhr and emailmin to reports the number of minutes the respondents spend on email weekly.
  2. Visualise the distribution of this new variable. Find the mean and the median number of minutes respondents spend on email weekly. Is the mean or the median a better measure of the typical amoung of time Americans spend on email weekly? Why?
  3. Using the infer package, calculate a 95% bootstrap confidence interval for the mean amount of time Americans spend on email weekly. Interpret this interval in context of the data, reporting its endpoints in “humanized” units (e.g. instead of 108 minutes, report 1 hr and 8 minutes). If you get a result that seems a bit odd, discuss why you think this might be the case.
  4. Would you expect a 99% confidence interval to be wider or narrower than the interval you calculated above? Explain your reasoning.

3 Gapminder revisited

Recall the gapminder data frame from the gapminder package. That data frame contains just six columns from the larger data in Gapminder World. In this part, you will join a few dataframes with more data than the ‘gapminder’ package. Specifically, you will look at data on

You must use the wbstats package to download data from the World Bank. The relevant World Bank indicators are SP.DYN.TFRT.IN, SE.PRM.NENR, NY.GDP.PCAP.KD, and SH.DYN.MORT

4 ```{r, get_data, cache=TRUE}

5

6 # load gapminder HIV data

7 # hiv <- read_csv(here::here(“data”,“adults_with_hiv_percent_age_15_49.csv”))

8 # life_expectancy <- read_csv(here::here(“data”,“life_expectancy_years.csv”))

9

10 # get World bank data using wbstats

11 indicators <- c(“SP.DYN.TFRT.IN”,“SE.PRM.NENR”, “SH.DYN.MORT”, “NY.GDP.PCAP.KD”)

12

13

14 library(wbstats)

15

16 worldbank_data <- wb_data(country=“countries_only”, #countries only- no aggregates like Latin America, Europe, etc.

17 indicator = indicators,

18 start_date = 1960,

19 end_date = 2016)

20

21 # get a dataframe of information regarding countries, indicators, sources, regions, indicator topics, lending types, income levels, from the World Bank API

22 countries <- wbstats::wb_cachelist$countries


You have to join the 3 dataframes (life_expectancy, worldbank_data, and HIV) into one. You may need to tidy your data first and then perform [join operations](http://r4ds.had.co.nz/relational-data.html). Think about what type makes the most sense **and explain why you chose it**.

1. What is the relationship between HIV prevalence and life expectancy? Generate a scatterplot with a smoothing line to report your results. You may find faceting useful
1. What is the relationship between fertility rate and GDP per capita? Generate a scatterplot with a smoothing line to report your results. You may find facetting by region useful
1. Which regions have the most observations with missing HIV data? Generate a bar chart (`geom_col()`), in descending order.
1. How has mortality rate for under 5 changed by region? In each region, find the top 5 countries that have seen the greatest improvement, as well as those 5 countries where mortality rates have had the least improvement or even deterioration.
1. Is there a relationship between primary school enrollment and fertility rate?


# Challenge 1: Excess rentals in TfL bike sharing

Recall the TfL data on how many bikes were hired every single day. We can get the latest data by running the following


```r
url <- "https://data.london.gov.uk/download/number-bicycle-hires/ac29363e-e0cb-47cc-a97a-e216d900a6b0/tfl-daily-cycle-hires.xlsx"

# Download TFL data to temporary file
httr::GET(url, write_disk(bike.temp <- tempfile(fileext = ".xlsx")))
## Response [https://airdrive-secure.s3-eu-west-1.amazonaws.com/london/dataset/number-bicycle-hires/2021-03-16T17%3A22%3A42/tfl-daily-cycle-hires.xlsx?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJJDIMAIVZJDICKHA%2F20210329%2Feu-west-1%2Fs3%2Faws4_request&X-Amz-Date=20210329T233055Z&X-Amz-Expires=300&X-Amz-Signature=acf4b177ea63fc09690e3f7bf59876a585dbc01fbfe9c66932191c489fa99864&X-Amz-SignedHeaders=host]
##   Date: 2021-03-29 23:31
##   Status: 200
##   Content-Type: application/vnd.openxmlformats-officedocument.spreadsheetml.sheet
##   Size: 169 kB
## <ON DISK>  C:\Users\USER\AppData\Local\Temp\Rtmp4skoIl\file418c35441004.xlsx
# Use read_excel to read it as dataframe
bike0 <- read_excel(bike.temp,
                   sheet = "Data",
                   range = cell_cols("A:B"))

# change dates to get year, month, and week
bike <- bike0 %>% 
  clean_names() %>% 
  rename (bikes_hired = number_of_bicycle_hires) %>% 
  mutate (year = year(day),
          month = lubridate::month(day, label = TRUE),
          week = isoweek(day))

We can easily create a facet grid that plots bikes hired by month and year.

Look at May and Jun and compare 2020 with the previous years. What’s happening?

However, the challenge I want you to work on is to reproduce the following two graphs.

The second one looks at percentage changes from the expected level of weekly rentals. The two grey shaded rectangles correspond to the second (weeks 14-26) and fourth (weeks 40-52) quarters.

For both of these graphs, you have to calculate the expected number of rentals per week or month between 2015-2019 and then, see how each week/month of 2020 compares to the expected rentals. Think of the calculation excess_rentals = actual_rentals - expected_rentals.

Should you use the mean or the median to calculate your expected rentals? Why?

In creating your plots, you may find these links useful:

23 Deliverables

As usual, there is a lot of explanatory text, comments, etc. You do not need these, so delete them and produce a stand-alone document that you could share with someone. Knit the edited and completed R Markdown file as an HTML document (use the “Knit” button at the top of the script editor window) and upload it to Canvas.

24 Details

  • Who did you collaborate with: TYPE NAMES HERE
  • Approximately how much time did you spend on this problem set: ANSWER HERE
  • What, if anything, gave you the most trouble: ANSWER HERE

Please seek out help when you need it, and remember the 15-minute rule. You know enough R (and have enough examples of code from class and your readings) to be able to do this. If you get stuck, ask for help from others, post a question on Slack– and remember that I am here to help too!

As a true test to yourself, do you understand the code you submitted and are you able to explain it to someone else?

25 Rubric

Check minus (1/5): Displays minimal effort. Doesn’t complete all components. Code is poorly written and not documented. Uses the same type of plot for each graph, or doesn’t use plots appropriate for the variables being analyzed.

Check (3/5): Solid effort. Hits all the elements. No clear mistakes. Easy to follow (both the code and the output).

Check plus (5/5): Finished all components of the assignment correctly and addressed both challenges. Code is well-documented (both self-documented and with additional comments as necessary). Used tidyverse, instead of base R. Graphs and tables are properly labelled. Analysis is clear and easy to follow, either because graphs are labeled clearly or you’ve written additional text to describe how you interpret the output.