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.

In the following chunk of code, I used the eval=FALSE argument, which does not run a chunk of code; I did so that you can knit the document before tidying the data and creating a new dataframe tidyweather. When you actually want to run this code and knit your document, you must delete eval=FALSE, not just here but in all chunks were eval=FALSE appears.

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.

>TEAM ANSWER>

After breaking the data down into months it looks like for the most part the affect of increasing temperature is similar accross the board.

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 period 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"
  ))

head(comparison)

## # A tibble: 6 × 5
##    year month delta date       interval 
##   <dbl> <ord> <dbl> <date>     <chr>    
## 1  1881 Jan   -0.3  1881-01-01 1881-1920
## 2  1881 Feb   -0.21 1881-02-01 1881-1920
## 3  1881 Mar   -0.03 1881-03-01 1881-1920
## 4  1881 Apr    0.01 1881-04-01 1881-1920
## 5  1881 May    0.04 1881-05-01 1881-1920
## 6  1881 Jun   -0.32 1881-06-01 1881-1920

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(mean_delta = mean(delta,na.rm = TRUE)
            ) 

#plotting the data:
ggplot(average_annual_anomaly, aes(x=year, y= mean_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"
  )                         

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(interval == "2011-present")%>%
  group_by(interval)%>%
  summarise(mean_delta = mean(delta, na.rm=TRUE),
            sd_delta = sd(delta,na.rm=TRUE),
            count_delta = n(),
            se_delta = sd_delta/ sqrt(count_delta),
            t_critical = qt(0.975, count_delta - 1 ),
            lower = mean_delta - t_critical * se_delta,
            upper = mean_delta + t_critical * se_delta)

  # choose the interval 2011-present
  # what dplyr verb will you use? 

  # calculate summary statistics for temperature deviation (delta) 
  # calculate mean, SD, count, SE, lower/upper 95% CI
  # what dplyr verb will you use? 

#print out formula_CI
formula_ci

## # A tibble: 1 × 8
##   interval     mean_delta sd_delta count_delta se_delta t_critical lower upper
##   <chr>             <dbl>    <dbl>       <int>    <dbl>      <dbl> <dbl> <dbl>
## 1 2011-present       1.06    0.274         132   0.0239       1.98  1.01  1.11

library(infer)
library(tidyverse)

set.seed(1234)

# use the infer package to construct a 95% CI for delta

# bootstrap for MEAN rent
boot_comparison <- comparison %>%
  # Select 2-bedroom flat
  filter(interval == "2011-present") %>%
  
  # Specify the variable of interest
  specify(response = delta) %>%
  
  # Generate a bunch of bootstrap samples
  generate(reps = 1000, type = "bootstrap") %>%
  
  # Find the mean of each sample
  calculate(stat = "mean")

percentile_ci <- boot_comparison %>%
  get_ci(level = 0.95, type = "percentile")



visualize(boot_comparison) + 
  shade_ci(endpoints = percentile_ci,fill = "khaki")+
  geom_vline(xintercept = formula_ci$lower, colour = "red")+
  geom_vline(xintercept = formula_ci$upper, colour = "red")

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!

TEAM ANSWER

To create this visual we first used boot strapping to get a random sample of deltas from our dataset. After the bootstrap sample was created we used the sample to calculate a 95% confidence interval for the mean of deltas. On the graph the green lines show our bootstrapped confidence interval and tell us that we are 95% confident that the true mean delta is between about 1.016 and 1.12, while the red line (1.013; 1.108) show the calculated confidence interval from the sample.