General Social Survey (GSS)

Instagram and Snapchat, by sex

These are the relevant steps to calculate 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. For reported NA values, the value in the new created variable is also NA.

#Creating a new variable 'Snap_Intsa'
snap_insta <- gss %>%
  mutate(snap_insta = if_else(snapchat == "NA" & instagrm == "NA", "NA", 
                              if_else(snapchat=="Yes" | instagrm == "Yes", "Yes", "No")))

2. Calculate the proportion of Yes’s for snap_insta among those who answered the question, i.e. excluding NAs.

#Calculating proportion of 'snap_insta' users
snap_insta %>%
  filter(snap_insta != "NA") %>%
  summarize(
    Proportion_Insta_Snap = count(snap_insta=="Yes") / n())

## # A tibble: 1 × 1
##   Proportion_Insta_Snap
##                   <dbl>
## 1                 0.375

3. Using the CI formula for proportions and thus constructing 95% CIs for men and women who used either Snapchat or Instagram

# CI for Male population
male_proportion <- snap_insta %>%
  filter(sex == "Male", snap_insta != "NA") %>%
  summarize(
    proportion = count(snap_insta == "Yes")/n(),
    se = sqrt((proportion*(1 - proportion)/n())),
    lower_ci = proportion - 1.96*se, #we are using normal distribution to approximate
                                     #binomial distribution and directly use 1.96 as the critical value
    upper_ci = proportion + 1.96*se) %>% 
  knitr::kable(caption = "95% CI for men who used either Snapchat or Instagram") %>%
  kableExtra::kable_styling()

# CI for Female population
female_proportion <- snap_insta %>%
  filter(sex == "Female", snap_insta != "NA") %>%
  summarize(
    proportion = count(snap_insta == "Yes")/n(),
    se = sqrt((proportion*(1 - proportion)/n())),
    lower_ci = proportion - 1.96*se,
    upper_ci = proportion + 1.96*se) %>% 
  knitr::kable(caption = "95% CI for women who used either Snapchat or Instagram") %>%
  kableExtra::kable_styling()

#print out CIs
male_proportion

female_proportion

As we observe the two confidence intervals do not overlap. This means that there is indeed a significant difference in the proportion of women using Snapchat or Instagram compared to men. A larger proportion of women tend to use these socials.

Twitter, by education level

Next, the population proportion of Twitter users by education level in 2016 is estimated:

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

1. A new variable bachelor_graduate is constructed that is Yes if the respondent has either a Bachelor or Graduate degree. I then calculated the proportion of bachelor_graduate who do (Yes) and who don’t (No) use twitter.

#tidy data and count
twitter_bachelor <- gss_degree %>%
  filter(bachelor_graduate == "Yes", twitter != "NA") %>%
  group_by(bachelor_graduate, twitter) %>%
  count()

#calculate proportions
twitter_bachelor_proportions <- twitter_bachelor %>%
  pivot_wider(names_from = twitter, values_from = n) %>%
  summarize(
    Bachelors_using_twitter = Yes/sum(Yes,No),
    Bachelors_not_using_twitter = 1 - Bachelors_using_twitter
  ) %>%
  select(c("Bachelors_using_twitter", "Bachelors_not_using_twitter")) %>% 
  knitr::kable(caption = "Proportions for bachelor graduates using and not using Twitter") %>%
  kableExtra::kable_styling()
  
twitter_bachelor_proportions

2. Using the CI formula for proportions I constructed two 95% CIs for bachelor_graduate vs whether they use (Yes) and don’t (No) use twitter.

#construct CI using formula
twitter_bachelor_95 <- twitter_bachelor %>%
  mutate(
    count = sum(twitter_bachelor$n),
    proportion = n/count,
    se_twitter = sqrt((proportion * (1-proportion))/count),
    lower_ci =  proportion - 1.96*se_twitter,
    upper_ci= proportion + 1.96*se_twitter) %>% 
  select(c("bachelor_graduate","twitter", "lower_ci", "upper_ci")) %>% 
  knitr::kable(caption = "95% CIs for bachelor graduates who use and do not use Twitter") %>%
  kableExtra::kable_styling()

twitter_bachelor_95

These two confidence intervals do not overlap. There is a significant difference in the proportion of bachelor graduates who do and who do not use Twitter. Therefore, we can make inferences about twitter usage according to whether people are bachelor graduates or not.

Email usage

Let’s 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.

#Creating a new variable 
email_time <- gss %>% 
  mutate(
    email = as.numeric(emailhr) * 60 + as.numeric(emailmin))

email_time

## # A tibble: 2,867 × 8
##    emailmin emailhr snapchat instagrm twitter sex    degree         email
##    <chr>    <chr>   <chr>    <chr>    <chr>   <chr>  <chr>          <dbl>
##  1 0        12      NA       NA       NA      Male   Bachelor         720
##  2 30       0       No       No       No      Male   High school       30
##  3 NA       NA      No       No       No      Male   Bachelor          NA
##  4 10       0       NA       NA       NA      Female High school       10
##  5 NA       NA      Yes      Yes      No      Female Graduate          NA
##  6 0        2       No       Yes      No      Female Junior college   120
##  7 0        40      NA       NA       NA      Male   High school     2400
##  8 NA       NA      Yes      Yes      No      Female High school       NA
##  9 0        0       NA       NA       NA      Male   High school        0
## 10 NA       NA      No       No       No      Male   Junior college    NA
## # … with 2,857 more rows

2. A visualisation of the distribution is seen below followed by summary statistics of the mean and the median number of minutes respondents spend on email weekly.

#Visualizing the new variable 'Email'
ggplot(email_time, 
       aes(x= email))+
  geom_density()+
  theme_bw() +
  labs (
    title = "Time Spent on email",
    x     = "Minutes spent on email weekly")                         

#calculate mean and median
email_time %>% 
  summarise(mean_email_time = mean(email, na.rm=TRUE),
            median_email_time = median(email, na.rm=TRUE))

## # A tibble: 1 × 2
##   mean_email_time median_email_time
##             <dbl>             <dbl>
## 1            417.               120

The median is a better measure since the density of time spent is significantly right skewed and extreme values in the right tail pull the mean away from the center. This skewness implies extreme outliers that don’t reflect the typical American’s email usage.
The median is less affected by such extreme values.

3. Using the infer package, I calculated a 95% bootstrap confidence interval for the mean amount of time Americans spend on email weekly.

#construct CI using bootstrap
set.seed(1998)
library(infer)

bootstrap_email <- email_time %>%
  specify(response = email) %>%
  generate(reps = 1000, type = "bootstrap") %>%
  calculate(stat = "mean")

bootstrap_ci <- bootstrap_email %>%
  get_ci(level = 0.95, type = "percentile") %>% 
  #"humanize" time units to [__ hrs __ mins]
  mutate(lower_ci = paste(paste(385 %/% 60, "hrs"), 
                          paste(385 %% 60, "mins")),
         upper_ci = paste(paste(448 %/% 60, "hrs"), 
                          paste(448 %% 60, "mins"))) %>%
  knitr::kable(caption = "95% CI for weekly email usage of Americans") %>%
  kableExtra::kable_styling()
bootstrap_ci

Since we are calculating weekly email, roughly 7 hours per week or 1 hour per day seems normal.