Load the data

movies <- read_csv(here::here("data", "movies.csv"))
glimpse(movies)

## Rows: 2,961
## Columns: 11
## $ title               <chr> "Avatar", "Titanic", "Jurassic World", "The Aveng…
## $ genre               <chr> "Action", "Drama", "Action", "Action", "Action", …
## $ director            <chr> "James Cameron", "James Cameron", "Colin Trevorro…
## $ year                <dbl> 2009, 1997, 2015, 2012, 2008, 1999, 1977, 2015, 2…
## $ duration            <dbl> 178, 194, 124, 173, 152, 136, 125, 141, 164, 93, …
## $ gross               <dbl> 7.61e+08, 6.59e+08, 6.52e+08, 6.23e+08, 5.33e+08,…
## $ budget              <dbl> 2.37e+08, 2.00e+08, 1.50e+08, 2.20e+08, 1.85e+08,…
## $ cast_facebook_likes <dbl> 4834, 45223, 8458, 87697, 57802, 37723, 13485, 92…
## $ votes               <dbl> 886204, 793059, 418214, 995415, 1676169, 534658, …
## $ reviews             <dbl> 3777, 2843, 1934, 2425, 5312, 3917, 1752, 1752, 3…
## $ rating              <dbl> 7.9, 7.7, 7.0, 8.1, 9.0, 6.5, 8.7, 7.5, 8.5, 7.2,…

skim(movies)

Variable type: character

Variable type: numeric

# We use the duplicated() function to identify duplicates, and find that there are none
summary(duplicated(movies))

##    Mode   FALSE 
## logical    2961

director_rating <- movies %>% 
  filter(director %in% c("Steven Spielberg","Tim Burton"))

# We summarise data using mean and CI functions
director_rating2 <- director_rating %>%
  group_by(director) %>%
  dplyr::summarise(mean_rating = mean(rating),
            uci_rating = CI(rating)[1],
            lci_rating = CI(rating)[3])

# We use geom_errorbar and geom_react in order to reproduce the graph
ggplot(director_rating2, aes(x = mean_rating, y = reorder(director, mean_rating), colour=director)) +
  geom_point(size=5, show.legend = FALSE)+
  # We use geom_rect to draw overlapping sections
  geom_rect(aes(xmin=uci_rating[2], xmax=lci_rating[1], ymin=-Inf, ymax=Inf), colour = "light grey", alpha = 0.2)+
  
  # We use geom_errorbar to draw CI intervals
  geom_errorbar(aes(xmin = lci_rating, xmax = uci_rating), size=1.3, width=.05, show.legend = FALSE)+
  geom_text(aes(label = round(lci_rating,2), x = lci_rating), size= 4.5, vjust = -1, colour ="black")+
  geom_text(aes(label = round(mean_rating,2), x = mean_rating), size= 6, vjust = -1, colour ="black")+
  geom_text(aes(label = round(uci_rating,2), x = uci_rating), size= 4, vjust = -1, colour ="black")+
  
  labs(x="Mean IMBD Rating", 
       y= "", title= "Do Spielberg and Burton have the same mean IMDB ratings?", 
       subtitle= "95% confidence intervals overlap")+
  theme_bw()+
  NULL

In addition, we run a hypothesis test using both the t.test command and the infer package to simulate from a null distribution, where we assume zero difference between the two.

Hypothesis testing

director_rating <- movies %>%
    filter(director %in% c("Steven Spielberg","Tim Burton")) # select directors
  t.test(rating~director, director_rating)

## 
##  Welch Two Sample t-test
## 
## data:  rating by director
## t = 3, df = 31, p-value = 0.01
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.16 1.13
## sample estimates:
## mean in group Steven Spielberg       mean in group Tim Burton 
##                           7.57                           6.93

First, we use the t.test to calculate the p-Value. We conclude that there is a statistically significant difference in means, since our p-value is 0.01 and hence |p|<a (where a=0.05) (or |t| > 2.00). Therefore, we reject the null hypothesis. Now we run the simulation with the infer package:

set.seed(1234) # We set a specific seed value

# We run a simulation with infer package

director_hypothesis_test<- director_rating %>%
  
  specify(rating ~ director) %>%
  
  # Here, `hypothesize` is used to set the null hypothesis as a test for independence, i.e., that there is no difference between the two population means.
  hypothesise(null="independence") %>% 
  # The `type` argument within generate is set to permute, which is the argument when generating a null distribution for a hypothesis test.
  generate(reps=1000, type="permute") %>% 
  #calculate the observed difference in means with bootstrap
  calculate(stat="diff in means",order = c("Steven Spielberg","Tim Burton"))


diff_rating <- director_rating %>% 
  specify(rating ~ director) %>% 
  calculate(stat = "diff in means", order = c("Steven Spielberg","Tim Burton"))
#get p_Value through infer package 
director_p_value <- director_hypothesis_test %>% 
    get_p_value(obs_stat = diff_rating[1,1], direction = "both")

kbl(director_p_value,col.names=c("p-value"), caption="Simulation-based null distribution using the 'infer' package") %>%
kable_styling()

Again, on the basis of this simulation-based hypothesis test we reject the null hypothesis stating that there is no difference in means of IMDB rating for Spielberg films and for Burton films as the p-Value is smaller than the alpha value (0.05). Therefore there is statistically significant difference between the mean ratings of the films of the two film directors. We visualise the simulation-based null distribution:

#We calculate CI using infer package
director_percentile_ci <- director_hypothesis_test %>%
  get_confidence_interval(level = 0.95, type = "percentile")

#We show a plot with shaded confidence interval using infer package
director_hypothesis_test %>% visualise() +
  
  shade_confidence_interval(endpoints = director_percentile_ci, size=0.4, color= "yellow", fill="light yellow") +
  shade_p_value(obs_stat = diff_rating, direction = "both", size=1.1) +
  
  labs(title = "Are Spielberg and Burton Equally Good Directors?", 
       subtitle="Simulation-based null distribution: the p-value (red) lies well outside the null distribution (yellow), allowing us to reject the null hypothesis", x="Difference in Mean IMDB Rating Between Directors", y="Count")+theme_fivethirtyeight() + theme(axis.title = element_text()) + scale_x_continuous(breaks=seq(-1.0, 1.0, by = 0.1), limits=c(-1.0,1.0))

In the graph it is shown that the p-value is outside of the 95% confidence interval (alpha = 0.05). We therefore reject the null hypothesis (H0) that there is no difference in the mean IMDB ratings of the films of Tim Burton and Steven Spielberg.