IMDB ratings: Differences between directors

We will explore whether the mean IMDB rating for Steven Spielberg and Tim Burton is the same or not. We produce the following graph to analyze any overlap in the 95% confidence intervals.

Reproduced graph:

#Prepare data and calculate confidence intervals
imdb_spielberg_burton <- imdb_movies %>%
  filter(director %in% c("Steven Spielberg", "Tim Burton" )) %>%
  group_by(director) %>%
  summarize(
    average_rating = mean(rating),
    sd_rating = sd(rating),
    count_movies = n(),
    t_critical = qt(0.975, count_movies-1),
    se = sd_rating/sqrt(count_movies),
    lower_ci = average_rating - t_critical*se,
    upper_ci = average_rating + t_critical*se
  )

#Use ggplot package to reproduce the required plot
ggplot(imdb_spielberg_burton, aes(x=average_rating, 
                                  y=director, 
                                  color=director)) +
  geom_point(size = 8)+
  geom_errorbarh(aes(xmax = upper_ci, 
                     xmin = lower_ci), 
                 height = 0.1, 
                 size=2)+
  annotate(geom = "rect", 
           xmin = 7.275, 
           xmax = 7.33, 
           ymin = -Inf, 
           ymax = Inf, 
           fill = "grey", 
           alpha=0.7)+
  scale_y_discrete(limits = c("Tim Burton","Steven Spielberg"))+
  theme_bw()+
  labs(
    title = "Do Spielberg and Burton have the same mean IMdB ratings?",
    subtitle = "95% confidence intervals overlap",
    x = "Mean IMdB Rating",
  )+
  geom_text(aes(label = round(average_rating,2)), 
            size = 7, 
            vjust = -2, 
            color = "black", 
            fontface = "bold")+
  geom_text(aes(label = round(lower_ci,2)), 
            size = 6, 
            vjust = -3,
            x = imdb_spielberg_burton$lower_ci,
            color = "black", 
            fontface = "bold")+
  geom_text(aes(label = round(upper_ci,2)), 
            size = 6, 
            vjust = -3,
            x = imdb_spielberg_burton$upper_ci,
            color = "black", 
            fontface = "bold")+
  theme(legend.position="none",
        plot.title = element_text(face = "bold", size = 18),
        plot.subtitle = element_text(size = 14, face = "bold"),
        axis.title.x = element_text(size = 14, face = "bold"),
        axis.title.y = element_text(size = 14, face = "bold"),
        axis.text.y = element_text(size = 14),
        axis.text.x = element_text(size = 12)
        )

From the graph we can see that the 95% confidence intervals for average IMdB ratings for Spielberg and Burton overlap.

In addition, we will run a hypothesis test:

I started by setting out my hypotheses followed by a t-test.

\(H_0: \mu_{Steven Spielberg}-\mu_{Tim Burton}= 0\) vs \(H_1: \mu_{Steven Spielberg}-\mu_{Tim Burton}\neq 0\)

director_data<- imdb_movies %>% 
  select(rating,director,title) %>%
  filter(director %in% c("Steven Spielberg","Tim Burton")) 

t.test(rating~director,data=director_data)

## 
##  Welch Two Sample t-test
## 
## data:  rating by director
## t = 2.7144, df = 30.812, p-value = 0.01078
## alternative hypothesis: true difference in means between group Steven Spielberg and group Tim Burton is not equal to 0
## 95 percent confidence interval:
##  0.1596624 1.1256637
## sample estimates:
## mean in group Steven Spielberg       mean in group Tim Burton 
##                       7.573913                       6.931250

t-stat= 3
p-value=0.01

From the Test statistics we reject the null hypothesis, as the p-value is less than 5%. In this case it is 1%, so we conclude that the mean IMDB rating for each director is different.

It seems that Steven Spielberg has a higher average IMDB rating than Tim Burton.