Part I: Introduction

Animes are increasingly popular for the variety of themes and story lines they offer. The top anime website, MyAnimeList.com, gave each anime a score based on a number of factors. Our goal for this project was to identify what attributes were weighed heavily in the website’s scoring and ranking process. The dataset contained the top 250 animes ranked by MyAnimeList.com in early 2023, with the columns as 12 potential factors that the website employed for scoring. Since the ranking was based on the scores, we chose to study the relationships between the potential predictors and the scores.

The 12 potential predictors were: the animes’ rank, titles, popularity rank, genres, production studios, types of media, numbers of episodes, duration of episodes, airing start dates, airing end dates, numbers of members who added the animes to their lists, and the scores. We identified 6 categorical variables: the tiles, genres, production studios, types of media, and the start and ending dates, and 6 quantitative variables: overall anime ranking, popularity ranking, number of episodes, duration of a single episode, number of members who added the series to their lists, and the score.

We would like to explore three research questions: 1) Are relationships between the score and the animes’ popularity metrics? 2) Are there relationships between the score and the animes’ characteristics, including production studio, type of media, genre, and length? 3) In the higher dimensional space, what clusters and additional behavior would be observed and what combinations of predictors would be optimal for analysis?

##  [1] "Rank"       "Title"      "Popularity" "Genre"      "Studio"    
##  [6] "Type"       "Episodes"   "Duration"   "Start_date" "End_date"  
## [11] "Members"    "Score"

Part II: Research Questions

Question 1: Relationship between Anime Score and Popularity Metrics

Our first research question was whether the anime’s score on myAnimeList.come had relationships with level of popularity and number of times the anime was added to members’ lists. To explore this potential relationship, we made a scatterplot of the variables. We first conducted a log transformation on times added to lists to rectify the skewness of number of times the animes were added to lists.Then we categorized animes with popularity ranking within 300 to have high popularity, greater than 1000 to be low popularity, and 301-1000 to be medium popularity to better visualize the data.

The scatterplot showed that animes with relatively higher popularity ranks and were added to members’ lists more often tend to have slightly higher scores. Animes with high scores (>8.75) tended to be added to members’ lists more often and have high or medium popularity levels, except for a few with low popularity level. This was expected as animes that were received more attention could have had great reviews. A few animes with high scores were not added to lists too often. Most animes were scored between 8.25 and 8.50 with medium or high popularity levels and were added to lists for more than 162,755 (exp(12)) times. However, lower-scored animes came from all popularity levels and the entire range of times added to lists.

Research Question 2: Relationships between Anime Genre/Studio/Type of Media and Anime Scores

This research question is to explore whether the genre of animes or studio that they were produced by would have impact on their scores. Firstly, we want to find whether the average score changes over year given different genres of anime. We extracted the start year of each anime from variable Start_date in the data, and also all genres of anime. Group by year and genre, we calculated the average score of each type of genre in each year. To see their relationship, we plotted a heatmap with year on the x-axis and genre on the y-axis, colored by their average scores.

From this heatmap we can’t see any clear pattern of scores over years according to their genres. However, we can see some that genres such as Action, Sci-Fi, Award Winning, Drama, and Adventure have darker blue which indicate relative high average scores over years. Comedy, Sports and Slice of life genres seems to have a trend scoring higher in more recent years as their cells color getting darker, whereas genre Avant Garde, Award Winning and Adventure seem to have less high average scores in recent years than years before 2010. Nevertheless, none of these information we see on the heatmap can confirm a direct relationship between genres and scores. Therefore, we still need to run a chi-square test to verify if there is an association between genres and scores.

Then, we plotted a density curve on anime studios’ scores. We firstly found the top 10 studios with the most anime produced in this top 250 ranking animes. To see if there is any relationship between studio and score, we plotted the counts of different scores received by the selected 10 studios. The plot has scores on x-axis, counts of different scores on y-axis, and colored by studios.

## 
##  Pearson's Chi-squared test
## 
## data:  table_anime_genre_scores
## X-squared = 342, df = 324, p-value = 0.2356

Based on the chi-square test result, the test statistic is X-squared = 342, with degrees of freedom (df) = 324 and a p-value of 0.2356. Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis that there is no association between Genre and avg_score. This means that we do not have enough evidence to support the claim that there is a significant association between the two variables. In other words, the analysis does not provide enough evidence to support the claim that the distribution of avg_score across the different Genre categories is different than what we would expect by chance.

Here we ran a chi-square test on studio and average scores with null hypothesis that there is a significant association between average score and studio.

## 
##  Pearson's Chi-squared test
## 
## data:  table_top_studios
## X-squared = 90, df = 81, p-value = 0.2313

Based on the results of the chi-square test of independence on the top 10 studios and average scores, the p-value is 0.2313, which is greater than the conventional significance level of 0.05. Therefore, we fail to reject the null hypothesis that there is no association between the top 10 studios and average scores. In other words, there is not enough evidence to conclude that there is a significant relationship between the top 10 studios and average scores. It is possible that any observed differences in average scores between the studios are due to chance and not a true association.

Another potential factor affecting the score could be the duration. Since the total duration of animes for different types of media are different, we assume that there might be a relationship between anime total time and score according to different type of media. We used another faceted scatterplot to show the impact of type of media and anime total length (or duration) on score. We added a new quantitative variable named total_time to represent the total length of all episodes.

Looking at the plot results, we can see that anime given different types of media do have different length since most of the plots are clustered vertically. However, looking at each plot we have, there is no clear association between the total duration of anime and their scores. Comparing across plots, media types including OVA, Music and Special have scores lower than 8.5 expect for two outliers in Music adn Special types. ONA animes have higher scores than Music animes. Nevertheless, the most common types Movie and TV have animes distributed almost evenly across low, medium and high scores. Therefore, we cannot conclude any relationship between type of media and anime score.

Question 3: Higher Dimensional Behavior

To further explore relationships between the animes’ characteristics and the scores in the higher dimensional space, we conducted Principal Component Analysis.

We can see that there were 5 principal components generated.

From the scree plot, we identified that the first two principal components would explain 62.28% of the total variation. The elbow plot flattened out afterwards and there were not much additional benefits. We can then reduce the dimensionality of our data into 2 dimensions.

Plotting the relationship between the two principal components, we discovered that animes with lower scores tended to have higher values of PC1 and lower values of PC2, while animes with higher scores tended to have lower values of PC1 but spread across the range of PC2. Animes with medium scores had a somewhat even spread across the two ranges. We also noticed that, at the center of the plot, there was almost a linear relationship indicating that values of PC2 decreased with PC1 and there were many animes clustered around 0 for both components, especially for lower-scored animes.

To further explore the higher dimensional space, we made a PCA biplot. We identified that the variables duration pointed to the first quadrant, meaning that animes with high values of both principal components tended to have longer duration per episode and were mostly low-scored animes. This was expected as the audience could lose patience with long episodes. Members who added to added the animes to their lists and scores pointed to the second quadrant, meaning that animes with high PC2 and low PC1 tended to be added by more members and had higher scores. This observation was consistent with our previous scatter plot, as animes that interested more watchers could have had good reviews and thus higher scores. Episodes pointed to the third quadrant, meaning that animes with lower values of both principal components tended to have more episodes and contained mostly animes with high or medium scores. This was somewhat intuitive as popularity could incentive the production studio to continue the series. As for popularity rank, which pointed to the fourth quadrant and had low values of both principal components, we interpreted it as animes with both lower values of both components tended to be less popular (the higher numeric value of popularity rank, the less popular) and were low-scored animes.

## 
## Call:
## lm(formula = anime1$Score ~ anime1$Members)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33192 -0.16571 -0.03963  0.10513  0.64458 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    8.500e+00  1.785e-02 476.294  < 2e-16 ***
## anime1$Members 7.237e-08  1.888e-08   3.834  0.00016 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2013 on 245 degrees of freedom
## Multiple R-squared:  0.0566, Adjusted R-squared:  0.05275 
## F-statistic:  14.7 on 1 and 245 DF,  p-value: 0.0001604

Lastly, as we discovered that number of members who added the anime to their lists could be associated with the scores, we fit a simple linear regression between the two variables to formally confirm our observation. At alpha = 0.05, the model with significant with a F-statistic of 14.7 and p-value of 0.0001604. The predictor, number of members who added the anime to their lists, was also significant with a t-statistic fo 3.834 and p-value of 0.00016. Therefore, there was sufficient evidence to conclude a relationship between number of members who added the anime to their lists and the anime’s score, meaning that the members variable was important in the scoring process.

Part III: Conclusion

In this project, we focused on analyzing the relationship between the animes’ score and potential predictors, including popularity measures, genre, type of media, length, and also higher dimensional behaviors. Based on our research questions, we drew the following conclusions:

1. From the popularity perspective, there was a between popularity ranks and scores; animes that were added to members’ lists more often and had higher popularity level tended to have higher scores.

2. Although the plots showed possible weak associations, we could not find sufficient evidence to conclude that the animes’ production studios and genres had relationships with the scores. Also, we could not verify any association between anime duration or type of media on anime score with the plots.

3. From the higher dimension, using PCA analysis, we discovered that the first two principal components could explain most of the variations in data, and animes with high scores tended to have low PC1 and spread PC2. Medium-scored animes spread across both components, while lower-scored animes mostly had low PC1 and high PC2. As an extension, we also found a relationship between number of members who added the anime to their lists and the anime’s score, meaning that the members variable was important in the scoring process.

Our analysis explained part of MyAnimeList.com’s potential score generation approach. However, our analysis was extremely limited. More analysis could be conducted on the relationships between the variables themselves to explore whether multicollinearity could have masked some of the underlying relationships. Additionally, our analysis was limited to the top 250 animes, which may have similar rankings and scores, and our data analysis approaches may not have detected other underlying scoring components. Future work could involve analyzing more animes and their scores, including lowly-ranked ones, to discover differences and compare them to the top ones. Furthermore, future work may focus on analyzing the influence of the content of the animation on popularity.