Homework_6
RMJ
2025-02-19
Code Outline
Step 1: generate a fake dataset using your chosen dataset as a model Step 2: generate relevant summary statistics Step 3: conduct a statistical test-regression anova Step 4: plot your data Step 5: use for loops to rerun your analysis but with changed parameters or sample sizes Step 6: store results from each loop and include a write-up
Dataset Description
For this assignment the chosen dataset will be one of video games released between 1980-2023. it includes the name of the game, the North American release date, the team, the rating, the gross numbner of reviews, the genre(s), the gross amount that i has been played, and the gross amount of current plays
Dataset Metadata
This dataset has the following liscense: Database Contents License (DbCL) v1.0
Source: https://www.kaggle.com/datasets/arnabchaki/popular-video-games-1980-2023?resource=download
Hypothesis and Thoughts
As a gamer myself I have some contextual observations that suggest that overtime there is less diversity of video game, that is to say the most popular games are all of the same or similar genre and that there are fewer genres released.
I’m also generally curious about a few relationships in the gamer data
- is there a relation between the Team that made the game and the review?
- is there a relation between the Team that made the game and the number of plays?
- is there a correlation between the Review score and the number of plays?
#bring in the libraries we need to run this ship
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(ggplot2)
library(MCMCglmm)## Warning: package 'MCMCglmm' was built under R version 4.4.2## Loading required package: Matrix
##
## Attaching package: 'Matrix'
##
## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack
##
## Loading required package: coda## Warning: package 'coda' was built under R version 4.4.2## Loading required package: ape## Warning: package 'ape' was built under R version 4.4.2##
## Attaching package: 'ape'
##
## The following object is masked from 'package:dplyr':
##
## where#and also since we'll be using ggplot we can set the theme to be a better aesthetic
theme_set(theme_bw(base_size = 16))# first we will load up the dataset
df <- read.csv(file = "../Datasets/games_edit.csv",header = TRUE,sep = ",")
#and check its general dimensions
dim(df)## [1] 1495 10#nice 1495 entries with 10 variables, lets take a peek
head(df)## Index Title
## 1 1104 Sekiro: Shadows Die Twice - GOTY Edition
## 2 43 Outer Wilds
## 3 369 Outer Wilds
## 4 819 Outer Wilds
## 5 28 Disco Elysium: The Final Cut
## 6 354 Disco Elysium: The Final Cut
## Team Release_Date Rating Number.of.Reviews
## 1 Activision-FromSoftware 28-Oct-20 4.6 173
## 2 Mobius Digital-Annapurna Interactive 28-May-19 4.6 1800
## 3 Mobius Digital-Annapurna Interactive 28-May-19 4.6 1800
## 4 Mobius Digital-Annapurna Interactive 28-May-19 4.6 1800
## 5 ZA/UM 1-May-20 4.6 1100
## 6 ZA/UM 1-May-20 4.6 1100
## Genres Plays_K Playing_K Release_year
## 1 Adventure-Brawler-RPG 1400 153 2020
## 2 Adventure-Indie-Puzzle-Simulator 7700 661 2019
## 3 Adventure-Indie-Puzzle-Simulator 7700 661 2019
## 4 Adventure-Indie-Puzzle-Simulator 7700 661 2019
## 5 Adventure-Indie-RPG 6000 1200 2020
## 6 Adventure-Indie-RPG 6000 1200 2020#and get a summary
summary(df)## Index Title Team Release_Date
## Min. : 0.0 Length:1495 Length:1495 Length:1495
## 1st Qu.: 373.5 Class :character Class :character Class :character
## Median : 754.0 Mode :character Mode :character Mode :character
## Mean : 752.5
## 3rd Qu.:1128.5
## Max. :1511.0
## Rating Number.of.Reviews Genres Plays_K
## Min. :0.700 Min. : 8.0 Length:1495 Min. : 8
## 1st Qu.:3.400 1st Qu.: 295.0 Class :character 1st Qu.: 1900
## Median :3.800 Median : 555.0 Mode :character Median : 4300
## Mean :3.718 Mean : 776.4 Mean : 6323
## 3rd Qu.:4.100 3rd Qu.:1000.0 3rd Qu.: 9100
## Max. :4.600 Max. :4300.0 Max. :33000
## Playing_K Release_year
## Min. : 0.0 Min. :1980
## 1st Qu.: 44.0 1st Qu.:2007
## Median : 115.0 Median :2014
## Mean : 270.3 Mean :2012
## 3rd Qu.: 302.0 3rd Qu.:2019
## Max. :3800.0 Max. :2023#we can do some quick summary statistics to see the spread of data
#we can check how many video games were released by year
hist(df$Release_year,breaks = 43)
#and the number of plays
hist(df$Plays_K)
#and the number of playing
hist(df$Playing_K)
#our data has a large time component, we can use this to track trends overtime
#lets see how the ratings change overtime as an example
ggplot(data = df,aes(x=Release_year,y=Rating,group = Release_year))+geom_boxplot()
ggplot(data = df,aes(x=Release_year,y=Rating,group = Release_year,colour = Rating))+geom_point()+scale_color_viridis_c()
var(df$Rating)## [1] 0.2834122Interesting! The bulk of the ratings across the years are above 3! There are of course some outliers, some true bombers, but the data are definitely skewed towards higher ratings. It does look like there might be a minor trend towards increasing negative reviews as years go on. we can check with ANOVA to see if there is any significance
res_aov <- aov(Rating ~ Release_year,
data = df
)
summary(res_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Release_year 1 0.1 0.08842 0.312 0.577
## Residuals 1493 423.3 0.28354This suhggests that no, there is no statistical significance between the year and the rating.
Ok lets dive a bit more into out hypotheses. We want to know first if there is a lack of diversity in game genres across time
# we will start by getting a general sense of the genres out there
ggplot(data = df, aes(x = Genres)) +
geom_bar()
Ah, as this shows because the genres are so mixed, there are a lot of them. 250 to be exact. lets filter the data a bit but first lets actually see how many unique genres there are each year
#group the data and count the genres by year
df.e <- df
df.e$count <- 1
df.g.year <- df.e %>%
group_by(Release_year,Genres) %>%
summarise(unique_types = sum(count))## `summarise()` has grouped output by 'Release_year'. You can override using the
## `.groups` argument.#and plot the counts
ggplot(data = df.g.year,aes(x=Release_year,y=unique_types))+geom_bar(stat = 'identity')
#first out of curiousity
#lets create a list of the most popular genres
pop <- unique(df$Genres)[(table(df$Genres)>10)]This data suggests that our hypothesis about the diversity of video game genres decreasing overtime seems to be at least partially incorrect! We see a clear trend upwards in the number of unique genres> not ethat 2023 should not be counted because at the time this data was acquired 2023 was not complete. So from 1980-2022 we see a noticable increase in video game genre diversity. But is there significance?
res_aov <- aov(unique_types ~ Release_year,
data = df.g.year
)
summary(res_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Release_year 1 49.1 49.10 18.36 2.05e-05 ***
## Residuals 800 2139.1 2.67
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1and we have significance!!
Relationship analysis
we have a few questions about relations which we can analyze through a general correlation analysis
- is there a relationship between the Team that made the game and the review score?
- is there a relationship between the Team that made the game and the number of plays?
- is there a correlation between the Review score and the number of plays?
#lets check how many teams there are
numteam <- table(df$Team)
#ok that is way too many lets think of a way to shrink them down. how about by popularity
df.g.team <- df.e %>%
group_by(Team) %>%
summarise(t.plays = sum(Plays_K))
hist(df.g.team$t.plays)
#thats still too many, maybe if we use the number of games made instead
df.g.team <- df.e %>%
group_by(Team) %>%
summarise(game.counts = sum(count))
hist(df.g.team$game.counts)
#much more reasonable. we can filter out teams that only have made 5 or more games
hiT <- unique(df.g.team$Team)[(df.g.team$game.counts>=5)]
df.teams <- filter(df, Team %in% hiT)
ggplot(data = df.teams,aes(x=Team,y=Rating,group = Team) )+geom_boxplot()+geom_point(aes(colour = Rating))+scale_color_viridis_c()
unfortunately the team names are too long to effectively display so we
won’’t rotate them, but the spread does show that each team may have a
spread of review scores i.e. most teams do not only make highly reviewed
games. an interesting observation too is that it appears as though the
more games that a team makes, the greater the spread of ratings (though
not always)
res_aov <- aov( Rating ~ Team,
data = df.teams
)
summary(res_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Team 45 50.87 1.131 5.889 <2e-16 ***
## Residuals 347 66.61 0.192
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1This is mostly just to verify that YES the team does matter in regards to the rating.
ggplot(data = df.teams,aes(x=Team,y=Plays_K,group = Team) )+geom_boxplot()+geom_point(aes(colour = Plays_K))+scale_color_viridis_c()
And this shows another big spread of data where each team had a wide array of number of plays
res_aov <- aov( Plays_K ~ Team,
data = df.teams
)
summary(res_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Team 45 9.129e+09 202867051 9.212 <2e-16 ***
## Residuals 347 7.642e+09 22021709
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1And this is also significant
Lastly because the both the variables are numeric we can do a proper correlation analysis between the reviews and the number of plays
cor(df$Rating, df$Plays_K,
method = "spearman"
)## [1] 0.1687317Interesting! So this suggests a fairly weak correlation between the rating and the number of plays which isn’t what I expected. Lets vizualize
ggplot(data = df,aes(x=Rating,y=Plays_K))+geom_jitter(aes(colour = Plays_K))+scale_color_viridis_c()
And this supports what we are seeing in the correlation analysis. There
is a general trend upwards however, the data are skewed to a high rating
with a relatively low play.
We can also check to see if there is a relationship between the rating and the number of reviews as well as the number of reviews and the number of plays
#plot the rating vs the number of reviews
ggplot(data = df,aes(x=Rating,y=Number.of.Reviews))+geom_jitter(aes(colour = Number.of.Reviews))+scale_color_viridis_c()
res_aov <- aov( Number.of.Reviews ~ Rating,
data = df)
summary(res_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Rating 1 141096808 141096808 371.5 <2e-16 ***
## Residuals 1493 567005382 379776
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#and plot the number of reviews vs the number of plays
ggplot(data = df,aes(x=Number.of.Reviews,y=Plays_K))+geom_jitter(aes(colour = Plays_K))+geom_smooth()+scale_color_viridis_c()## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
res_aov <- aov( Number.of.Reviews ~ Plays_K,
data = df)
summary(res_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Plays_K 1 471339837 471339837 2972 <2e-16 ***
## Residuals 1493 236762353 158582
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1There does appear to be a trend that the more reviews there are the more plays there typically are as well, however we cannot ignore the bulking of the data which are concentrated in the <1000 reviews and <10000 plays area.
it is also worth noting that the number of reviews is typically much smaller than the number of plays (which doesn’t equate to the number of players necessarily) but this suggests that the number of reviews is a small subset of the total possible reviewers
df <- df %>% mutate(play.to.review=(Number.of.Reviews/Plays_K))
hist(df$play.to.review)
finding normal review structure
From our observations we can see that the reviews skew to the right towards 5 i.e. people who do rate disproportionately rate high. As an analysis lets see what a normal distribution of different sample sizes up to the total number of reviews would be based on the mean rating that we observe
#first we will look at our distribution
hist(df$Rating,breaks=20,xlim = c(1,5))
#get the average rating and variance
mean.rating <- mean(df$Rating)
var.rating <- var(df$Rating)
#and the total number of reviews
sum.rev <- sum(df$Number.of.Reviews)
hist(rtnorm(sum.rev,mean=mean.rating,lower=1,upper=5),col="gray")
#This isn't a true representation though as the rating in this dataset is an amalgamation of the number of reviews, the average of an average. let's instead create a for loop to see how this changes as change the number of possible reviews
z <- c(100,1000,1500,5000,10000,50000,10000)
for(i in 1:length(z)){
set.seed(666)
hist(rtnorm(z[i],mean=mean.rating,lower=1,upper=5),col="gray")
cat("the mean of the data is=", mean(rtnorm(z[i],mean=mean.rating,lower=1,upper=5)),"\n")
}
## the mean of the data is= 3.597865
## the mean of the data is= 3.541642
## the mean of the data is= 3.545738
## the mean of the data is= 3.557799
## the mean of the data is= 3.529601
## the mean of the data is= 3.536589
## the mean of the data is= 3.529601As we can see from the output, with our mean if the data were normal we would expect that between 3.75-4 would be our most frequent bin, which is less than our actual data.
As a last analysis lets see how the mean review changes when we sample randomly and increase the random sample size (of our actual data)
z <- c(5,10,20,50,100,200,500,1000)
for(i in 1:length(z)){
set.seed(666)
df.ran <- sample_n(df,z[i])
mm <- mean(df.ran$Rating)
vv <- var(df.ran$Rating)
n <- runif(z[i],min = 1,max = 5)
mm.n <- mean(n)
vv.n <- var(n)
cat("at a sample size of",z[i], "the mean rating is", mm, "and the variance is", vv,"the normal mean is",mm.n,"and the normal variance is", vv.n,"\n")
}## at a sample size of 5 the mean rating is 3.76 and the variance is 0.048 the normal mean is 2.250918 and the normal variance is 1.716584
## at a sample size of 10 the mean rating is 3.76 and the variance is 0.07822222 the normal mean is 2.866351 and the normal variance is 2.000215
## at a sample size of 20 the mean rating is 3.725 and the variance is 0.0725 the normal mean is 3.349179 and the normal variance is 0.9132684
## at a sample size of 50 the mean rating is 3.724 and the variance is 0.1708408 the normal mean is 3.104717 and the normal variance is 1.378083
## at a sample size of 100 the mean rating is 3.745 and the variance is 0.2374495 the normal mean is 2.826366 and the normal variance is 1.233508
## at a sample size of 200 the mean rating is 3.747 and the variance is 0.2689357 the normal mean is 3.101026 and the normal variance is 1.253976
## at a sample size of 500 the mean rating is 3.7408 and the variance is 0.2526006 the normal mean is 2.949901 and the normal variance is 1.380475
## at a sample size of 1000 the mean rating is 3.7189 and the variance is 0.279172 the normal mean is 3.050816 and the normal variance is 1.306682As we can see, regardless of the sample size the mean stays the same but the variance increases and plateaus. The empirical mean is greater than the normal mean again suggesting the skew of the data.
Summary
In this analysis we examined a few aspects of our gaming dataset that will be summarized here.
Hypothesis: There is a decrease in video game genres (less video game diversity) over time. verdict: FALSE
We found that in fact the number of video game genres increases over time. This may owe to the fact that video games are classified more liberally as time goes on (i.e. they are genre inclusive) but regardless, the types of video games from a mixed genre perspective was shown to increase.
Hypothesis: There is a relationship between the Team and the rating of the game. verdict: TRUE
While the data are highly variable in the amount of games attributed to each team we observed that there was statistical significance between the team and the rating implying that the ratings are not necessarily random. This does not directly convey whether certain teams only produce games of a certain rating more that the two variables are not independent.
Hypothesis: There is a correlation between the rating and the number of plays. verdict: FALSE
There is a weak correlation between the two variables which might be explained by the clustering of the data in that most data fall into the category of having few plays but a high rating
Hypothesis: There is a relationship between the number of plays and the number of reviews. Verdict: TRUE
There is a distinct positive trend that shows that games with more plays typically have more reviews. However, as with the previous hypothesis there is a skew in the data to games that have both a low number of plays and a low number of reviews.
Hypothesis: The distribution of reviews is not normal and skews higher. Verdict: TRUE
In compared to a normal distribution with the same mean we see that our data skews towards a overall higher review score. When randomly sampled the mean remained high as opposed to representing a more normal spread that would trend towrds the middle.
Conclusions: This dataset was an interesting exploration into how the ratings of video games relate to the number of plays and teams. We saw that ratings of video games tend to skew higher and away from the possible average and there is a large variability in play.