RPubs link information

• Rpubs link: https://rpubs.com/dgoh/1237476

Introduction

• The video game industry continues to grow rapidly, with various platforms and genres driving global sales.
  
• Analyzing the factors that influence sales can help game developers and publishers understand market dynamics.
  
• This study will explore the relationship between video game platforms, genres, and global sales, providing insights into market preferences.

Introduction Cont.

• The analysis will focus on how global sales vary between different platforms (e.g., PlayStation, Xbox, etc.).
  
• We will investigate whether there is a connection between the genre of a game (e.g., Action, Sports, etc.) and the platform it was released on.
  
• This analysis will offer insights that could help companies make data-driven decisions on which platforms to target for specific genres.

Elden Ring image

Problem Statement

• Question 1: Is there a significant difference in global sales between video games released on two different platforms?
  
• Question 2: Is there an association between the genre of a video game and the platform it is released on?
  
• Approach: Statistical methods such as hypothesis testing and categorical association will be used to answer these questions.
  
• Specifically:
  • A t-test will be used to answer Question 1, as we are comparing the means of global sales between two platforms.
  • A chi-squared test of independence will be used to answer Question 2 to determine if there is an association between the genre and the platform of the video game.

Data

Data Source: Link to data source on Kaggle

• Key Variables:

  • Rank (Factor): Represents the popularity ranking based on the overall sales made for the video game. Ordinal Variable: Each unique rank (e.g. 1, 2, 99, etc.) represents a meaningful order.

  • Name (Character): Represents the name of the video game.

  • Year (Numeric): Represents the year of the video game’s release.

  • Genre (Character): Represents the genre of the video game (Action, Sports, RPG, etc.).

  • Platform (Factor): Represents the platform on which the video game was released (e.g., PlayStation, Xbox, PC). Levels: Each unique platform (e.g., PS4, Xbox One, PC) represents a level.

  • Genre (Factor): Represents the genre of the game (e.g., Action, Sports, RPG). Levels: Each unique game genre (Action, Adventure, Sports, etc.) represents a level in this factor. Like Platform, this variable will need to be treated as a factor.

  • Global_Sales, NA_Sales, EU_Sales, JP_Sales, Other_Sales (Numeric): Represents the total worldwide sales of the game (in millions). For instance, if Global_Sales is 1.5, it means the game sold 1.5 million units globally.

Import, clean and Prepare Data for Statistical Analysis

# Import data
vgSales <- read_csv('vgsales.csv', show_col_types = FALSE)

# Convert Platform and Genre to factors
vgSales$Platform <- as.factor(vgSales$Platform)
vgSales$Genre <- as.factor(vgSales$Genre)

# Check for missing Values
colSums(is.na(vgSales[, c("Platform", "Genre", "Global_Sales")]))

##     Platform        Genre Global_Sales 
##            0            0            0

# Check the number of games for each platform to ensure sample sizes > 30 
table(vgSales$Platform)

## 
## 2600  3DO  3DS   DC   DS   GB  GBA   GC  GEN   GG  N64  NES   NG   PC PCFX   PS 
##  133    3  509   52 2163   98  822  556   27    1  319   98   12  960    1 1196 
##  PS2  PS3  PS4  PSP  PSV  SAT  SCD SNES TG16  Wii WiiU   WS X360   XB XOne 
## 2161 1329  336 1213  413  173    6  239    2 1325  143    6 1265  824  213

# Check the number of games for each genre to ensure sample sizes  > 30 
table(vgSales$Genre)

## 
##       Action    Adventure     Fighting         Misc     Platform       Puzzle 
##         3316         1286          848         1739          886          582 
##       Racing Role-Playing      Shooter   Simulation       Sports     Strategy 
##         1249         1488         1310          867         2346          681

Descriptive Statistics and Visualisation for Platfrom vs Global Sales

# Group by Platform and summarize Global Sales statistics
platform_sales_summary <- vgSales %>%
  group_by(Platform) %>%
  summarise(
    Min = min(Global_Sales, na.rm = TRUE),
    Q1 = quantile(Global_Sales, probs = 0.25, na.rm = TRUE),
    Median = median(Global_Sales, na.rm = TRUE),
    Q3 = quantile(Global_Sales, probs = 0.75, na.rm = TRUE),
    Max = max(Global_Sales, na.rm = TRUE),
    Mean = mean(Global_Sales, na.rm = TRUE),
    SD = sd(Global_Sales, na.rm = TRUE),
    n = n(),
    Missing = sum(is.na(Global_Sales))
  )

# Display the summary statistics in a table format
kable(platform_sales_summary)

# Visualize Global Sales by Platform using a boxplot
ggplot(vgSales, aes(x = Platform, y = Global_Sales)) +
  geom_boxplot() +
  labs(title = "Distribution of Global Sales by Platform", x = "Platform", y = "Global Sales (in millions)") +
  theme_minimal() +
  theme(plot.title = element_text(size = 18),
        axis.text.x = element_text(size = 6),
        axis.text.y = element_text(size = 12),
        axis.title = element_text(size = 14))

Descriptive Statistics and Visualisation for Genre vs Global Sales

# Group by Genre and summarize Global Sales statistics
genre_sales_summary <- vgSales %>%
  group_by(Genre) %>%
  summarise(
    Min = min(Global_Sales, na.rm = TRUE),
    Q1 = quantile(Global_Sales, probs = 0.25, na.rm = TRUE),
    Median = median(Global_Sales, na.rm = TRUE),
    Q3 = quantile(Global_Sales, probs = 0.75, na.rm = TRUE),
    Max = max(Global_Sales, na.rm = TRUE),
    Mean = mean(Global_Sales, na.rm = TRUE),
    SD = sd(Global_Sales, na.rm = TRUE),
    n = n(),
    Missing = sum(is.na(Global_Sales))
  )

# Display the summary statistics for Genre
kable(genre_sales_summary)

# Visualize Global Sales by Genre using a boxplot
ggplot(vgSales, aes(x = Genre, y = Global_Sales)) +
  geom_boxplot() +
  labs(title = "Distribution of Global Sales by Genre", x = "Genre", y = "Global Sales (in millions)") +
  theme_minimal() +
  theme(plot.title = element_text(size = 18),
        axis.text.x = element_text(size = 8),
        axis.text.y = element_text(size = 12),
        axis.title = element_text(size = 14))

Hypothesis Testing 1

• Question 1: Is there a significant difference in global sales between video games released on two different platforms?
• Null Hypothesis (H0): The average global sales of video games on PS4 is equal to the average global sales on Xbox 360. \[H_0: \mu_1PS4 = \mu_2X360 \]
• Alternative Hypothesis (HA): The average global sales of video games on PS4 is different from the average global sales on Xbox 360. \[H_A: \mu_1PS4 \neq \mu_2X360 \]
• Check Assumptions:
  • Normality can be assumed for as from the previous slides (Slide 7), we can see that PS4 n = 336 and X360 n = 1265, which according to Central Limit Theorem (CLT), we can assume data normality if n > 30.
  • Equal Variance: Levene’s Test will be used to check if variances of global sales are equal between PS4 and XBOX360

# Subset the data for PS4 and Xbox 360
ps4_xbox <- vgSales[vgSales$Platform %in% c("PS4", "X360"), ]

# Perform Levene's test to check for equal variances
leveneTest(Global_Sales ~ Platform, data = ps4_xbox)

Hypothesis Testing 1 Cont.

Levene’s Test for Equal Variance:
If p > 0.05, we assume equal variances and proceed with a regular t-test.
If p < 0.05, we assume unequal variances and use the Welch’s t-test (which adjusts for unequal variances).

We can see from the Levene’s Test, p = 0.3068 > 0.05. Therefore, we can assume equal variance between Global Sales of PS4 and Global Sales of Xbox 360. So we can proceed with a regular t-test.

# Perform t-test assuming equal variances
t.test(Global_Sales ~ Platform, data = ps4_xbox, var.equal = TRUE)

## 
##  Two Sample t-test
## 
## data:  Global_Sales by Platform
## t = 0.53349, df = 1599, p-value = 0.5938
## alternative hypothesis: true difference in means between group PS4 and group X360 is not equal to 0
## 95 percent confidence interval:
##  -0.1418803  0.2478935
## sample estimates:
##  mean in group PS4 mean in group X360 
##          0.8276786          0.7746719

Interpretation of the T-Test Results:
From the output shown:

t-statistic (t = 0.53349): This value represents the number of standard deviations the difference between the means is from 0.

Degrees of freedom (df = 1599): This indicates the number of independent data points that went into calculating the t-statistic.

p-value (p = 0.5938): The p-value is 0.5938, which is greater than 0.05. This means we fail to reject the null hypothesis, indicating that there is no statistically significant difference in global sales between PS4 and Xbox 360.

Confidence Interval (-0.1418803 to 0.2478935): This shows the range in which the true difference in means lies with 95% confidence. Since the interval includes 0, it further confirms that there is no significant difference between the global sales of the two platforms.

Conclusion: The results indicate that the difference in global sales between PS4 and Xbox 360 is not statistically significant. The p-value of 0.5938 suggests that any observed difference in the means is likely due to random variation rather than a true underlying difference between the two platforms.

Reminder that: Null Hypothesis (H0): The average global sales of video games on PS4 is equal to the average global sales on Xbox 360.
Alternative Hypothesis (Ha): The average global sales of video games on PS4 is different from the average global sales on Xbox 360.

We fail to reject the null hypothesis, which indicates that there is no significant difference in global sales between PS4 and Xbox 360.

Therefore, the data do not provide sufficient evidence to support that the global sales of video games on PS4 are different from those on Xbox 360.

Hypothesis Testing 1 Mathematical Formulaes.

Hypothesis 1 (T-Test):
For a two-sample t-test, the formula for the t-statistic is:

\[ t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{s_p^2 \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} \] The pooled variance, \(s_p^2\), is a weighted average of the variances of the two groups, assuming equal variances between the groups. It is calculated as:

\[s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}\]

where \(s_1^2\) and \(s_2^2\) are the sample variances of each group, and \(n_1\) and \(n_2\) are the sample sizes of each group.

With Degrees of freedom: \[ df = n_1 + n_2 - 2 \]

Hypothesis Testing 2

• Question 2: Is there an association between the genre of a video game and the platform it is released on?
  
• Null Hypothesis (H0): There is no association between the genre of a video game and the platform it is released on.
  \[H_0: \text{Genre and Platform are independent} \]
• Alternative Hypothesis (HA): There is an association between the genre of a video game and the platform it is released on. \[H_A: \text{Genre and Platform are dependent (not independent)} \]

# Contingency table of Genre and Platform
contingency_table <- table(vgSales$Genre, vgSales$Platform)

# Chi-squared test
chisq.test(contingency_table)

## 
##  Pearson's Chi-squared test
## 
## data:  contingency_table
## X-squared = 5910, df = 330, p-value < 2.2e-16

Hypothesis Testing 2 Cont.

Interpretation of the Chi-Squared Test Results:
From the output shown:

Chi-Squared Statistic (\(X^2 = 5910)\): This value represents the sum of the squared differences between the observed and expected frequencies, normalized by the expected frequencies. It indicates how far the observed data deviate from the expected data under the null hypothesis of no association.

Degrees of Freedom (df = 330): The degrees of freedom for this test, calculated as \((r - 1)(c - 1)\), where \( r \) is the number of rows (genres) and \( c \) is the number of columns (platforms). This represents the number of independent comparisons that can be made in the contingency table.

p-value (p < 2.2e-16): The p-value is extremely small, effectively 0, which is much less than the significance level of 0.05. This means we reject the null hypothesis, indicating that there is a statistically significant association between Genre and Platform.

Conclusion: The results indicate a significant association between the genre of a video game and the platform it is released on. The p-value of p < 2.2e-16 suggests that the observed differences in the distribution of genres across platforms are unlikely to have occurred by chance alone. Therefore, we conclude that certain genres are more likely to be associated with specific platforms.

Reminder that: Null Hypothesis (H0): There is no association between the genre of a video game and the platform it is released on.
Alternative Hypothesis (HA): There is an association between the genre of a video game and the platform it is released on.
We reject the null hypothesis, which indicates that there is a significant association between genre and platform.

Therefore, the data provide strong evidence to suggest that the genre of a video game is associated with the platform it is released on, meaning that certain platforms may favor specific genres or vice versa.

Hypothesis Testing 2 Mathematical Formulaes.

Hypothesis 2 (Chi-Squared Test of Independence) Formula:
\[ \chi^2 = \sum \frac{(O_{ij} - E_{ij})^2}{E_{ij}} \] With Degrees of freedom:
\[ df = (r - 1)(c - 1) \]

Discussion

Major Findings:
This investigation explored the relationship between Platforms and Global Sales of video games, as well as the association between Genre and Platform. For Hypothesis 1, comparing PS4 and Xbox 360 sales, we found no statistically significant difference in average global sales between the two platforms. For Hypothesis 2, the chi-squared test revealed a statistically significant association between Genre and Platform, indicating that certain genres are more likely to be associated with specific platforms.

Strengths and Limitations:
- Strengths: This analysis used a large dataset, providing robust insights into video game sales across multiple platforms and genres. The use of both t-tests and chi-squared tests allowed us to examine relationships between different variables effectively.
- Limitations: The analysis focused only on select platforms for the t-test, limiting broader insights across all platforms. Additionally, the chi-squared test does not reveal the nature of the association (i.e., which specific genres are most popular on which platforms), only that an association exists. Additionally, the dataset might be slightly outdated and new data needs/should be collected to reflect the current state of the video game industry.

Future Directions:
Future research could involve:
1. Expanded platform comparisons: Conducting an analysis across multiple platforms (using ANOVA or similar methods) to provide a more comprehensive view of sales patterns.
2. Genre popularity by region: Examining whether certain genres are more popular in specific regions or among specific demographics.
3. Temporal trends: Analyzing how platform and genre associations change over time to understand trends in the gaming industry.

Conclusion:
The key takeaway from this investigation is that while global sales do not significantly differ between PS4 and Xbox 360, game genre is significantly associated with the platform it is released on. This suggests that platform choice may be influenced by genre-specific trends or audience preferences. Future investigations should explore these genre-platform relationships in greater depth to guide industry decisions on game development and platform-specific releases.

References

Base R: R Core Team (2024). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.

dplyr: Wickham H, François R, Henry L, Müller K, Vaughan D (2023). dplyr: A Grammar of Data Manipulation. R package version 1.1.4, https://CRAN.R-project.org/package=dplyr.

readr: Wickham H, Hester J, Bryan J (2024). readr: Read Rectangular Text Data. R package version 2.1.5, https://CRAN.R-project.org/package=readr.

magrittr: Bache S, Wickham H (2022). magrittr: A Forward-Pipe Operator for R. R package version 2.0.3, https://CRAN.R-project.org/package=magrittr.

knitr: Xie Y (2024). knitr: A General-Purpose Package for Dynamic Report Generation in R. R package version 1.48, https://yihui.org/knitr/.

Yihui Xie (2015) Dynamic Documents with R and knitr. 2nd edition. Chapman and Hall/CRC. ISBN 978-1498716963

Yihui Xie (2014) knitr: A Comprehensive Tool for Reproducible Research in R. In Victoria Stodden, Friedrich Leisch and Roger D. Peng, editors, Implementing Reproducible Computational Research. Chapman and Hall/CRC. ISBN 978-1466561595

tibble: Müller K, Wickham H (2023). tibble: Simple Data Frames. R package version 3.2.1, https://CRAN.R-project.org/package=tibble.

kable: Zhu H (2024). kableExtra: Construct Complex Table with ‘kable’ and Pipe Syntax. R package version 1.4.0, https://CRAN.R-project.org/package=kableExtra.

car: Fox J, Weisberg S (2019). An R Companion to Applied Regression, Third edition. Sage, Thousand Oaks CA. https://www.john-fox.ca/Companion/.