Week 4 | Data Dive — Sampling and Drawing Conclusions
2024-09-23
data <- read.csv("C:\\Users\\gajaw\\OneDrive\\Desktop\\STATS\\vgsales.csv")library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# Create 5 random samples with replacement
set.seed(123) # Setting seed for reproducibilitydf_1 <- data[sample(nrow(data), replace = TRUE, size = round(0.5 * nrow(data))), ]
df_2 <- data[sample(nrow(data), replace = TRUE, size = round(0.5 * nrow(data))), ]
df_3 <- data[sample(nrow(data), replace = TRUE, size = round(0.5 * nrow(data))), ]
df_4 <- data[sample(nrow(data), replace = TRUE, size = round(0.5 * nrow(data))), ]
df_5 <- data[sample(nrow(data), replace = TRUE, size = round(0.5 * nrow(data))), ]head(df_1)## Rank Name Platform Year Genre
## 2986 2987 Prince of Persia: The Two Thrones PS2 2005 Action
## 1842 1843 NBA Jam Tournament Edition GEN 1994 Sports
## 3371 3372 Xena: Warrior Princess PS 1998 Adventure
## 11638 11639 Daniel X: The Ultimate Power DS 2010 Action
## 4761 4762 TNA iMPACT! PS3 2008 Fighting
## 6746 6747 Cradle of Rome DS 2008 Puzzle
## Publisher NA_Sales EU_Sales JP_Sales Other_Sales Global_Sales
## 2986 Ubisoft 0.57 0.02 0 0.09 0.68
## 1842 Acclaim Entertainment 0.95 0.14 0 0.03 1.11
## 3371 Electronic Arts 0.33 0.23 0 0.04 0.60
## 11638 THQ 0.07 0.00 0 0.01 0.08
## 4761 Midway Games 0.22 0.12 0 0.06 0.41
## 6746 Rising Star Games 0.06 0.16 0 0.03 0.25head(df_2)## Rank Name Platform Year
## 8086 8087 Battle Commander: Hachibushu Shura no Heihou SNES 1991
## 1964 1965 Apollo Justice: Ace Attorney DS 2007
## 11691 11692 Storybook Workshop Wii 2009
## 3638 3639 Harry Potter and the Deathly Hallows - Part 1 Wii 2010
## 6793 6794 Madden NFL 13 WiiU 2012
## 12343 12344 Arc the Lad: End of Darkness PS2 2004
## Genre Publisher NA_Sales EU_Sales JP_Sales
## 8086 Strategy Banpresto 0.00 0.00 0.18
## 1964 Adventure Capcom 0.32 0.06 0.64
## 11691 Misc Konami Digital Entertainment 0.07 0.00 0.00
## 3638 Action Electronic Arts 0.22 0.28 0.00
## 6793 Sports Electronic Arts 0.22 0.00 0.00
## 12343 Role-Playing Sony Computer Entertainment 0.03 0.02 0.00
## Other_Sales Global_Sales
## 8086 0.00 0.18
## 1964 0.04 1.06
## 11691 0.01 0.08
## 3638 0.05 0.55
## 6793 0.02 0.24
## 12343 0.01 0.06head(df_3)## Rank
## 5129 5130
## 6834 6835
## 15748 15750
## 14239 14241
## 10627 10628
## 313 313
## Name
## 5129 Custom Robo
## 6834 Super Monkey Ball Deluxe
## 15748 Kochira Katsushikaku Kameari Kouenmae Hashutsujo: Machiteba Tengoku! Makereba Jigoku! Ryoutsuryuu Ikkakusenkin Daisakusen!
## 14239 Prince of Persia: The Forgotten Sands
## 10627 Nodame Cantabile
## 313 Dragon Warrior III
## Platform Year Genre Publisher NA_Sales EU_Sales JP_Sales
## 5129 GC 2004 Role-Playing Nintendo 0.29 0.07 0.00
## 6834 PS2 2005 Misc Sega 0.12 0.09 0.00
## 15748 DS 2010 Misc Namco Bandai Games 0.00 0.00 0.02
## 14239 PC 2010 Action Ubisoft 0.00 0.03 0.00
## 10627 DS 2007 Misc Namco Bandai Games 0.00 0.00 0.10
## 313 NES 1988 Role-Playing Enix Corporation 0.10 0.00 3.77
## Other_Sales Global_Sales
## 5129 0.01 0.37
## 6834 0.03 0.24
## 15748 0.00 0.02
## 14239 0.00 0.03
## 10627 0.00 0.10
## 313 0.00 3.87head(df_4)## Rank Name Platform Year Genre
## 15925 15927 RollerCoaster Tycoon: Gold Edition PC 2002 Strategy
## 11033 11034 Fullmetal Alchemist: Dual Sympathy DS 2005 Role-Playing
## 14497 14499 CIMA: The Enemy GBA 2003 Role-Playing
## 7066 7067 Tetris 2 (weekly jp sales) GB 1992 Puzzle
## 9794 9795 Atelier Annie: Alchemists of Sera Island DS 2009 Role-Playing
## 2555 2556 Dying Light XOne 2015 Action
## Publisher NA_Sales EU_Sales JP_Sales
## 15925 Infogrames 0.01 0.00 0.00
## 11033 Empire Interactive 0.05 0.00 0.04
## 14497 Marvelous Interactive 0.02 0.01 0.00
## 7066 Nintendo 0.00 0.00 0.23
## 9794 Gust 0.08 0.00 0.03
## 2555 Warner Bros. Interactive Entertainment 0.43 0.30 0.01
## Other_Sales Global_Sales
## 15925 0.00 0.02
## 11033 0.00 0.09
## 14497 0.00 0.03
## 7066 0.00 0.23
## 9794 0.01 0.12
## 2555 0.07 0.81head(df_5)## Rank Name Platform
## 12122 12123 Katekyoo Hitman Reborn! DS: Fate of Heat - Hono no Unmei DS
## 9581 9582 Star Wars: Clone Wars XB
## 13613 13614 Emergency Room: Real Life Rescues DS
## 258 258 Call of Duty: Advanced Warfare X360
## 4975 4976 Jam Sessions: Sing and Play Guitar (US sales) DS
## 14679 14681 The IdolM@ster: Gravure For You! Vol. 6 PS3
## Year Genre Publisher NA_Sales EU_Sales JP_Sales
## 12122 2008 Role-Playing Takara Tomy 0.00 0.00 0.07
## 9581 2003 Shooter LucasArts 0.10 0.03 0.00
## 13613 2009 Simulation 505 Games 0.04 0.00 0.00
## 258 2014 Shooter Activision 2.75 1.18 0.00
## 4975 2007 Misc Ubisoft 0.38 0.00 0.00
## 14679 2012 Action Namco Bandai Games 0.00 0.00 0.03
## Other_Sales Global_Sales
## 12122 0.00 0.07
## 9581 0.00 0.13
## 13613 0.00 0.04
## 258 0.37 4.31
## 4975 0.00 0.38
## 14679 0.00 0.03Insight Gathered:
Similar to the original data set, the produced samples correctly captured both continuous (like sales data, release years) and categorical (like game genres, publishers) data. We were able to see how various subsets of data could differ by using sampling with replacement, which revealed the diversity and possible variability present across the dataset.
Significance:
Because unpredictable nature and variability are common in real-world data collection, this sampling procedure is significant. We may learn how statistical measures such as means, medians, and distributions may vary amongst subgroups by modelling this variability. This method forms the basis for bootstrapping, which assists in evaluating the precision and dependability of statistical estimations in order to guarantee that results are typical of the greater population rather than just sample-specific.
Further Questions for Investigation:
What are the differences between the original data set and the average sales statistics between the samples? Do they vary or are they consistent?
Which game genres or publishers are systematically over-represented in the samples, or under-represented?
In what ways do correlations between variables (such sales and release year) differ between samples? Do these relationships remain consistent over time, or do they vary greatly?
# Analyzing each subsample with group_by
analyze_subsamples_grouped <- function(subsample, subsample_number) {
cat("\n--- Analysis for Subsample", subsample_number, "---\n")
# using Group by for Genre and summarize sales
genre_summary <- subsample %>%
group_by(Genre) %>%
summarise(
Count = n(),
Mean_Sales = mean(Global_Sales, na.rm = TRUE),
Median_Sales = median(Global_Sales, na.rm = TRUE)
)
print(genre_summary)
# Using Group by for Publisher and Genre
publisher_genre_summary <- subsample %>%
group_by(Publisher, Genre) %>%
summarise(
Count = n(),
Total_Sales = sum(Global_Sales, na.rm = TRUE)
) %>%
arrange(desc(Total_Sales))
print("Publisher-Genre Summary:")
print(publisher_genre_summary)
return(list(genre_summary = genre_summary, publisher_genre_summary = publisher_genre_summary))
}
# Applying the function to each subsample
list_dfs = list(df_1, df_2, df_3, df_4, df_5)
results_list <- lapply(1:5, function(i) analyze_subsamples_grouped(list_dfs[[i]], i))##
## --- Analysis for Subsample 1 ---
## # A tibble: 12 × 4
## Genre Count Mean_Sales Median_Sales
## <chr> <int> <dbl> <dbl>
## 1 Action 1723 0.520 0.19
## 2 Adventure 600 0.181 0.05
## 3 Fighting 397 0.553 0.24
## 4 Misc 893 0.523 0.17
## 5 Platform 416 0.832 0.22
## 6 Puzzle 309 0.350 0.11
## 7 Racing 583 0.550 0.16
## 8 Role-Playing 736 0.712 0.205
## 9 Shooter 647 0.893 0.24
## 10 Simulation 440 0.383 0.13
## 11 Sports 1226 0.532 0.21
## 12 Strategy 329 0.239 0.09## `summarise()` has grouped output by 'Publisher'. You can override using the
## `.groups` argument.## [1] "Publisher-Genre Summary:"
## # A tibble: 1,184 × 4
## # Groups: Publisher [407]
## Publisher Genre Count Total_Sales
## <chr> <chr> <int> <dbl>
## 1 Electronic Arts Sports 277 237.
## 2 Activision Shooter 69 198.
## 3 Nintendo Role-Playing 57 195.
## 4 Nintendo Platform 48 173.
## 5 Take-Two Interactive Action 48 116.
## 6 Nintendo Misc 54 111.
## 7 Activision Action 167 92.6
## 8 Nintendo Sports 32 83.6
## 9 Electronic Arts Racing 78 81.4
## 10 Electronic Arts Shooter 67 78.0
## # ℹ 1,174 more rows
##
## --- Analysis for Subsample 2 ---
## # A tibble: 12 × 4
## Genre Count Mean_Sales Median_Sales
## <chr> <int> <dbl> <dbl>
## 1 Action 1655 0.560 0.19
## 2 Adventure 620 0.194 0.05
## 3 Fighting 455 0.511 0.2
## 4 Misc 854 0.437 0.16
## 5 Platform 443 1.06 0.24
## 6 Puzzle 281 0.440 0.13
## 7 Racing 676 0.492 0.195
## 8 Role-Playing 739 0.527 0.18
## 9 Shooter 668 0.801 0.23
## 10 Simulation 405 0.365 0.14
## 11 Sports 1197 0.537 0.23
## 12 Strategy 306 0.270 0.11## `summarise()` has grouped output by 'Publisher'. You can override using the
## `.groups` argument.## [1] "Publisher-Genre Summary:"
## # A tibble: 1,200 × 4
## # Groups: Publisher [394]
## Publisher Genre Count Total_Sales
## <chr> <chr> <int> <dbl>
## 1 Nintendo Platform 55 262.
## 2 Electronic Arts Sports 288 247.
## 3 Activision Shooter 98 172.
## 4 Take-Two Interactive Action 49 163.
## 5 Nintendo Role-Playing 47 90.9
## 6 Ubisoft Action 113 86.9
## 7 Nintendo Misc 53 79.3
## 8 Electronic Arts Shooter 58 78.6
## 9 Activision Action 143 74.1
## 10 Electronic Arts Racing 93 70.8
## # ℹ 1,190 more rows
##
## --- Analysis for Subsample 3 ---
## # A tibble: 12 × 4
## Genre Count Mean_Sales Median_Sales
## <chr> <int> <dbl> <dbl>
## 1 Action 1627 0.531 0.19
## 2 Adventure 679 0.170 0.06
## 3 Fighting 433 0.584 0.2
## 4 Misc 894 0.529 0.17
## 5 Platform 445 0.786 0.28
## 6 Puzzle 306 0.395 0.09
## 7 Racing 650 0.648 0.23
## 8 Role-Playing 700 0.699 0.19
## 9 Shooter 666 0.749 0.205
## 10 Simulation 412 0.459 0.135
## 11 Sports 1181 0.605 0.22
## 12 Strategy 306 0.260 0.09## `summarise()` has grouped output by 'Publisher'. You can override using the
## `.groups` argument.## [1] "Publisher-Genre Summary:"
## # A tibble: 1,200 × 4
## # Groups: Publisher [404]
## Publisher Genre Count Total_Sales
## <chr> <chr> <int> <dbl>
## 1 Electronic Arts Sports 320 282.
## 2 Nintendo Role-Playing 59 189.
## 3 Nintendo Platform 59 167.
## 4 Activision Shooter 84 166.
## 5 Nintendo Misc 44 124.
## 6 Sony Computer Entertainment Racing 42 108.
## 7 Nintendo Sports 26 102.
## 8 Activision Action 151 92.1
## 9 Electronic Arts Shooter 75 86.4
## 10 Take-Two Interactive Action 41 80.9
## # ℹ 1,190 more rows
##
## --- Analysis for Subsample 4 ---
## # A tibble: 12 × 4
## Genre Count Mean_Sales Median_Sales
## <chr> <int> <dbl> <dbl>
## 1 Action 1744 0.527 0.19
## 2 Adventure 663 0.211 0.06
## 3 Fighting 412 0.544 0.19
## 4 Misc 877 0.422 0.15
## 5 Platform 410 0.929 0.29
## 6 Puzzle 274 0.385 0.09
## 7 Racing 628 0.598 0.19
## 8 Role-Playing 733 0.556 0.18
## 9 Shooter 643 0.659 0.2
## 10 Simulation 411 0.419 0.16
## 11 Sports 1161 0.546 0.23
## 12 Strategy 343 0.237 0.09## `summarise()` has grouped output by 'Publisher'. You can override using the
## `.groups` argument.## [1] "Publisher-Genre Summary:"
## # A tibble: 1,216 × 4
## # Groups: Publisher [415]
## Publisher Genre Count Total_Sales
## <chr> <chr> <int> <dbl>
## 1 Electronic Arts Sports 282 251.
## 2 Nintendo Platform 54 168.
## 3 Activision Shooter 75 155.
## 4 Take-Two Interactive Action 50 148.
## 5 Nintendo Role-Playing 55 123.
## 6 Nintendo Sports 36 90.0
## 7 Activision Action 172 72.7
## 8 Sony Computer Entertainment Racing 32 71.7
## 9 Microsoft Game Studios Misc 22 71.7
## 10 Nintendo Action 45 70.8
## # ℹ 1,206 more rows
##
## --- Analysis for Subsample 5 ---
## # A tibble: 12 × 4
## Genre Count Mean_Sales Median_Sales
## <chr> <int> <dbl> <dbl>
## 1 Action 1666 0.512 0.2
## 2 Adventure 677 0.195 0.06
## 3 Fighting 432 0.526 0.19
## 4 Misc 877 0.534 0.17
## 5 Platform 454 0.814 0.26
## 6 Puzzle 278 0.503 0.11
## 7 Racing 636 0.673 0.22
## 8 Role-Playing 789 0.550 0.19
## 9 Shooter 653 0.682 0.22
## 10 Simulation 435 0.492 0.14
## 11 Sports 1101 0.521 0.23
## 12 Strategy 301 0.289 0.11## `summarise()` has grouped output by 'Publisher'. You can override using the
## `.groups` argument.## [1] "Publisher-Genre Summary:"
## # A tibble: 1,210 × 4
## # Groups: Publisher [421]
## Publisher Genre Count Total_Sales
## <chr> <chr> <int> <dbl>
## 1 Electronic Arts Sports 266 226.
## 2 Nintendo Platform 47 156.
## 3 Nintendo Misc 52 110.
## 4 Nintendo Racing 21 110.
## 5 Nintendo Role-Playing 63 103.
## 6 Activision Shooter 74 95.7
## 7 Activision Action 154 92.2
## 8 Electronic Arts Shooter 77 80.6
## 9 Electronic Arts Racing 86 78.9
## 10 Nintendo Puzzle 33 74.9
## # ℹ 1,200 more rows# Monte Carlo simulation function
perform_monte_carlo <- function(subsample, column_to_simulate, num_simulations = 1000) {
simulated_means <- numeric(num_simulations)
for (i in 1:num_simulations) {
simulated_sample <- sample(subsample[[column_to_simulate]], replace = TRUE)
simulated_means[i] <- mean(simulated_sample, na.rm = TRUE)
}
# Display the histogram of simulated means
hist(simulated_means, main = paste("Simulation for", column_to_simulate, "Means"),
xlab = "Simulated Means", col = "red")
return(simulated_means)
}
# Applying simulation to all subsamples for "Global_Sales"
for (i in 1:5) {
cat("\n--- Monte Carlo Simulation for Subsample", i, "---\n")
perform_monte_carlo(list_dfs[[i]], "Global_Sales")
}##
## --- Monte Carlo Simulation for Subsample 1 ---
##
## --- Monte Carlo Simulation for Subsample 2 ---
##
## --- Monte Carlo Simulation for Subsample 3 ---
##
## --- Monte Carlo Simulation for Subsample 4 ---
##
## --- Monte Carlo Simulation for Subsample 5 ---
Insight Gathered:
Variability in sales across publishers and genres was found via
subsample analysis. Certain genres exhibited continuous high sales
across all subsamples, but others showed notable variation, indicating
the dominance and stability of particular trends. Furthermore, the Monte
Carlo simulation illustrated the range of average sales values for the
“Global_Sales” variable, giving rise to a more comprehensive
understanding of the dataset’s possible variability.
Significance:
This study emphasises how crucial it is to understand variability and uncertainty when analysing data. Reliability of trends is shown by constant patterns across subsamples on the other hand, variations highlight the possibility of incorrect inferences drawn from single samples. The Monte Carlo simulation reinforces the necessity to take data variability into account when forming conclusions by illustrating the range of possible outcomes.
Further Questions for Investigation:
Why do some publishers or genres have consistent sales patterns while others exhibit large variations among sub samples?
Are there any outside variables impacting these tendencies that should be investigated further?
What impact might other factors (such area or release year) have on the patterns of sales that have been noticed?