Super Inference Smash Lite
master yeoda
a long, long time ago in a galaxy far, far away
1. Independent samples t-test
1.1 Load data
smash <- read.csv("smash_3.csv", header = TRUE)
head(smash)## character game regular_fall fast_fall weight walk_speed run_speed
## 1 mario Super Mario 1.50 2.400 98 1.155 1.760
## 2 donkey kong Donkey Kong 1.63 2.608 127 1.365 1.873
## 3 link Zelda 1.60 3.040 104 1.247 1.534
## 4 samus Metroid 1.33 2.168 108 1.115 1.654
## 5 dark samus Metroid 1.33 2.168 108 1.115 1.654
## 6 yoshi Super Mario 1.29 2.064 104 1.208 2.046
## full_hop_height short_hop_height double_hop_height before after expertise
## 1 36.33 17.54 36.33 3 8 Amateur
## 2 34.00 17.30 35.50 8 10 Expert
## 3 27.80 13.38 29.00 10 7 Expert
## 4 37.00 18.00 37.00 6 9 Expert
## 5 37.00 18.00 37.00 2 5 Amateur
## 6 36.09 14.43 51.56 5 9 Amateurtable(smash$game)##
## Animal Crossing Banjo Kazooie Bayonetta Castlevania Donkey Kong
## 2 1 1 2 3
## Dragon Quest Duck Hunt Earthbound F-Zero Final Fantasy
## 1 1 1 2 1
## Fire Emblem Icarus Kirby Mega Man Metal Gear
## 6 2 4 1 1
## Metroid Mother Nintendo Pikmin Pokemon
## 4 1 1 1 7
## Punch Out Sonic Splatoon Stack Up Star Fox
## 1 1 1 1 2
## Street Fighter Super Mario Wii Xenoblade Zelda
## 2 10 4 1 61.2 Independent samples t-test
H0: Metroid = Zelda
H1: Metroid <> Zelda
Subset required data.
Compare Metroid vs. Zelda.
subset_1 <- subset(smash, game == "Metroid" | game == "Zelda")
head(subset_1)## character game regular_fall fast_fall weight walk_speed run_speed
## 3 link Zelda 1.60 3.040 104 1.247 1.534
## 4 samus Metroid 1.33 2.168 108 1.115 1.654
## 5 dark samus Metroid 1.33 2.168 108 1.115 1.654
## 17 sheik Zelda 1.75 2.800 78 1.470 2.420
## 18 zelda Zelda 1.35 2.160 85 0.914 1.430
## 23 young link Zelda 1.80 2.880 88 1.260 1.749
## full_hop_height short_hop_height double_hop_height before after expertise
## 3 27.80 13.38 29.00 10 7 Expert
## 4 37.00 18.00 37.00 6 9 Expert
## 5 37.00 18.00 37.00 2 5 Amateur
## 17 39.00 18.75 40.00 6 5 Expert
## 18 31.55 15.24 31.55 4 7 Amateur
## 23 33.66 16.26 33.66 7 10 ExpertAssuming unequal variance by default.
t.test(subset_1$run_speed ~ subset_1$game)##
## Welch Two Sample t-test
##
## data: subset_1$run_speed by subset_1$game
## t = 0.94211, df = 7.1841, p-value = 0.3767
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.3363160 0.7856494
## sample estimates:
## mean in group Metroid mean in group Zelda
## 1.954500 1.729833Assuming equal variance.
t.test(subset_1$run_speed ~ subset_1$game, var.equal = TRUE)##
## Two Sample t-test
##
## data: subset_1$run_speed by subset_1$game
## t = 0.91593, df = 8, p-value = 0.3865
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.3409716 0.7903049
## sample estimates:
## mean in group Metroid mean in group Zelda
## 1.954500 1.7298332. One direction t-test
2.1 Subset data
Compare Kirby vs. Super Mario.
subset_2 <- subset(smash, game == "Kirby" | game == "Super Mario")
head(subset_2)## character game regular_fall fast_fall weight walk_speed run_speed
## 1 mario Super Mario 1.50 2.400 98 1.155 1.760
## 6 yoshi Super Mario 1.29 2.064 104 1.208 2.046
## 7 kirby Kirby 1.23 1.968 79 0.977 1.727
## 10 luigi Super Mario 1.32 2.112 97 1.134 1.650
## 14 peach Super Mario 1.19 1.904 89 0.924 1.595
## 15 daisy Super Mario 1.19 1.904 89 0.924 1.595
## full_hop_height short_hop_height double_hop_height before after expertise
## 1 36.33 17.54 36.33 3 8 Amateur
## 6 36.09 14.43 51.56 5 9 Amateur
## 7 25.37 12.24 22.00 5 9 Amateur
## 10 44.00 19.98 41.31 7 10 Expert
## 14 30.03 14.50 30.03 2 5 Amateur
## 15 30.03 14.50 30.03 10 8 Expert2.2 Execute t-test
2.2.1 Less than alternate hypothesis
H0: Kirby >= Super Mario
H1: Kirby < Super Mario
Assuming unequal variance by default.
t.test(subset_2$regular_fall ~ subset_2$game, alternative = "less")##
## Welch Two Sample t-test
##
## data: subset_2$regular_fall by subset_2$game
## t = 0.48396, df = 4.7882, p-value = 0.6751
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
## -Inf 0.4319869
## sample estimates:
## mean in group Kirby mean in group Super Mario
## 1.580 1.497Assuming equal variance.
t.test(subset_2$regular_fall ~ subset_2$game, alternative = "less", var.equal = TRUE)##
## Two Sample t-test
##
## data: subset_2$regular_fall by subset_2$game
## t = 0.52578, df = 12, p-value = 0.6957
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
## -Inf 0.3643548
## sample estimates:
## mean in group Kirby mean in group Super Mario
## 1.580 1.4972.2.2 Greater than alternate hypothesis
H0: Kirby <= Super Mario
H1: Kirby > Super Mario
Assuming unequal variance by default.
t.test(subset_2$regular_fall ~ subset_2$game, alternative = "greater")##
## Welch Two Sample t-test
##
## data: subset_2$regular_fall by subset_2$game
## t = 0.48396, df = 4.7882, p-value = 0.3249
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## -0.2659869 Inf
## sample estimates:
## mean in group Kirby mean in group Super Mario
## 1.580 1.497Assuming equal variance.
t.test(subset_2$regular_fall ~ subset_2$game, alternative = "greater", var.equal = TRUE)##
## Two Sample t-test
##
## data: subset_2$regular_fall by subset_2$game
## t = 0.52578, df = 12, p-value = 0.3043
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## -0.1983548 Inf
## sample estimates:
## mean in group Kirby mean in group Super Mario
## 1.580 1.4973. Paired-samples t-test
Player skill level by character before and after training.
3.1 Paired samples t-test
H0: before = after
H1: before <> after
t.test(smash$before, smash$after, paired = TRUE)##
## Paired t-test
##
## data: smash$before and smash$after
## t = -4.4097, df = 71, p-value = 3.606e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2.0370808 -0.7684747
## sample estimates:
## mean of the differences
## -1.4027783.1 Less than alternate hypothesis
t.test(smash$before, smash$after, paired = TRUE, alternative = "less")##
## Paired t-test
##
## data: smash$before and smash$after
## t = -4.4097, df = 71, p-value = 1.803e-05
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
## -Inf -0.8726076
## sample estimates:
## mean of the differences
## -1.4027783.2 Greater than alternate hypothesis
t.test(smash$before, smash$after, paired = TRUE, alternative = "greater")##
## Paired t-test
##
## data: smash$before and smash$after
## t = -4.4097, df = 71, p-value = 1
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## -1.932948 Inf
## sample estimates:
## mean of the differences
## -1.4027784. F-Test
2-sided test.
H0: Variance of walk_speed = Variance of run_speed
H1: Variance of walk_speed <> Variance of run_speed
var.test(smash$walk_speed, smash$run_speed,
alternative = "two.sided")##
## F test to compare two variances
##
## data: smash$walk_speed and smash$run_speed
## F = 0.2979, num df = 71, denom df = 71, p-value = 7.777e-07
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.1863816 0.4761475
## sample estimates:
## ratio of variances
## 0.29790121-sided upper
H0: Variance of walk_speed <= Variance of run_speed
H1: Variance of walk_speed > Variance of run_speed
var.test(smash$walk_speed, smash$run_speed,
alternative = "greater")##
## F test to compare two variances
##
## data: smash$walk_speed and smash$run_speed
## F = 0.2979, num df = 71, denom df = 71, p-value = 1
## alternative hypothesis: true ratio of variances is greater than 1
## 95 percent confidence interval:
## 0.2010832 Inf
## sample estimates:
## ratio of variances
## 0.29790121-sided lower
H0: Variance of walk_speed >= Variance of run_speed
H1: Variance of walk_speed < Variance of run_speed
var.test(smash$walk_speed, smash$run_speed,
alternative = "less")##
## F test to compare two variances
##
## data: smash$walk_speed and smash$run_speed
## F = 0.2979, num df = 71, denom df = 71, p-value = 3.888e-07
## alternative hypothesis: true ratio of variances is less than 1
## 95 percent confidence interval:
## 0.0000000 0.4413354
## sample estimates:
## ratio of variances
## 0.29790125. ANOVA
Compare 3 groups for simplicity.
subset_4 <- subset(smash, game == "Pokemon" | game == "Super Mario" |
game == "Fire Emblem")
head(subset_4)## character game regular_fall fast_fall weight walk_speed run_speed
## 1 mario Super Mario 1.50 2.400 98 1.155 1.760
## 6 yoshi Super Mario 1.29 2.064 104 1.208 2.046
## 9 pikachu Pokemon 1.55 2.480 79 1.302 2.039
## 10 luigi Super Mario 1.32 2.112 97 1.134 1.650
## 13 jigglypuff Pokemon 0.98 1.568 68 0.735 1.271
## 14 peach Super Mario 1.19 1.904 89 0.924 1.595
## full_hop_height short_hop_height double_hop_height before after expertise
## 1 36.33 17.54 36.33 3 8 Amateur
## 6 36.09 14.43 51.56 5 9 Amateur
## 9 35.50 17.12 35.50 8 9 Expert
## 10 44.00 19.98 41.31 7 10 Expert
## 13 19.79 11.26 19.79 3 7 Amateur
## 14 30.03 14.50 30.03 2 5 AmateurH0: The means of fast_fall by game are equal
H1: The means of fast_fall by game are not equal
anova <- aov(fast_fall ~ game, data = subset_4)
summary(anova)## Df Sum Sq Mean Sq F value Pr(>F)
## game 2 0.353 0.1765 1.44 0.26
## Residuals 20 2.452 0.1226Use post hoc test to determine the mean differences.
TukeyHSD((anova))## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = fast_fall ~ game, data = subset_4)
##
## $game
## diff lwr upr p adj
## Pokemon-Fire Emblem -0.1624762 -0.6552818 0.3303294 0.6867043
## Super Mario-Fire Emblem -0.3051333 -0.7625510 0.1522844 0.2343060
## Super Mario-Pokemon -0.1426571 -0.5791770 0.2938628 0.6911360Test for normality.
shapiro.test(subset_4$fast_fall)##
## Shapiro-Wilk normality test
##
## data: subset_4$fast_fall
## W = 0.91682, p-value = 0.05698Next game!!
