# 1. Comparison with 5 item score -----------------------------------------
Awards <- read.csv("comparison_score_v5.csv")
Awards
## Year X_Score Y_Score
## 1 1987 6.527027 4.828947
## 2 1987 6.705752 4.952586
## 3 1987 5.899263 5.394366
## 4 1987 5.915493 4.664835
## 5 1987 6.894397 5.672269
## 6 1987 4.950495 2.850877
## 7 1987 4.975124 3.448276
## 8 1987 4.986877 3.755869
## 9 1987 4.788732 4.395604
## 10 1987 4.906542 3.361345
## 11 1987 3.106430 6.355263
## 12 1987 3.065646 6.683190
## 13 1987 3.207407 5.406103
## 14 1987 3.638655 5.769231
## 15 1987 2.980851 6.720588
## 16 1987 9.312639 5.186937
## 17 1987 9.846827 6.860619
## 18 1987 8.888889 4.420147
## 19 1987 8.403361 3.943662
## 20 1987 10.212766 6.034483
## 21 1988 2.793548 4.086022
## 22 1988 2.500000 4.166667
## 23 1988 2.706250 4.166667
## 24 1988 2.723270 3.983229
## 25 1988 2.752119 4.025424
## 26 1988 5.128205 6.984716
## 27 1988 5.084746 7.399577
## 28 1988 5.106383 7.383966
## 29 1988 5.530973 7.177215
## 30 1988 5.393258 7.462687
## 31 1988 9.475771 6.117904
## 32 1988 9.383795 6.342495
## 33 1988 9.383795 6.329114
## 34 1988 9.693833 6.329114
## 35 1988 9.581292 6.396588
Awards1987_v2 <- subset(Awards, Year=='1987')
Awards1987_v2
## Year X_Score Y_Score
## 1 1987 6.527027 4.828947
## 2 1987 6.705752 4.952586
## 3 1987 5.899263 5.394366
## 4 1987 5.915493 4.664835
## 5 1987 6.894397 5.672269
## 6 1987 4.950495 2.850877
## 7 1987 4.975124 3.448276
## 8 1987 4.986877 3.755869
## 9 1987 4.788732 4.395604
## 10 1987 4.906542 3.361345
## 11 1987 3.106430 6.355263
## 12 1987 3.065646 6.683190
## 13 1987 3.207407 5.406103
## 14 1987 3.638655 5.769231
## 15 1987 2.980851 6.720588
## 16 1987 9.312639 5.186937
## 17 1987 9.846827 6.860619
## 18 1987 8.888889 4.420147
## 19 1987 8.403361 3.943662
## 20 1987 10.212766 6.034483
Awards1988_v2 <- subset(Awards, Year =='1988')
Awards1988_v2
## Year X_Score Y_Score
## 21 1988 2.793548 4.086022
## 22 1988 2.500000 4.166667
## 23 1988 2.706250 4.166667
## 24 1988 2.723270 3.983229
## 25 1988 2.752119 4.025424
## 26 1988 5.128205 6.984716
## 27 1988 5.084746 7.399577
## 28 1988 5.106383 7.383966
## 29 1988 5.530973 7.177215
## 30 1988 5.393258 7.462687
## 31 1988 9.475771 6.117904
## 32 1988 9.383795 6.342495
## 33 1988 9.383795 6.329114
## 34 1988 9.693833 6.329114
## 35 1988 9.581292 6.396588
# Check for normal distribution
names(Awards)
## [1] "Year" "X_Score" "Y_Score"
shapiro.test(Awards1987_v2$X_Score)
##
## Shapiro-Wilk normality test
##
## data: Awards1987_v2$X_Score
## W = 0.92033, p-value = 0.1006
shapiro.test(Awards1988_v2$X_Score)
##
## Shapiro-Wilk normality test
##
## data: Awards1988_v2$X_Score
## W = 0.81839, p-value = 0.006393
shapiro.test(Awards1987_v2$Y_Score)
##
## Shapiro-Wilk normality test
##
## data: Awards1987_v2$Y_Score
## W = 0.96849, p-value = 0.7227
shapiro.test(Awards1988_v2$Y_Score)
##
## Shapiro-Wilk normality test
##
## data: Awards1988_v2$Y_Score
## W = 0.81752, p-value = 0.006225
kruskal.test(Awards1987_v2$X_Score ~ Awards1987_v2$Y_Score, data = Awards1987_v2)
##
## Kruskal-Wallis rank sum test
##
## data: Awards1987_v2$X_Score by Awards1987_v2$Y_Score
## Kruskal-Wallis chi-squared = 19, df = 19, p-value = 0.4568
kruskal.test(Awards1988_v2$X_Score ~ Awards1988_v2$Y_Score, data = Awards1988_v2)
##
## Kruskal-Wallis rank sum test
##
## data: Awards1988_v2$X_Score by Awards1988_v2$Y_Score
## Kruskal-Wallis chi-squared = 13.668, df = 12, p-value = 0.3224
# 2. Convert to linear then use t test ----------------------------------------
library(reshape2)
Awards1987_v2
## Year X_Score Y_Score
## 1 1987 6.527027 4.828947
## 2 1987 6.705752 4.952586
## 3 1987 5.899263 5.394366
## 4 1987 5.915493 4.664835
## 5 1987 6.894397 5.672269
## 6 1987 4.950495 2.850877
## 7 1987 4.975124 3.448276
## 8 1987 4.986877 3.755869
## 9 1987 4.788732 4.395604
## 10 1987 4.906542 3.361345
## 11 1987 3.106430 6.355263
## 12 1987 3.065646 6.683190
## 13 1987 3.207407 5.406103
## 14 1987 3.638655 5.769231
## 15 1987 2.980851 6.720588
## 16 1987 9.312639 5.186937
## 17 1987 9.846827 6.860619
## 18 1987 8.888889 4.420147
## 19 1987 8.403361 3.943662
## 20 1987 10.212766 6.034483
Awards1987_v2$X_Score_log <- log(Awards1987_v2$X_Score)
Awards1987_v2$Y_Score_log <- log(Awards1987_v2$Y_Score)
# Check for normal distribution
shapiro.test(Awards1987_v2$X_Score_log)
##
## Shapiro-Wilk normality test
##
## data: Awards1987_v2$X_Score_log
## W = 0.93276, p-value = 0.1745
shapiro.test(Awards1987_v2$Y_Score_log)
##
## Shapiro-Wilk normality test
##
## data: Awards1987_v2$Y_Score_log
## W = 0.95396, p-value = 0.4312
myvars <- c("Year", "X_Score_log", "Y_Score_log")
Awards1987_v2_log <- Awards1987_v2[myvars]
Awards1987_v2_log
## Year X_Score_log Y_Score_log
## 1 1987 1.875952 1.574629
## 2 1987 1.902966 1.599910
## 3 1987 1.774827 1.685355
## 4 1987 1.777575 1.540052
## 5 1987 1.930709 1.735589
## 6 1987 1.599488 1.047627
## 7 1987 1.604450 1.237874
## 8 1987 1.606810 1.323320
## 9 1987 1.566266 1.480605
## 10 1987 1.590569 1.212341
## 11 1987 1.133474 1.849283
## 12 1987 1.120258 1.899595
## 13 1987 1.165463 1.687529
## 14 1987 1.291614 1.752539
## 15 1987 1.092209 1.905176
## 16 1987 2.231372 1.646143
## 17 1987 2.287149 1.925798
## 18 1987 2.184802 1.486173
## 19 1987 2.128632 1.372110
## 20 1987 2.323639 1.797490
Awards1987_v2_log_long <- melt(Awards1987_v2_log, id.vars=c("Year"))
Awards1987_v2_log_long
## Year variable value
## 1 1987 X_Score_log 1.875952
## 2 1987 X_Score_log 1.902966
## 3 1987 X_Score_log 1.774827
## 4 1987 X_Score_log 1.777575
## 5 1987 X_Score_log 1.930709
## 6 1987 X_Score_log 1.599488
## 7 1987 X_Score_log 1.604450
## 8 1987 X_Score_log 1.606810
## 9 1987 X_Score_log 1.566266
## 10 1987 X_Score_log 1.590569
## 11 1987 X_Score_log 1.133474
## 12 1987 X_Score_log 1.120258
## 13 1987 X_Score_log 1.165463
## 14 1987 X_Score_log 1.291614
## 15 1987 X_Score_log 1.092209
## 16 1987 X_Score_log 2.231372
## 17 1987 X_Score_log 2.287149
## 18 1987 X_Score_log 2.184802
## 19 1987 X_Score_log 2.128632
## 20 1987 X_Score_log 2.323639
## 21 1987 Y_Score_log 1.574629
## 22 1987 Y_Score_log 1.599910
## 23 1987 Y_Score_log 1.685355
## 24 1987 Y_Score_log 1.540052
## 25 1987 Y_Score_log 1.735589
## 26 1987 Y_Score_log 1.047627
## 27 1987 Y_Score_log 1.237874
## 28 1987 Y_Score_log 1.323320
## 29 1987 Y_Score_log 1.480605
## 30 1987 Y_Score_log 1.212341
## 31 1987 Y_Score_log 1.849283
## 32 1987 Y_Score_log 1.899595
## 33 1987 Y_Score_log 1.687529
## 34 1987 Y_Score_log 1.752539
## 35 1987 Y_Score_log 1.905176
## 36 1987 Y_Score_log 1.646143
## 37 1987 Y_Score_log 1.925798
## 38 1987 Y_Score_log 1.486173
## 39 1987 Y_Score_log 1.372110
## 40 1987 Y_Score_log 1.797490
Awards1988_v2
## Year X_Score Y_Score
## 21 1988 2.793548 4.086022
## 22 1988 2.500000 4.166667
## 23 1988 2.706250 4.166667
## 24 1988 2.723270 3.983229
## 25 1988 2.752119 4.025424
## 26 1988 5.128205 6.984716
## 27 1988 5.084746 7.399577
## 28 1988 5.106383 7.383966
## 29 1988 5.530973 7.177215
## 30 1988 5.393258 7.462687
## 31 1988 9.475771 6.117904
## 32 1988 9.383795 6.342495
## 33 1988 9.383795 6.329114
## 34 1988 9.693833 6.329114
## 35 1988 9.581292 6.396588
Awards1988_v2$X_Score_log <- log(Awards1988_v2$X_Score)
Awards1988_v2$Y_Score_log <- log(Awards1988_v2$Y_Score)
# Check for normal distribution
shapiro.test(Awards1988_v2$X_Score_log)
##
## Shapiro-Wilk normality test
##
## data: Awards1988_v2$X_Score_log
## W = 0.83967, p-value = 0.01244
shapiro.test(Awards1988_v2$Y_Score_log)
##
## Shapiro-Wilk normality test
##
## data: Awards1988_v2$Y_Score_log
## W = 0.79064, p-value = 0.002795
myvars <- c("Year", "X_Score_log", "Y_Score_log")
Awards1988_v2_log <- Awards1988_v2[myvars]
Awards1988_v2_log
## Year X_Score_log Y_Score_log
## 21 1988 1.0273126 1.407572
## 22 1988 0.9162907 1.427116
## 23 1988 0.9955639 1.427116
## 24 1988 1.0018335 1.382093
## 25 1988 1.0123710 1.392630
## 26 1988 1.6347557 1.943724
## 27 1988 1.6262450 2.001423
## 28 1988 1.6304913 1.999311
## 29 1988 1.7103638 1.970911
## 30 1988 1.6851497 2.009915
## 31 1988 2.2487381 1.811220
## 32 1988 2.2389843 1.847272
## 33 1988 2.2389843 1.845160
## 34 1988 2.2714899 1.845160
## 35 1988 2.2598124 1.855765
Awards1988_v2_log_long <- melt(Awards1988_v2_log, id.vars=c("Year"))
Awards1988_v2_log_long
## Year variable value
## 1 1988 X_Score_log 1.0273126
## 2 1988 X_Score_log 0.9162907
## 3 1988 X_Score_log 0.9955639
## 4 1988 X_Score_log 1.0018335
## 5 1988 X_Score_log 1.0123710
## 6 1988 X_Score_log 1.6347557
## 7 1988 X_Score_log 1.6262450
## 8 1988 X_Score_log 1.6304913
## 9 1988 X_Score_log 1.7103638
## 10 1988 X_Score_log 1.6851497
## 11 1988 X_Score_log 2.2487381
## 12 1988 X_Score_log 2.2389843
## 13 1988 X_Score_log 2.2389843
## 14 1988 X_Score_log 2.2714899
## 15 1988 X_Score_log 2.2598124
## 16 1988 Y_Score_log 1.4075718
## 17 1988 Y_Score_log 1.4271164
## 18 1988 Y_Score_log 1.4271164
## 19 1988 Y_Score_log 1.3820927
## 20 1988 Y_Score_log 1.3926302
## 21 1988 Y_Score_log 1.9437244
## 22 1988 Y_Score_log 2.0014229
## 23 1988 Y_Score_log 1.9993109
## 24 1988 Y_Score_log 1.9709115
## 25 1988 Y_Score_log 2.0099155
## 26 1988 Y_Score_log 1.8112195
## 27 1988 Y_Score_log 1.8472722
## 28 1988 Y_Score_log 1.8451602
## 29 1988 Y_Score_log 1.8451602
## 30 1988 Y_Score_log 1.8557648
# Independent samples t-test
library(lsr)
independentSamplesTTest (formula = value ~ variable, data = Awards1987_v2_log_long)
##
## Welch's independent samples t-test
##
## Outcome variable: value
## Grouping variable: variable
##
## Descriptive statistics:
## X_Score_log Y_Score_log
## mean 1.709 1.588
## std dev. 0.404 0.251
##
## Hypotheses:
## null: population means equal for both groups
## alternative: different population means in each group
##
## Test results:
## t-statistic: 1.142
## degrees of freedom: 31.713
## p-value: 0.262
##
## Other information:
## two-sided 95% confidence interval: [-0.095, 0.338]
## estimated effect size (Cohen's d): 0.361
independentSamplesTTest (formula = value ~ variable, data = Awards1988_v2_log_long)
##
## Welch's independent samples t-test
##
## Outcome variable: value
## Grouping variable: variable
##
## Descriptive statistics:
## X_Score_log Y_Score_log
## mean 1.633 1.744
## std dev. 0.534 0.255
##
## Hypotheses:
## null: population means equal for both groups
## alternative: different population means in each group
##
## Test results:
## t-statistic: -0.728
## degrees of freedom: 20.066
## p-value: 0.475
##
## Other information:
## two-sided 95% confidence interval: [-0.43, 0.207]
## estimated effect size (Cohen's d): 0.266