library(pacman); p_load(psych)
CRITR <- function(n, alpha = .05) {
df <- n - 2; CRITT <- qt(alpha/2, df, lower.tail = F)
CRITR <- sqrt((CRITT^2)/((CRITT^2) + df ))
return(CRITR)}data <- data.frame("BWJR" = c(0.79, 0.94, 0.79, 0.93, 0.88, 0.61, 0.47, 0.81, 0.77, 0.82),
"DutchOrder" = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10),
"SimpleAverageOrder" = c(1, 7, 5, 2, 8, 9, 4, 10, 3, 6),
"AverageExcludingDutch" = c(1, 2, 6, 4, 2, 7, 4, 8, 3, 5), #n-weighted averaging unfortunately not available because of unreported n's.
"FlynnWISCOrder" = c(1, 8, 6, 5, 9, 7, 3, 10, 2, 4),
"gJRW" = c(0.67, 0.6, 0.51, 0.65, 0.72, 0.47, 0.37, 0.67, 0.49, 0.5),
"gJRB" = c(0.62, 0.61, 0.57, 0.61, 0.71, 0.6, 0.36, 0.65, 0.49, 0.53),
"gJRWeighted" = c(0.66, 0.60, 0.52, 0.64, 0.72, 0.49, 0.37, 0.67, 0.49, 0.50), #White n = 1868 and Black n = 305
"gJRAverage" = c(0.645, 0.605, 0.54, 0.63, 0.715, 0.535, 0.365, 0.66, 0.49, 0.515),
"BWNJ" = c(0.67, 0.47, 0.41, 0.80, 0.53, 0.43, 0.07, 0.54, 0.38, 0.66),
"gNJW" = c(0.623, 0.520, 0.455, 0.334, 0.669, 0.500, 0.230, 0.591, 0.334, 0.534),
"gNJB" = c(0.623, 0.670, 0.503, 0.495, 0.619, 0.498, 0.285, 0.618, 0.495, 0.397),
"gNJAverage" = c(0.623, 0.595, 0.479, 0.415, 0.644, 0.499, 0.258, 0.605, 0.415, 0.466)) #Sample sizes were equal, with n = 86 in both groups
CRITR(10)## [1] 0.6318969This is for https://osf.io/nxzw2/. It contains results for supplementary analyses.
"\ Pearson"; round(cor(data, method = "pearson"), 3); "\ Spearman"## [1] " Pearson"## BWJR DutchOrder SimpleAverageOrder
## BWJR 1.000 -0.315 -0.009
## DutchOrder -0.315 1.000 0.297
## SimpleAverageOrder -0.009 0.297 1.000
## AverageExcludingDutch -0.293 0.463 0.574
## FlynnWISCOrder 0.323 -0.018 0.867
## gJRW 0.770 -0.421 0.093
## gJRB 0.706 -0.400 0.381
## gJRWeighted 0.763 -0.422 0.145
## gJRAverage 0.763 -0.424 0.233
## BWNJ 0.766 -0.217 -0.143
## gNJW 0.469 -0.248 0.455
## gNJB 0.695 -0.535 0.256
## gNJAverage 0.614 -0.405 0.391
## AverageExcludingDutch FlynnWISCOrder gJRW gJRB
## BWJR -0.293 0.323 0.770 0.706
## DutchOrder 0.463 -0.018 -0.421 -0.400
## SimpleAverageOrder 0.574 0.867 0.093 0.381
## AverageExcludingDutch 1.000 0.431 -0.283 -0.035
## FlynnWISCOrder 0.431 1.000 0.412 0.612
## gJRW -0.283 0.412 1.000 0.883
## gJRB -0.035 0.612 0.883 1.000
## gJRWeighted -0.245 0.456 0.998 0.912
## gJRAverage -0.173 0.519 0.975 0.966
## BWNJ -0.109 0.073 0.715 0.678
## gNJW -0.079 0.459 0.703 0.820
## gNJB -0.252 0.476 0.822 0.851
## gNJAverage -0.169 0.501 0.813 0.896
## gJRWeighted gJRAverage BWNJ gNJW gNJB gNJAverage
## BWJR 0.763 0.763 0.766 0.469 0.695 0.614
## DutchOrder -0.422 -0.424 -0.217 -0.248 -0.535 -0.405
## SimpleAverageOrder 0.145 0.233 -0.143 0.455 0.256 0.391
## AverageExcludingDutch -0.245 -0.173 -0.109 -0.079 -0.252 -0.169
## FlynnWISCOrder 0.456 0.519 0.073 0.459 0.476 0.501
## gJRW 0.998 0.975 0.715 0.703 0.822 0.813
## gJRB 0.912 0.966 0.678 0.820 0.851 0.896
## gJRWeighted 1.000 0.987 0.706 0.730 0.840 0.838
## gJRAverage 0.987 1.000 0.719 0.780 0.861 0.877
## BWNJ 0.706 0.719 1.000 0.488 0.471 0.516
## gNJW 0.730 0.780 0.488 1.000 0.733 0.943
## gNJB 0.840 0.861 0.471 0.733 1.000 0.918
## gNJAverage 0.838 0.877 0.516 0.943 0.918 1.000## [1] " Spearman"round(cor(data, method = "spearman"), 3)## BWJR DutchOrder SimpleAverageOrder
## BWJR 1.000 -0.298 0.116
## DutchOrder -0.298 1.000 0.297
## SimpleAverageOrder 0.116 0.297 1.000
## AverageExcludingDutch -0.281 0.494 0.537
## FlynnWISCOrder 0.450 -0.018 0.867
## gJRW 0.662 -0.426 0.085
## gJRB 0.573 -0.444 0.328
## gJRWeighted 0.665 -0.401 0.176
## gJRAverage 0.596 -0.467 0.248
## BWNJ 0.638 -0.236 -0.139
## gNJW 0.415 -0.195 0.389
## gNJB 0.463 -0.693 0.231
## gNJAverage 0.360 -0.426 0.426
## AverageExcludingDutch FlynnWISCOrder gJRW gJRB
## BWJR -0.281 0.450 0.662 0.573
## DutchOrder 0.494 -0.018 -0.426 -0.444
## SimpleAverageOrder 0.537 0.867 0.085 0.328
## AverageExcludingDutch 1.000 0.390 -0.330 -0.196
## FlynnWISCOrder 0.390 1.000 0.401 0.584
## gJRW -0.330 0.401 1.000 0.921
## gJRB -0.196 0.584 0.921 1.000
## gJRWeighted -0.245 0.486 0.994 0.945
## gJRAverage -0.189 0.552 0.960 0.985
## BWNJ -0.140 0.067 0.675 0.620
## gNJW -0.223 0.389 0.756 0.790
## gNJB -0.401 0.426 0.701 0.771
## gNJAverage -0.242 0.498 0.768 0.869
## gJRWeighted gJRAverage BWNJ gNJW gNJB gNJAverage
## BWJR 0.665 0.596 0.638 0.415 0.463 0.360
## DutchOrder -0.401 -0.467 -0.236 -0.195 -0.693 -0.426
## SimpleAverageOrder 0.176 0.248 -0.139 0.389 0.231 0.426
## AverageExcludingDutch -0.245 -0.189 -0.140 -0.223 -0.401 -0.242
## FlynnWISCOrder 0.486 0.552 0.067 0.389 0.426 0.498
## gJRW 0.994 0.960 0.675 0.756 0.701 0.768
## gJRB 0.945 0.985 0.620 0.790 0.771 0.869
## gJRWeighted 1.000 0.979 0.675 0.765 0.698 0.784
## gJRAverage 0.979 1.000 0.636 0.754 0.742 0.827
## BWNJ 0.675 0.636 1.000 0.529 0.274 0.383
## gNJW 0.765 0.754 0.529 1.000 0.683 0.927
## gNJB 0.698 0.742 0.274 0.683 1.000 0.866
## gNJAverage 0.784 0.827 0.383 0.927 0.866 1.000OGMarks <- data.frame("BWGap.FlynnEffect" = c("Above", "Below"), "Above" = c("Similarities, Comprehension, Vocabulary, Block Design", "Picture Completion"), "Below" = c("Object Assembly, Information", "Arithmetic, Picture Arrangement, Digit Span, Digit-Symbol Coding")); OGMarksWith all data cited considered, those subtests with above-median Flynn effects were Similarities, Picture Completion, Block Design, Digit-Symbol Coding, and Picture Arrangement. Likewise, the above-median Black-White gaps on the WISC-R were observed in the Similarities, Block Design, Vocabulary, Information, and Object Assembly subtests. Below-median Flynn effects were observed in Comprehension, Vocabulary, Arithmetic, Information, and Object Assembly and below-median Black-White gaps were found in Comprehension, Picture Completion, Arithmetic, Digit-Symbol Coding, and Picture Arrangement.
MoreData <- data.frame("BWGap.FlynnEffect" = c("Above", "Below"), "Above" = c("Similarities, Block Design", "Picture Completion, Digit-Symbol Coding, Picture Arrangement"), "Below" = c("Vocabulary, Information, Object Assembly", "Comprehension, Arithmetic")); MoreDataThe differences between Marks’ and the comprehensive cross-tabulations are stark and do not favor his literacy-based theory. His literacy-based explanation would see verbal tests (Similarities, Comprehension, Vocabulary, and Information) located in the above-median Flynn effect and above-median Black-White gap quadrant. Instead, referencing all of the data, it is apparent that Similarities had an above-median Black-White gap and Flynn effect, while Comprehension had a below-median Black-White gap and Flynn effect and the remaining verbal tests showed below-median Flynn effects and above-median Black-White gaps. Three of four verbal subtests had below-median Flynn effects and above-median Black-white gaps whereas four of six non-verbal subtests had above-median Flynn effects and 2/6 had above-median Black-White gaps. Per this method, Flynn effects covary with tests that show lower Black-White gaps (although with this data, not yet significantly), consistent with Spearman’s hypothesis and the observation that the Flynn effect is not a Jensen effect. g Loadings, on the other hand, were related to Black-White differences and not as much or negatively to Flynn effects. Using all of the data reveals Marks’ hypothesis was not supported. Note that Digit Span was not included because it was not used in all available data. Weighting Flynn effects by n does not meaningfully change the results.