library(SimDesign)
Design <- createDesign(df = c(1000, 7.4, 2.2, .83), # skewness levels 0 to 3
sample_size = c(24,48,96),
sample_size_ratio = 1:3,
var_ratio = c(5:1, 1/2, 1/3, 1/4, 1/5))
Design
#-------------------------------------------------------------------
Generate <- function(condition, fixed_objects = NULL) {
Attach(condition)
N1 <- sample_size * sample_size_ratio / (sample_size_ratio + 1)
N2 <- sample_size - N1
DV <- c(rchisq(N1, df) * sqrt(var_ratio), rchisq(N2, df))
dat <- data.frame(DV=DV, group=c(rep('G1', N1), rep('G2', N2)))
dat
}
Analyse <- function(condition, dat, fixed_objects = NULL) {
BF <- with(dat, levene.test(DV, group, location = 'median'))$p.value
Levene <- with(dat, levene.test(DV, group, location = 'mean'))$p.value
F <- var.test(DV ~ group, dat)$p.value
ret <- c(BF=BF, Levene=Levene, F=F)
ret
}
Summarise <- function(condition, results, fixed_objects = NULL) {
ret <- EDR(results, alpha = .05)
ret
}
#-------------------------------------------------------------------
# save results to the drive
res <- runSimulation(design=Design, replications=5000, generate=Generate,
analyse=Analyse, summarise=Summarise, parallel=TRUE,
packages='lawstat', filename='Nordstokke_Zumbo2007')
resNordstokke and Zumbo (2007) simulation
Simulation from:
- Nordstokke, D. W., & Zumbo B. D. (2007). A Cautionary Tale About Levene’s Tests for Equal Variances. Journal of Educational Research and Policy Studies, 7, 1-14.
Simulation code
# A tibble: 324 × 11
df sample_size sample_size_ratio var_ratio BF Levene F
<dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
1 1000 24 1 5 0.4988 0.6046 0.7074
2 7.4 24 1 5 0.4262 0.5818 0.6778
3 2.2 24 1 5 0.295 0.5196 0.6498
4 0.83 24 1 5 0.156 0.4636 0.634
5 1000 48 1 5 0.9 0.9202 0.9618
6 7.4 48 1 5 0.8224 0.8766 0.9218
7 2.2 48 1 5 0.63 0.7848 0.8518
8 0.83 48 1 5 0.327 0.6422 0.7866
9 1000 96 1 5 0.9992 0.9996 0.9998
10 7.4 96 1 5 0.9888 0.992 0.9952
# ℹ 314 more rows
# ℹ 4 more variables: REPLICATIONS <int>, SIM_TIME <chr>, COMPLETED <chr>,
# SEED <int>Extras
# Type I errors
TypeI <- subset(res, var_ratio == 1)
Table1 <- TypeI[order(TypeI$df, TypeI$sample_size), ]
Table1# A tibble: 36 × 11
df sample_size sample_size_ratio var_ratio BF Levene F
<dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
1 0.83 24 1 1 0.0486 0.2276 0.4062
2 0.83 24 2 1 0.0522 0.2302 0.4026
3 0.83 24 3 1 0.045 0.201 0.378
4 0.83 48 1 1 0.0462 0.2094 0.4316
5 0.83 48 2 1 0.0492 0.2126 0.4148
6 0.83 48 3 1 0.0432 0.2004 0.4248
7 0.83 96 1 1 0.0478 0.2018 0.4544
8 0.83 96 2 1 0.045 0.197 0.4504
9 0.83 96 3 1 0.043 0.1892 0.4332
10 2.2 24 1 1 0.044 0.1408 0.2254
# ℹ 26 more rows
# ℹ 4 more variables: REPLICATIONS <int>, SIM_TIME <chr>, COMPLETED <chr>,
# SEED <int># Power
Power <- subset(res, var_ratio != 1)
Power# A tibble: 288 × 11
df sample_size sample_size_ratio var_ratio BF Levene F
<dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
1 1000 24 1 5 0.4988 0.6046 0.7074
2 7.4 24 1 5 0.4262 0.5818 0.6778
3 2.2 24 1 5 0.295 0.5196 0.6498
4 0.83 24 1 5 0.156 0.4636 0.634
5 1000 48 1 5 0.9 0.9202 0.9618
6 7.4 48 1 5 0.8224 0.8766 0.9218
7 2.2 48 1 5 0.63 0.7848 0.8518
8 0.83 48 1 5 0.327 0.6422 0.7866
9 1000 96 1 5 0.9992 0.9996 0.9998
10 7.4 96 1 5 0.9888 0.992 0.9952
# ℹ 278 more rows
# ℹ 4 more variables: REPLICATIONS <int>, SIM_TIME <chr>, COMPLETED <chr>,
# SEED <int>