One-way ANOVA (CR-p design)
TODO
- link to normality, varianceHom, regressionDiag, regression for model comparison, resamplingPerm, resamplingBootALM
Install required packages
car, effectsize, DescTools, multcomp
wants <- c("car", "effectsize", "multcomp", "DescTools")
has <- wants %in% rownames(installed.packages())
if(any(!has)) install.packages(wants[!has])CR-\(p\) ANOVA
Simulate data
set.seed(123)
P <- 4
Nj <- c(41, 37, 42, 40)
muJ <- rep(c(-1, 0, 1, 2), Nj)
dfCRp <- data.frame(IV=factor(rep(LETTERS[1:P], Nj)),
DV=rnorm(sum(Nj), muJ, 5))
Using oneway.test()
Assuming variance homogeneity
One-way analysis of means
data: DV and IV
F = 2.0057, num df = 3, denom df = 156, p-value = 0.1154Generalized Welch-test without assumption of variance homogeneity
One-way analysis of means (not assuming equal variances)
data: DV and IV
F = 2.0203, num df = 3.000, denom df = 85.503, p-value = 0.1171Using aov()
Df Sum Sq Mean Sq F value Pr(>F)
IV 3 133 44.35 2.006 0.115
Residuals 156 3450 22.11 Tables of means
Grand mean
0.4318522
IV
A B C D
-0.8643 0.05185 1.042 1.471
rep 41.0000 37.00000 42.000 40.000Model comparisons using anova(lm())
Analysis of Variance Table
Response: DV
Df Sum Sq Mean Sq F value Pr(>F)
IV 3 133.1 44.353 2.0057 0.1154
Residuals 156 3449.7 22.113 Analysis of Variance Table
Model 1: DV ~ 1
Model 2: DV ~ IV
Res.Df RSS Df Sum of Sq F Pr(>F)
1 159 3582.8
2 156 3449.7 3 133.06 2.0057 0.1154[1] 3449.703Effect size estimates
\(\hat{\eta^{2}}\), \(\hat{\omega^{2}}\), \(\hat{f^{2}}\)
Parameter | Eta2 (partial) | 90% CI
-----------------------------------------
IV | 0.04 | [0.00, 0.08]Parameter | Omega2 (partial) | 90% CI
-------------------------------------------
IV | 0.02 | [0.00, 0.05]Parameter | Cohen's f (partial) | 90% CI
----------------------------------------------
IV | 0.20 | [0.00, 0.30]Planned comparisons - a-priori
General contrasts using glht() from package multcomp
cntrMat <- rbind("A-D" =c( 1, 0, 0, -1),
"1/3*(A+B+C)-D"=c(1/3, 1/3, 1/3, -1),
"B-C" =c( 0, 1, -1, 0))
library(multcomp) # for glht()
summary(glht(aovCRp, linfct=mcp(IV=cntrMat), alternative="less"),
test=adjusted("none"))
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: User-defined Contrasts
Fit: aov(formula = DV ~ IV, data = dfCRp)
Linear Hypotheses:
Estimate Std. Error t value Pr(<t)
A-D >= 0 -2.3351 1.0451 -2.234 0.0134 *
1/3*(A+B+C)-D >= 0 -1.3941 0.8589 -1.623 0.0533 .
B-C >= 0 -0.9906 1.0603 -0.934 0.1758
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Adjusted p values reported -- none method)Pairwise \(t\)-tests
Pairwise comparisons using t tests with pooled SD
data: dfCRp$DV and dfCRp$IV
A B C
B 1.00 - -
C 0.40 1.00 -
D 0.16 1.00 1.00
P value adjustment method: bonferroni Planned comparisons - post-hoc
Scheffe tests
Posthoc multiple comparisons of means: Scheffe Test
95% family-wise confidence level
$IV
diff lwr.ci upr.ci pval
A-D -2.3351002 -5.288758 0.6185575 0.1770
A,B,C-D -1.3941211 -3.821531 1.0332885 0.4538
B-C -0.9906183 -3.987210 2.0059738 0.8319
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Tukey’s simultaneous confidence intervals
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = DV ~ IV, data = dfCRp)
$IV
diff lwr upr p adj
B-A 0.9161596 -1.8529795 3.685299 0.8257939
C-A 1.9067779 -0.7743204 4.587876 0.2555117
D-A 2.3351002 -0.3789061 5.049107 0.1185540
C-B 0.9906183 -1.7628388 3.744075 0.7864641
D-B 1.4189406 -1.3665697 4.204451 0.5497967
D-C 0.4283223 -2.2696814 3.126326 0.9762890
Using glht() from package multcomp
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: aov(formula = DV ~ IV, data = dfCRp)
Linear Hypotheses:
Estimate Std. Error t value Pr(>|t|)
B - A == 0 0.9162 1.0663 0.859 0.826
C - A == 0 1.9068 1.0324 1.847 0.255
D - A == 0 2.3351 1.0451 2.234 0.119
C - B == 0 0.9906 1.0603 0.934 0.786
D - B == 0 1.4189 1.0726 1.323 0.550
D - C == 0 0.4283 1.0389 0.412 0.976
(Adjusted p values reported -- single-step method)
Simultaneous Confidence Intervals
Multiple Comparisons of Means: Tukey Contrasts
Fit: aov(formula = DV ~ IV, data = dfCRp)
Quantile = 2.5981
95% family-wise confidence level
Linear Hypotheses:
Estimate lwr upr
B - A == 0 0.9162 -1.8542 3.6865
C - A == 0 1.9068 -0.7755 4.5890
D - A == 0 2.3351 -0.3801 5.0503
C - B == 0 0.9906 -1.7640 3.7453
D - B == 0 1.4189 -1.3678 4.2057
D - C == 0 0.4283 -2.2709 3.1275Detach (automatically) loaded packages (if possible)
try(detach(package:multcomp))
try(detach(package:mvtnorm))
try(detach(package:TH.data))
try(detach(package:survival))
try(detach(package:MASS))
try(detach(package:effectsize))
try(detach(package:DescTools))Get the article source from GitHub
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