# First example -----------------------------------------------------------
# Data input
Y <- c(34.5,31.2,37.8,38.9,40,39.1,32,35,41)
Trat <- as.factor(c(1,1,2,2,2,3,3,3,3))
d1 <- data.frame(Y,Trat)
head (d1)
## Y Trat
## 1 34.5 1
## 2 31.2 1
## 3 37.8 2
## 4 38.9 2
## 5 40.0 2
## 6 39.1 3
# Model
f <- Y~Trat
# Homegeneity of variances
bartlett.test(f, data = d1)
##
## Bartlett test of homogeneity of variances
##
## data: Y by Trat
## Bartlett's K-squared = 2.3847, df = 2, p-value = 0.3035
car::leveneTest(f, d1)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 4.6617 0.06003 .
## 6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
fligner.test(f, d1)
##
## Fligner-Killeen test of homogeneity of variances
##
## data: Y by Trat
## Fligner-Killeen:med chi-squared = 6.4106, df = 2, p-value =
## 0.04055
# Analysis of variance
summary (aov ( lm (f, d1))) # Similar to anova
## Df Sum Sq Mean Sq F value Pr(>F)
## Trat 2 44.12 22.058 2.319 0.179
## Residuals 6 57.07 9.512
# Weighted analysis of variance
car::Anova (mod = aov ( lm (f, d1)))
## Anova Table (Type II tests)
##
## Response: Y
## Sum Sq Df F value Pr(>F)
## Trat 44.116 2 2.319 0.1794
## Residuals 57.072 6
# Power of the test
p1 <- power.anova.test(groups = 3, n = c(2,3,4), between.var = 22.058, within.var = 9.512, sig.level = .05, power = NULL)
1-p1$power
## [1] 0.64234966 0.27387225 0.09313386