detergent.RdDetergent durability in an incomplete two-way design.
data("detergent")This data frame contains the following variables
detergent, a factor at levels A, B,
C, D, and E.
block, a factor at levels B_1, ..., B_10.
response variable: number of plates washed before the foam disappears.
Plates were washed with five detergent varieties, in ten blocks. A complete design would have 50 combinations, here only three detergent varieties in each block were applied in a balanced incomplete block design. Note that there are six observations taken at each detergent level.
H. Scheffe (1959). The Analysis of Variance. New York: John Wiley & Sons, page 189.
P. H. Westfall, R. D. Tobias, D. Rom, R. D. Wolfinger, Y. Hochberg (1999). Multiple Comparisons and Multiple Tests Using the SAS System. Cary, NC: SAS Institute Inc., page 189.
### set up two-way ANOVA without interactions
amod <- aov(plates ~ block + detergent, data = detergent)
### set up all-pair comparisons
dht <- glht(amod, linfct = mcp(detergent = "Tukey"))
### see Westfall et al. (1999, p. 190)
confint(dht)
#>
#> Simultaneous Confidence Intervals
#>
#> Multiple Comparisons of Means: Tukey Contrasts
#>
#>
#> Fit: aov(formula = plates ~ block + detergent, data = detergent)
#>
#> Quantile = 3.0632
#> 95% family-wise confidence level
#>
#>
#> Linear Hypotheses:
#> Estimate lwr upr
#> B - A == 0 -2.1333 -4.7920 0.5254
#> C - A == 0 3.6000 0.9413 6.2587
#> D - A == 0 2.2000 -0.4587 4.8587
#> E - A == 0 -4.3333 -6.9920 -1.6746
#> C - B == 0 5.7333 3.0746 8.3920
#> D - B == 0 4.3333 1.6746 6.9920
#> E - B == 0 -2.2000 -4.8587 0.4587
#> D - C == 0 -1.4000 -4.0587 1.2587
#> E - C == 0 -7.9333 -10.5920 -5.2746
#> E - D == 0 -6.5333 -9.1920 -3.8746
#>
### see Westfall et al. (1999, p. 192)
summary(dht, test = univariate())
#>
#> Simultaneous Tests for General Linear Hypotheses
#>
#> Multiple Comparisons of Means: Tukey Contrasts
#>
#>
#> Fit: aov(formula = plates ~ block + detergent, data = detergent)
#>
#> Linear Hypotheses:
#> Estimate Std. Error t value Pr(>|t|)
#> B - A == 0 -2.1333 0.8679 -2.458 0.025762 *
#> C - A == 0 3.6000 0.8679 4.148 0.000757 ***
#> D - A == 0 2.2000 0.8679 2.535 0.022075 *
#> E - A == 0 -4.3333 0.8679 -4.993 0.000133 ***
#> C - B == 0 5.7333 0.8679 6.606 6.05e-06 ***
#> D - B == 0 4.3333 0.8679 4.993 0.000133 ***
#> E - B == 0 -2.2000 0.8679 -2.535 0.022075 *
#> D - C == 0 -1.4000 0.8679 -1.613 0.126291
#> E - C == 0 -7.9333 0.8679 -9.140 9.45e-08 ***
#> E - D == 0 -6.5333 0.8679 -7.527 1.21e-06 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> (Univariate p values reported)
#>
if (FALSE) { # \dontrun{
summary(dht, test = adjusted("Shaffer"))
summary(dht, test = adjusted("Westfall"))
} # }