Detergent Durability Data Set

Detergent durability in an incomplete two-way design.

Usage

data("detergent")

Format

This data frame contains the following variables

detergent

detergent, a factor at levels A, B, C, D, and E.

block

block, a factor at levels B_1, ..., B_10.

plates

response variable: number of plates washed before the foam disappears.

Details

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. The data were published by multcomp::westfall1999.

References

*

Examples

  ### 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 = 3.0642
#> 95% family-wise confidence level
#>  
#> 
#> Linear Hypotheses:
#>            Estimate lwr      upr     
#> B - A == 0  -2.1333  -4.7929   0.5262
#> C - A == 0   3.6000   0.9404   6.2596
#> D - A == 0   2.2000  -0.4596   4.8596
#> E - A == 0  -4.3333  -6.9929  -1.6738
#> C - B == 0   5.7333   3.0738   8.3929
#> D - B == 0   4.3333   1.6738   6.9929
#> E - B == 0  -2.2000  -4.8596   0.4596
#> D - C == 0  -1.4000  -4.0596   1.2596
#> E - C == 0  -7.9333 -10.5929  -5.2738
#> E - D == 0  -6.5333  -9.1929  -3.8738
#> 

  ### 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"))
  } # }