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A study was conducted investigating the effectiveness of different kinds of psychological treatment on the sensitivity of headache sufferers to noise, described in Hand and Taylor (1987), Study E.

Format

A data frame with 98 observations on the following 6 variables.

type

Type of headache, a factor with levels Migrane Tension

treatment

Treatment group, a factor with levels T1 T2 T3 Control. See Details

u1

Noise level rated as Uncomfortable, initial measure

du1

Noise level rated as Definitely Uncomfortable, initial measure

u2

Noise level rated as Uncomfortable, final measure

du2

Noise level rated as Definitely Uncomfortable, final measure

Source

D. J. Hand and C. C. Taylor (1987). Multivariate analysis of variance and repeated measures: a practical approach for behavioural scientists London: Chapman and Hall. ISBN: 0412258005. Table E.1.

Details

In a pre-post design, 98 patients were first assessed for the volume of noise which they found uncomfortable (U) and definitely uncomfortable (DU). They were then given relaxation training, where they listened to the noise at the DU level and given instruction breathing techniques and the use of visual imagery to distract them from discomfort. One of four treatments was then applied, and all patients were reassessed for the noise volume they considered uncomfortable (U) and definitely uncomfortable (DU).

The treatments are described as follows:

T1

Listened again to the tone at their initial DU level, for the same amount of time they were able to tolerate it before.

T2

Same as T1, with one additional minute exposure

T3

Same as T2, but were explicitly instructed to use the relaxation techniques

Control

These subject experienced no further exposure to the noise tone until the final sensitivity measures were taken

Hand and Taylor described several substantive hypotheses related to the differences among treatments. In the Headache data frame, these have been included as contrasts(Headache$treatment)

Examples


library(car)
data(Headache)
str(Headache)
#> 'data.frame':	98 obs. of  6 variables:
#>  $ type     : Factor w/ 2 levels "Migrane","Tension": 1 1 2 1 1 1 1 1 1 2 ...
#>  $ treatment: Factor w/ 4 levels "T1","T2","T3",..: 3 1 1 3 3 3 2 1 1 3 ...
#>   ..- attr(*, "contrasts")= num [1:4, 1:3] 1 -1 0 0 1 1 0 -2 0 0 ...
#>   .. ..- attr(*, "dimnames")=List of 2
#>   .. .. ..$ : chr [1:4] "T1" "T2" "T3" "Control"
#>   .. .. ..$ : NULL
#>  $ u1       : num  2.34 2.73 0.37 7.5 4.63 3.6 2.45 2.31 1.38 0.85 ...
#>  $ du1      : num  5.3 6.85 0.53 9.12 7.21 7.3 3.75 3.25 2.33 1.42 ...
#>  $ u2       : num  5.8 4.68 0.55 5.7 5.63 4.83 2.5 2 2.23 1.37 ...
#>  $ du2      : num  8.52 6.68 0.84 7.88 6.75 7.32 3.18 3.3 3.98 1.89 ...

# basic MLM, specifying between-S effects
headache.mod <- lm(cbind(u1, du1, u2, du2) ~ type * treatment, data=Headache)

##############################
## between-S tests
##############################
Anova(headache.mod, test="Roy")
#> 
#> Type II MANOVA Tests: Roy test statistic
#>                Df test stat approx F num Df den Df   Pr(>F)   
#> type            1  0.042678   0.9283      4     87 0.451426   
#> treatment       3  0.136154   3.0294      4     89 0.021609 * 
#> type:treatment  3  0.161202   3.5867      4     89 0.009281 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# test each contrast separately
print(linearHypothesis(headache.mod, hypothesis="treatment1", test="Roy"), SSP=FALSE)
#> 
#> Multivariate Test: 
#>     Df  test stat  approx F num Df den Df  Pr(>F)
#> Roy  1 0.01305284 0.2838993      4     87 0.88769
print(linearHypothesis(headache.mod, hypothesis="treatment2", test="Roy"), SSP=FALSE)
#> 
#> Multivariate Test: 
#>     Df  test stat approx F num Df den Df  Pr(>F)
#> Roy  1 0.08267735 1.798232      4     87 0.13645
print(linearHypothesis(headache.mod, hypothesis="treatment3", test="Roy"), SSP=FALSE)
#> 
#> Multivariate Test: 
#>     Df test stat approx F num Df den Df    Pr(>F)   
#> Roy  1 0.1902026 4.136907      4     87 0.0040827 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


heplot(headache.mod, variables=c(1,3),
  hypotheses=paste("treatment", 1:3, sep=""),
  hyp.labels=c("extra.exp", "no.inst", "explicit.inst"),
  xlab="u1: Initial sensitivity", ylab="u2: Final sensitivity",
  main="Headache data: Unpleasant levels")
abline(0, 1, lty=5, col="gray")


heplot(headache.mod, variables=c(2,4),
  hypotheses=paste("treatment", 1:3, sep=""),
  xlab="du1: Initial sensitivity", ylab="du2: Final sensitivity",
  main="Headache data: Definitely Unpleasant levels")
abline(0, 1, lty=5, col="gray")


pairs(headache.mod)


##############################
# between-S and within-S tests
##############################
idata = expand.grid(level=factor(c("U", "DU")), phase=factor(1:2))
Anova(headache.mod, idata=idata, idesign=~level*phase)
#> 
#> Type II Repeated Measures MANOVA Tests: Pillai test statistic
#>                            Df test stat approx F num Df den Df  Pr(>F)    
#> (Intercept)                 1   0.64648  164.580      1     90 < 2e-16 ***
#> type                        1   0.00691    0.627      1     90 0.43072    
#> treatment                   3   0.04122    1.290      3     90 0.28275    
#> type:treatment              3   0.00118    0.035      3     90 0.99106    
#> level                       1   0.60226  136.276      1     90 < 2e-16 ***
#> type:level                  1   0.00000    0.000      1     90 0.99653    
#> treatment:level             3   0.00660    0.199      3     90 0.89661    
#> type:treatment:level        3   0.05360    1.699      3     90 0.17287    
#> phase                       1   0.02459    2.269      1     90 0.13546    
#> type:phase                  1   0.02267    2.088      1     90 0.15193    
#> treatment:phase             3   0.08074    2.635      3     90 0.05459 .  
#> type:treatment:phase        3   0.06236    1.995      3     90 0.12033    
#> level:phase                 1   0.03465    3.231      1     90 0.07563 .  
#> type:level:phase            1   0.00820    0.744      1     90 0.39070    
#> treatment:level:phase       3   0.02164    0.663      3     90 0.57669    
#> type:treatment:level:phase  3   0.03475    1.080      3     90 0.36173    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1