Cushny-Peebles Data: Soporific Effects of Scopolamine Derivatives

Description

Cushny and Peebles (1905) studied the effects of hydrobromides related to scopolamine and atropine in producing sleep. The sleep of mental patients was measured without hypnotic (Control) and after treatment with one of three drugs: L. hyoscyamine hydrobromide (L_hyoscyamine), L. hyoscine hydrobromide (L_hyoscyine), and a mixture (racemic) form, DL_hyoscine, called atropine. The L (levo) and D (detro) form of a given molecule are optical isomers (mirror images).

The drugs were given on alternate evenings, and the hours of sleep were compared with the intervening control night. Each of the drugs was tested in this manner a varying number of times in each subject. The average number of hours of sleep for each treatment is the response.

Student (1908) used these data to illustrate the paired-sample t-test in small samples, testing the hypothesis that the mean difference between a given drug and the control condition was zero. This data set became well known when used by Fisher (1925). Both Student and Fisher had problems labeling the drugs correctly (see Senn & Richardson (1994)), and consequently came to wrong conclusions.

But as well, the sample sizes (number of nights) for each mean differed widely, ranging from 3-9, and this was not taken into account in their analyses. To allow weighted analyses, the number of observations for each mean is contained in the data frame CushnyPeeblesN.

Usage

data(CushnyPeebles)
data(CushnyPeeblesN)
	

Format

CushnyPeebles: A data frame with 11 observations on the following 4 variables.

Control

a numeric vector: mean hours of sleep

L_hyoscyamine

a numeric vector: mean hours of sleep

L_hyoscine

a numeric vector: mean hours of sleep

D_hyoscine

a numeric vector: mean hours of sleep

CushnyPeeblesN: A data frame with 11 observations on the following 4 variables.

Control

a numeric vector: number of observations

L_hyoscyamine

a numeric vector: number of observations

L_hyoscine

a numeric vector: number of observations

DL_hyoscine

a numeric vector: number of observations

Details

The last patient (11) has no Control observations, and so is often excluded in analyses or other versions of this data set.

Source

Cushny, A. R., and Peebles, A. R. (1905), "The Action of Optical Isomers. II: Hyoscines," Journal of Physiology, 32, 501-510.

Senn, Stephen, Data from Cushny and Peebles, http://www.senns.demon.co.uk/Data/Cushny.xls

References

Fisher, R. A. (1925), Statistical Methods for Research Workers, Edinburgh and London: Oliver & Boyd.

Student (1908), "The Probable Error of a Mean," Biometrika, 6, 1-25.

Senn, S.J. and Richardson, W. (1994), "The first t-test", Statistics in Medicine, 13, 785-803.

See Also

sleep for an alternative form of this data set.

Examples

data(CushnyPeebles)
# quick looks at the data
plot(CushnyPeebles)
boxplot(CushnyPeebles, ylab="Hours of Sleep", xlab="Treatment")

##########################
# Repeated measures MANOVA
require(car)

CPmod <- lm(cbind(Control, L_hyoscyamine, L_hyoscine, DL_hyoscine) ~ 1, data=CushnyPeebles)

# Assign within-S factor and contrasts
Treatment <- factor(colnames(CushnyPeebles), levels=colnames(CushnyPeebles))
contrasts(Treatment) <- matrix(
	c(-3, 1, 1, 1,
	   0,-2, 1, 1,
	   0, 0,-1, 1), ncol=3)
colnames(contrasts(Treatment)) <- c("Control.Drug", "L.DL", "L_hy.DL_hy")

Treats <- data.frame(Treatment)
(CPaov <- Anova(CPmod, idata=Treats, idesign= ~Treatment))
summary(CPaov, univariate=FALSE)

if (require(heplots)) {
  heplot(CPmod, idata=Treats, idesign= ~Treatment, iterm="Treatment", 
	xlab="Control vs Drugs", ylab="L vs DL drug")
  pairs(CPmod, idata=Treats, idesign= ~Treatment, iterm="Treatment")
}

################################
# reshape to long format, add Ns

CPlong <- stack(CushnyPeebles)[,2:1]
colnames(CPlong) <- c("treatment", "sleep")
CPN <- stack(CushnyPeeblesN)
CPlong <- data.frame(patient=rep(1:11,4), CPlong, n=CPN$values)
str(CPlong)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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> library(HistData)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/HistData/CushnyPeebles.Rd_%03d_medium.png", width=480, height=480)
> ### Name: CushnyPeebles
> ### Title: Cushny-Peebles Data: Soporific Effects of Scopolamine
> ###   Derivatives
> ### Aliases: CushnyPeebles CushnyPeeblesN
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(CushnyPeebles)
> # quick looks at the data
> plot(CushnyPeebles)
> boxplot(CushnyPeebles, ylab="Hours of Sleep", xlab="Treatment")
> 
> ##########################
> # Repeated measures MANOVA
> require(car)
Loading required package: car
> 
> CPmod <- lm(cbind(Control, L_hyoscyamine, L_hyoscine, DL_hyoscine) ~ 1, data=CushnyPeebles)
> 
> # Assign within-S factor and contrasts
> Treatment <- factor(colnames(CushnyPeebles), levels=colnames(CushnyPeebles))
> contrasts(Treatment) <- matrix(
+ 	c(-3, 1, 1, 1,
+ 	   0,-2, 1, 1,
+ 	   0, 0,-1, 1), ncol=3)
> colnames(contrasts(Treatment)) <- c("Control.Drug", "L.DL", "L_hy.DL_hy")
> 
> Treats <- data.frame(Treatment)
> (CPaov <- Anova(CPmod, idata=Treats, idesign= ~Treatment))
Note: model has only an intercept; equivalent type-III tests substituted.

Type III Repeated Measures MANOVA Tests: Pillai test statistic
            Df test stat approx F num Df den Df    Pr(>F)    
(Intercept)  1   0.90437   85.113      1      9 6.969e-06 ***
Treatment    1   0.70354    5.537      3      7   0.02896 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> summary(CPaov, univariate=FALSE)

Type III Repeated Measures MANOVA Tests:

------------------------------------------
 
Term: (Intercept) 

 Response transformation matrix:
              (Intercept)
Control                 1
L_hyoscyamine           1
L_hyoscine              1
DL_hyoscine             1

Sum of squares and products for the hypothesis:
            (Intercept)
(Intercept)      3385.6

Sum of squares and products for error:
            (Intercept)
(Intercept)         358

Multivariate Tests: (Intercept)
                 Df test stat approx F num Df den Df     Pr(>F)    
Pillai            1  0.904370 85.11285      1      9 6.9692e-06 ***
Wilks             1  0.095630 85.11285      1      9 6.9692e-06 ***
Hotelling-Lawley  1  9.456983 85.11285      1      9 6.9692e-06 ***
Roy               1  9.456983 85.11285      1      9 6.9692e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

------------------------------------------
 
Term: Treatment 

 Response transformation matrix:
              TreatmentControl.Drug TreatmentL.DL TreatmentL_hy.DL_hy
Control                          -3             0                   0
L_hyoscyamine                     1            -2                   0
L_hyoscine                        1             1                  -1
DL_hyoscine                       1             1                   1

Sum of squares and products for the hypothesis:
                      TreatmentControl.Drug TreatmentL.DL TreatmentL_hy.DL_hy
TreatmentControl.Drug                291.60       170.100              -0.540
TreatmentL.DL                        170.10        99.225              -0.315
TreatmentL_hy.DL_hy                   -0.54        -0.315               0.001

Sum of squares and products for error:
                      TreatmentControl.Drug TreatmentL.DL TreatmentL_hy.DL_hy
TreatmentControl.Drug                299.04        49.230              13.330
TreatmentL.DL                         49.23        58.665               3.745
TreatmentL_hy.DL_hy                   13.33         3.745               3.289

Multivariate Tests: Treatment
                 Df test stat approx F num Df den Df   Pr(>F)  
Pillai            1 0.7035419  5.53737      3      7 0.028955 *
Wilks             1 0.2964581  5.53737      3      7 0.028955 *
Hotelling-Lawley  1 2.3731584  5.53737      3      7 0.028955 *
Roy               1 2.3731584  5.53737      3      7 0.028955 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> if (require(heplots)) {
+   heplot(CPmod, idata=Treats, idesign= ~Treatment, iterm="Treatment", 
+ 	xlab="Control vs Drugs", ylab="L vs DL drug")
+   pairs(CPmod, idata=Treats, idesign= ~Treatment, iterm="Treatment")
+ }
Loading required package: heplots
Note: model has only an intercept; equivalent type-III tests substituted.
Note: model has only an intercept; equivalent type-III tests substituted.
> 
> ################################
> # reshape to long format, add Ns
> 
> CPlong <- stack(CushnyPeebles)[,2:1]
> colnames(CPlong) <- c("treatment", "sleep")
> CPN <- stack(CushnyPeeblesN)
> CPlong <- data.frame(patient=rep(1:11,4), CPlong, n=CPN$values)
> str(CPlong)
'data.frame':	44 obs. of  4 variables:
 $ patient  : int  1 2 3 4 5 6 7 8 9 10 ...
 $ treatment: Factor w/ 4 levels "Control","DL_hyoscine",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ sleep    : num  0.6 3 4.7 5.5 6.2 3.2 2.5 2.8 1.1 2.9 ...
 $ n        : int  9 9 8 9 9 8 8 7 8 9 ...
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>