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The data are from a study of weight gain, where investigators randomly assigned 30 rats to three treatment groups: treatment 1 was a control (no additive); treatments 2 and 3 consisted of two different additives (thiouracil and thyroxin respectively) to the rats drinking water. Weight was measured at baseline (week 0) and at weeks 1, 2, 3, and 4. Due to an accident at the beginning of the study, data on 3 rats from the thyroxin group are unavailable.

Format

A data frame with 27 observations on the following 6 variables.

trt

a factor with levels Control Thiouracil Thyroxin

wt0

Weight at Week 0 (baseline weight)

wt1

Weight at Week 1

wt2

Weight at Week 2

wt3

Weight at Week 3

wt4

Weight at Week 4

Source

Originally from Box (1950), Table D (page 389), where the values for weeks 1-4 were recorded as the gain in weight for that week.

Fitzmaurice, G. M. and Laird, N. M. and Ware, J. H (2004). Applied Longitudinal Analysis, New York, NY: Wiley-Interscience. https://rdrr.io/rforge/ALA/.

Details

The trt factor comes supplied with contrasts comparing Control to each of Thiouracil and Thyroxin.

References

Box, G.E.P. (1950). Problems in the analysis of growth and wear curves. Biometrics, 6, 362-389.

Friendly, Michael (2010). HE Plots for Repeated Measures Designs. Journal of Statistical Software, 37(4), 1-40. doi:10.18637/jss.v037.i04 .

Examples


data(RatWeight)
contrasts(RatWeight$trt)
#>            [,1] [,2]
#> Control      -1   -1
#> Thiouracil    1    0
#> Thyroxin      0    1

rat.mod <- lm(cbind(wt0, wt1, wt2, wt3, wt4) ~ trt, data=RatWeight)
rat.mod
#> 
#> Call:
#> lm(formula = cbind(wt0, wt1, wt2, wt3, wt4) ~ trt, data = RatWeight)
#> 
#> Coefficients:
#>              wt0        wt1        wt2        wt3        wt4      
#> (Intercept)   54.75714   76.88571  102.21905  123.67143  149.15238
#> trt1          -0.05714   -0.58571   -6.41905  -15.47143  -25.15238
#> trt2           0.81429   -1.02857    2.63810    9.04286   13.70476
#> 

idata <- data.frame(week = ordered(0:4))
car::Anova(rat.mod, idata=idata, idesign=~week, test="Roy")
#> 
#> Type II Repeated Measures MANOVA Tests: Roy test statistic
#>             Df test stat approx F num Df den Df    Pr(>F)    
#> (Intercept)  1   140.617   3374.8      1     24 < 2.2e-16 ***
#> trt          2     0.657      7.9      2     24  0.002334 ** 
#> week         1    56.188    295.0      4     21 < 2.2e-16 ***
#> trt:week     2     1.979     10.9      4     22 5.059e-05 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# quick look at between group effects
pairs(rat.mod)


# between-S, baseline & week 4
heplot(rat.mod, col=c("red", "blue", "green3", "green3"),
  variables=c(1,5),
  hypotheses=c("trt1", "trt2"),
  main="Rat weight data, Between-S effects") 


# within-S
heplot(rat.mod, idata=idata, idesign=~week, iterm="week",
  col=c("red", "blue", "green3"),
#  hypotheses=c("trt1", "trt2"),
  main="Rat weight data, Within-S effects")