case1301 {Sleuth2}

Seaweed Grazers

Description

To study the influence of ocean grazers on regeneration rates of seaweed in the intertidal zone, a researcher scraped rock plots free of seaweed and observed the degree of regeneration when certain types of seaweed-grazing animals were denied access. The grazers were limpets (L), small fishes (f) and large fishes (F). Each plot received one of six treatments named by which grazers were allowed access. In addition, the researcher applied the treatments in eight blocks of 12 plots each. Within each block she randomly assigned treatments to plots. The blocks covered a wide range of tidal conditions.

Usage

case1301

Format

A data frame with 96 observations on the following 3 variables.

Cover

percent of regenerated seaweed cover

Block

a factor with levels "B1", "B2", "B3", "B4", "B5", "B6", "B7" and "B8"

Treat

a factor indicating treatment, with levels "C", "f", "fF", "L", "Lf" and "LfF"

Source

Ramsey, F.L. and Schafer, D.W. (2002). The Statistical Sleuth: A Course in Methods of Data Analysis (2nd ed), Duxbury.

References

Olson, A. (1993). Evolutionary and Ecological Interactions Affecting Seaweeds, Ph.D. Thesis. Oregon State University.

Examples

str(case1301)

# full two-way model with interactions
fitfull <- aov(Cover ~ Treat*Block, case1301)
# Residual plot indicates a transformation might help
plot(fitfull)  

# Log of seaweed "regeneration ratio" 
y <- with(case1301, log(Cover/(100-Cover)))
# Full two-way model with interactions
fitfull <- aov(y~Treat*Block, case1301)
# No problems indicated by residual plot
plot(fitfull)
# Note that interactions are not statistically significant
anova(fitfull) 
# Additive model (no interactions)
fitadditive <- aov(y ~ Treat + Block, case1301) 

# Make indicator variables for presence of limpets, small fish, and large fish 
lmp <- with(case1301, ifelse(Treat %in% c("L", "Lf", "LfF"), 1, 0))
sml <- with(case1301, ifelse(Treat %in% c("f", "fF", "Lf", "LfF"), 1, 0))
big <- with(case1301, ifelse(Treat %in% c("fF", "LfF"), 1, 0))

fitsimple <- lm(y ~ Block + lmp + sml + big, case1301)
# Model with main effects of 3 "presence" factors seems ok.
anova(fitsimple, fitadditive)  
summary(fitsimple, cor=FALSE)