case1301: Seaweed Grazers

In Sleuth2: Data Sets from Ramsey and Schafer's "Statistical Sleuth (2nd Ed)"

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)

Example output

'data.frame':	96 obs. of  3 variables:
 $ Cover: num  14 23 22 35 67 82 94 95 34 53 ...
 $ Block: Factor w/ 8 levels "B1","B2","B3",..: 1 1 2 2 3 3 4 4 5 5 ...
 $ Treat: Factor w/ 6 levels "C","f","fF","L",..: 1 1 1 1 1 1 1 1 1 1 ...
Analysis of Variance Table

Response: y
            Df Sum Sq Mean Sq F value Pr(>F)    
Treat        5 96.993 19.3986 64.0553 <2e-16 ***
Block        7 76.239 10.8912 35.9634 <2e-16 ***
Treat:Block 35 15.230  0.4352  1.4369 0.1209    
Residuals   48 14.536  0.3028                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Variance Table

Model 1: y ~ Block + lmp + sml + big
Model 2: y ~ Treat + Block
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     85 29.996                           
2     83 29.767  2   0.22928 0.3197 0.7273

Call:
lm(formula = y ~ Block + lmp + sml + big, data = case1301)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.47682 -0.40585  0.03001  0.33617  1.30143 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -1.2545     0.2011  -6.238 1.66e-08 ***
BlockB2       0.4600     0.2425   1.897  0.06127 .  
BlockB3       2.1046     0.2425   8.678 2.42e-13 ***
BlockB4       2.9807     0.2425  12.291  < 2e-16 ***
BlockB5       1.2160     0.2425   5.014 2.87e-06 ***
BlockB6       2.0251     0.2425   8.350 1.11e-12 ***
BlockB7       1.1085     0.2425   4.571 1.64e-05 ***
BlockB8       1.3300     0.2425   5.484 4.19e-07 ***
lmp          -1.8288     0.1213 -15.082  < 2e-16 ***
sml          -0.3933     0.1485  -2.648  0.00965 ** 
big          -0.6140     0.1485  -4.135 8.31e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.5941 on 85 degrees of freedom
Multiple R-squared:  0.8522,	Adjusted R-squared:  0.8349 
F-statistic: 49.02 on 10 and 85 DF,  p-value: < 2.2e-16

Sleuth2 documentation built on May 2, 2019, 7:01 a.m.