Anova Inclass

Read in the fisheries data

rr fisheries <- read.csv(_FishData.csv, header = TRUE)

Check for normality:

rr boxplot(fisheries\(Low, fisheries\)Med, fisheries$High)

rr shapiro.test(fisheries$Low)

    Shapiro-Wilk normality test

data:  fisheries$Low
W = 0.91761, p-value = 0.4883

rr shapiro.test(fisheries$Med)

    Shapiro-Wilk normality test

data:  fisheries$Med
W = 0.9816, p-value = 0.9592

rr shapiro.test(fisheries$High)

    Shapiro-Wilk normality test

data:  fisheries$High
W = 0.79945, p-value = 0.05811

Prepare data for anova and perform anova:

rr fish_stack <- stack(fisheries) names(fish_stack) <- c(, ) fish.aov <- aov(fish_stack\(Mass~fish_stack\)Treatment) fish.aov

Call:
   aov(formula = fish_stack$Mass ~ fish_stack$Treatment)

Terms:
                fish_stack$Treatment Residuals
Sum of Squares              490.0544  252.6683
Deg. of Freedom                    2        15

Residual standard error: 4.104212
Estimated effects may be unbalanced

rr summary(fish.aov)

                     Df Sum Sq Mean Sq F value   Pr(>F)    
fish_stack$Treatment  2  490.1  245.03   14.55 0.000308 ***
Residuals            15  252.7   16.84                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Showing that the F value is the ratio of the mean squares and that using the f distribution you can find the p-value with the degrees of freedom indicated.

rr 245.03/16.84

[1] 14.55048

rr 1-pf(14.55, 2, 15)

[1] 0.0003071815

Perform posthoc analysis:

rr TukeyHSD(fish.aov)

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = fish_stack$Mass ~ fish_stack$Treatment)

$`fish_stack$Treatment`
              diff       lwr      upr     p adj
Med-Low   7.466667  1.311785 13.62155 0.0170662
High-Low 12.716667  6.561785 18.87155 0.0002185
High-Med  5.250000 -0.904882 11.40488 0.1008030