8.1 Interation in ANOVA

Oneway ANOVA means there is a single factor with two or more levels (e.g., book formats such as hard cover, paperback and eBook). Factorial ANOVA means there are two or more independent factors with two or more levels. Fully crossed means that all combinations of the levels of the factors “(beef/high protein + beef/low protein + cereal/high protein + cereal/low protein)” are present in the experiment.

aovOut <- aov(weightgain ~ source * type, data=weightgain)
summary(aovOut)
##             Df Sum Sq Mean Sq F value Pr(>F)  
## source       1    221   220.9   0.988 0.3269  
## type         1   1300  1299.6   5.812 0.0211 *
## source:type  1    884   883.6   3.952 0.0545 .
## Residuals   36   8049   223.6                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The p-value suggests that there is no statistically significant interaction between food source and diet type. There is no significant effect for the main effect of source (F(1,36)=0.988, N.S.)

testF <- rf(n=10000, df1=1, df2=36)  # Generate random Fs for F(1,36)
hist(testF)
abline(v=quantile(testF,c(0.95)),col="black")

quantile(testF,c(0.95))
##     95% 
## 4.00811

The code above draws a vertical line at the point where the F distribution is split into a tail on the right and a central region on the left, each of which contains 5% of the points. The statistical significance criterion is indicated by that vertical line.