Analysis of Variance

ANOVA-One Factor

str(chickwts)
'data.frame':   71 obs. of  2 variables:
 $ weight: num  179 160 136 227 217 168 108 124 143 140 ...
 $ feed  : Factor w/ 6 levels "casein","horsebean",..: 2 2 2 2 2 2 2 2 2 2 ...
summary(chickwts)
     weight             feed   
 Min.   :108.0   casein   :12  
 1st Qu.:204.5   horsebean:10  
 Median :258.0   linseed  :12  
 Mean   :261.3   meatmeal :11  
 3rd Qu.:323.5   soybean  :14  
 Max.   :423.0   sunflower:12  
with(chickwts,boxplot(weight~feed,
     col= "lightgray",
     main= "",
     xlab= "Feed type", ylab= "Weight (g)", ylim= c(100,450), las= 1)) 

with(chickwts, tapply(weight, feed, mean))
   casein horsebean   linseed  meatmeal   soybean sunflower 
 323.5833  160.2000  218.7500  276.9091  246.4286  328.9167 
with(chickwts, tapply(weight, feed, sd))
   casein horsebean   linseed  meatmeal   soybean sunflower 
 64.43384  38.62584  52.23570  64.90062  54.12907  48.83638 
with(chickwts, bartlett.test(weight ~ feed))  

    Bartlett test of homogeneity of variances

data:  weight by feed
Bartlett's K-squared = 3.2597, df = 5, p-value = 0.66


Implementing Analysis of Variance Test
with(chickwts, oneway.test(weight ~ feed, var.equal = TRUE))

    One-way analysis of means

data:  weight and feed
F = 15.365, num df = 5, denom df = 65, p-value = 5.936e-10


Pairwise Comparison

with(chickwts, pairwise.t.test(weight, feed, pool.sd = TRUE))

    Pairwise comparisons using t tests with pooled SD 

data:  weight and feed 

          casein  horsebean linseed meatmeal soybean
horsebean 2.9e-08 -         -       -        -      
linseed   0.00016 0.09435   -       -        -      
meatmeal  0.18227 9.0e-05   0.09435 -        -      
soybean   0.00532 0.00298   0.51766 0.51766  -      
sunflower 0.81249 1.2e-08   8.1e-05 0.13218  0.00298

P value adjustment method: holm