17.1 ANOVA - One Factor
# get summary & structure and create a boxplot of our differences
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
Anova Test
Step 1: Set the Null and Alternate Hypotheses
Step 2: Implement 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
Step 3: Interpret the Results
17.1.1 Pair-wise Comparisons
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