H0: Mu1 = Mu2 = Mu3
Syntax
aov(formula, data = name.data) Example
aov(Y~X, data = name.data)
x=c(4,2,3,1,2)
y=c(4,5,1,3)
z=c(1,2,4,5,1,1,1)
Y=c(x,y,z)
X=c(rep("x",5),rep("y",4),rep("z",7))
aov(Y~X)## Call:
## aov(formula = Y ~ X)
##
## Terms:
## X Residuals
## Sum of Squares 3.192857 30.807143
## Deg. of Freedom 2 13
##
## Residual standard error: 1.539409
## Estimated effects may be unbalancedsummary(aov(Y~X))## Df Sum Sq Mean Sq F value Pr(>F)
## X 2 3.193 1.596 0.674 0.527
## Residuals 13 30.807 2.370H0: Mu1 = Mu2 = Mu3
Syntax
aov(formula, data = name.data)
Example
aov(Y~X, data = name.data)
Equal observations (in each cell)
x=c(14,9,3,7,2)
y=c(4,5,1,3,4)
z=c(1,1,1,1,1)
Y=c(x,y,z)
X=c(rep("x",5),rep("y",5),rep("z",5))
aov(Y~X)## Call:
## aov(formula = Y ~ X)
##
## Terms:
## X Residuals
## Sum of Squares 91.2 103.2
## Deg. of Freedom 2 12
##
## Residual standard error: 2.932576
## Estimated effects may be unbalancedsummary(aov(Y~X))## Df Sum Sq Mean Sq F value Pr(>F)
## X 2 91.2 45.6 5.302 0.0224 *
## Residuals 12 103.2 8.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1H0: Mu1 = Mu2 = Mu3 H0: beta1 = beta2 = beta3 = beta4 = beta5
Syntax
aov(formula, data = name.data)
x=c(14,9,3,7,2)
y=c(4,5,1,3,4)
z=c(1,1,1,1,1)
Y=c(x,y,z)
X=c(rep("x",5),rep("y",5),rep("z",5))
Z=rep(LETTERS[1:5],3)
cbind(Y,X,Z)## Y X Z
## [1,] "14" "x" "A"
## [2,] "9" "x" "B"
## [3,] "3" "x" "C"
## [4,] "7" "x" "D"
## [5,] "2" "x" "E"
## [6,] "4" "y" "A"
## [7,] "5" "y" "B"
## [8,] "1" "y" "C"
## [9,] "3" "y" "D"
## [10,] "4" "y" "E"
## [11,] "1" "z" "A"
## [12,] "1" "z" "B"
## [13,] "1" "z" "C"
## [14,] "1" "z" "D"
## [15,] "1" "z" "E"aov(Y~X+Z)## Call:
## aov(formula = Y ~ X + Z)
##
## Terms:
## X Z Residuals
## Sum of Squares 91.20000 43.73333 59.46667
## Deg. of Freedom 2 4 8
##
## Residual standard error: 2.726414
## Estimated effects may be unbalancedsummary(aov(Y~X+Z))## Df Sum Sq Mean Sq F value Pr(>F)
## X 2 91.20 45.60 6.135 0.0243 *
## Z 4 43.73 10.93 1.471 0.2971
## Residuals 8 59.47 7.43
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1