Section 41 ANOVA with Blocking: function aov


  • The function aov also fits an analysis of variance model by a call to lm for each stratum for a balanced experimental design.

  • If the formula contains an Error term, this is used to specify error strata, and appropriate models are fitted within each error stratum.

  • If you have multiple error terms in the data, then the aov is the appropriate function to fit anova model.

41.1 Estimates: Effects


\[ \large fm.aov \leftarrow aov(SBP \sim Centre + Group + DM + Group:DM, \space data=BP) \]


\[ \large aov(fm.aov) \]


\[ \large summary(fm.aov) \]


41.2 Using aov function

# function `aov`
fm.aov <- aov(SBP ~ Centre + Group + DM + Group:DM, data = BP)


# function `aov` with error stratum

# fm1.aov <- aov(SBP ~ Group + DM + Error(Centre), data=BP)


# Analysis of variance
summary(fm.aov)
             Df Sum Sq Mean Sq F value  Pr(>F)    
Centre        4   16.5     4.1   0.257 0.90522    
Group         3 2655.1   885.0  55.202 < 2e-16 ***
DM            1 2373.6  2373.6 148.051 < 2e-16 ***
Group:DM      3  240.8    80.3   5.006 0.00231 ** 
Residuals   188 3014.1    16.0                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Estimates of effects
model.tables(fm.aov, type = "effects", se = TRUE)
Tables of effects

 Centre 
Centre
    H1     H2     H3     H4     H5 
-0.095 -0.470  0.130  0.030  0.405 

 Group 
Group
     A      B      C      D 
-2.645 -4.065  1.475  5.235 

 DM 
DM
     N      Y 
-3.445  3.445 

 Group:DM 
     DM
Group N      Y     
    A  1.345 -1.345
    B  0.365 -0.365
    C -0.015  0.015
    D -1.695  1.695

Standard errors of effects
        Centre  Group     DM Group:DM
        0.6331 0.5663 0.4004   0.8008
replic.     40     50    100       25
# Estimates of means
model.tables(fm.aov, type = "means", se = TRUE)
Tables of means
Grand mean
        
104.745 

 Centre 
Centre
    H1     H2     H3     H4     H5 
104.65 104.28 104.88 104.78 105.15 

 Group 
Group
     A      B      C      D 
102.10 100.68 106.22 109.98 

 DM 
DM
     N      Y 
101.30 108.19 

 Group:DM 
     DM
Group N      Y     
    A 100.00 104.20
    B  97.60 103.76
    C 102.76 109.68
    D 104.84 115.12

Standard errors for differences of means
        Centre  Group     DM Group:DM
        0.8953 0.8008 0.5663   1.1325
replic.     40     50    100       25
# Plot of residuals
plot(fm.aov)