> Wheat <- read.csv("C:/Users/Pandion/Desktop/WheatYield.csv")
> View(Wheat)
> WheatAOVcrossed <-aov(Yield~Trtmnt*Pot, data=Wheat)  # show crossed factor MS
> anova(WheatAOVcrossed)
Analysis of Variance Table

Response: Yield
           Df Sum Sq Mean Sq  F value    Pr(>F)    
Trtmnt      3 393.32 131.107 458.6832 < 2.2e-16 ***
Pot         2   1.71   0.854   2.9893  0.069310 .  
Trtmnt:Pot  6   6.38   1.063   3.7201  0.009318 ** 
Residuals  24   6.86   0.286                       
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Default F-ratio from Trtmnt / Residual

> 131.107/0.286   #ambiguous F-ratio, two uncancelled components in numerator
[1] 458.4161

# Calculate correct F-ratio using interaction term
# Model I calculation, as in most text books. See Quinn and Keough

> 131.107/1.063
[1]


# Now Model II calculation.  See Quinn and Keough.
# Calculate nested factor MS
> WheatAOVnested <-aov(Yield~Trtmnt+Trtmnt/Pot, data=Wheat)
> anova(WheatAOVnested)  
Analysis of Variance Table

Response: Yield
           Df Sum Sq Mean Sq  F value    Pr(>F)    
Trtmnt      3 393.32 131.107 458.6832 < 2.2e-16 ***
Trtmnt:Pot  8   8.09   1.011   3.5374  0.007675 ** 
Residuals  24   6.86   0.286                       
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Default F-ratio from Trtmnt / Residual

> 131.107/0.286   #ambiguous F-ratio, two uncancelled components in numerator
[1] 458.4161

# Calculate F-ratio from Pot within treatment  (see Quinn and Keough)

> 131.107/1.011   #unambigous F-ratio, one uncancelled component
[1] 129.6805
> prF<-(1-pf(c(131.107/1.011),3,8))   # p-value from correct F-ratio
> prF      
[1] 4.023346e-07

# Use +Error() to force correct F-ratio, as shown in textbook

> WheatAOVnested <-aov(Yield~Trtmnt+Error(Trtmnt/Pot), data=Wheat)
> WheatAOVnestedError <-aov(Yield~Trtmnt+Error(Trtmnt/Pot), data=Wheat)
> anova(WheatAOVnestedError)
Error in UseMethod("anova") : 
  no applicable method for 'anova' applied to an object of class "c('aovlist', 'listof')