How can I classify post-hoc test results in R?

Question

I am trying to understand how to work with ANOVAs and post-hoc tests in R. So far, I have used aov() and TukeyHSD() to analyse my data. Example:

uni2.anova <- aov(Sum_Uni ~ Micro, data= uni2)

uni2.anova

Call:
aov(formula = Sum_Uni ~ Micro, data = uni2)

Terms:
                    Micro  Residuals
Sum of Squares  0.04917262 0.00602925
Deg. of Freedom         15         48

Residual standard error: 0.01120756 
Estimated effects may be unbalanced

My problem is, now I have a huge list of pairwise comparisons but cannot do anything with it:

 TukeyHSD(uni2.anova)
 Tukey multiple comparisons of means
   95% family-wise confidence level

Fit: aov(formula = Sum_Uni ~ Micro, data = uni2)

$Micro
                               diff          lwr           upr     p adj
Act_Glu2-Act_Ala2     -0.0180017863 -0.046632157  0.0106285840 0.6448524
Ana_Ala2-Act_Ala2     -0.0250134285 -0.053643799  0.0036169417 0.1493629
NegI_Ala2-Act_Ala2     0.0702274527  0.041597082  0.0988578230 0.0000000

This dataset has 40 rows... Idealy, I would like to get a dataset that looks something like this:

• Act_Glu2 : a
• Act_Ala2 : a
• NegI_Ala2: b...

I hope you get the point. So far, I have found nothing comparable online... I also tried to select only significant pairs in the file resulting from TukeyHSD, but the file does not "acknowlegde" that it is made up of rows & columns, making selecting impossible...

Maybe there is something fundamentally wrong with my approach?

Answer 1

The results from the TukeyHSD are a list. Use str to look at the structure. In your case you'll see that it's a list of one item and that item is basically a matrix. So, to extract the first column you'll want to save the TukeyHSD result

hsd <- TukeyHSD(uni2.anova)

If you look at str(hsd) you can that you can then get at bits...

hsd$Micro[,1]

That will give you the column of your differences. You should be able to extract what you want now.

Answer 2

Hard to tell without example data, but assuming Micro is just a factor with 4 levels and uni2 looks something like

n = 40
Micro = c('Act_Glu2', 'Act_Ala2', 'Ana_Ala2', 'NegI_Ala2')[sample(4, 40, rep=T)]
Sum_Uni = rnorm(n, 5, 0.5)
Sum_Uni[Micro=='Act_Glu2'] = Sum_Uni[Micro=='Act_Glu2'] + 0.5

uni2 = data.frame(Sum_Uni, Micro)

> uni2
   Sum_Uni     Micro
1 4.964061  Ana_Ala2
2 4.807680  Ana_Ala2
3 4.643279 NegI_Ala2
4 4.793383  Act_Ala2
5 5.307951 NegI_Ala2
6 5.171687  Act_Glu2
...

then I think what you're actually trying to get at is the basic multiple regression output:

fit = lm(Sum_Uni ~ Micro, data = uni2)

summary(fit)
anova(fit)

> summary(fit)

Call:
lm(formula = Sum_Uni ~ Micro, data = uni2)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.26301 -0.35337 -0.04991  0.29544  1.07887 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)      4.8364     0.1659  29.157  < 2e-16 ***
MicroAct_Glu2    0.9542     0.2623   3.638 0.000854 ***
MicroAna_Ala2    0.1844     0.2194   0.841 0.406143    
MicroNegI_Ala2   0.1937     0.2158   0.898 0.375239    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.4976 on 36 degrees of freedom
Multiple R-squared: 0.2891, Adjusted R-squared: 0.2299 
F-statistic:  4.88 on 3 and 36 DF,  p-value: 0.005996 

> anova(fit)
Analysis of Variance Table

Response: Sum_Uni
          Df Sum Sq Mean Sq F value   Pr(>F)   
Micro      3 3.6254 1.20847  4.8801 0.005996 **
Residuals 36 8.9148 0.24763                    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

You can access the numbers in any of these tables like, for example,

> summary(fit)$coef[2,4]
[1] 0.0008536287

To see the list of what is stored in each object, use names():

> names(summary(fit))
 [1] "call"          "terms"         "residuals"     "coefficients" 
 [5] "aliased"       "sigma"         "df"            "r.squared"    
 [9] "adj.r.squared" "fstatistic"    "cov.unscaled" 

In addition to the TukeyHSD() function you found, there are many other options for looking at the pairwise tests further, and correcting the p-values if desired. These include pairwise.table(), estimable() in gmodels, the resampling and boot packages, and others...

Answer 3

I think the OP wants the letters to get a view of the comparisons.

library(multcompView)
multcompLetters(extract_p(TukeyHSD(uni2.anova)))

That will get you the letters.

You can also use the multcomp package

library(multcomp)
cld(glht(uni2.anova, linct = mcp(Micro = "Tukey")))

I hope this is what you need.