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Dunnett’s Multiple Test of The Difference Using ‘R’

I recently have encountered a statistical question simultaneously comparing multiple groups on the difference of certain characteristics. Normally, I use some statistical programs like Minitab, to run multiple t-test (e.g. Dunnett’s, Duncan etc), but I couldn’t find the way to compare the difference among groups using these programs straight.

Here is an example, there are 4 class rooms and each class room is divided by  male group and female group. Then took a measurement of height of students. I want to test whether the difference in height between male and female students are statistically significant when all classes are compared to each other.

Class     Sex            Height [cm]
A         Male           175
A         Male           169
A         Male           177
A         Female         162
A         Female         167
A         Female         155
B         Male           183
B         Male           171
B         Male           179
B         Female         171
B         Female         166
B         Female         164
C         Male           162
C         Male           175
C         Male           176
C         Female         161
C         Female         165
C         Female         152
D         Male           175
D         Male           178
D         Male           172
D         Female         161
D         Female         167
D         Female         153

Calculate the difference of average height for each group.

      Avg Male   - Avg Female
A     173.6      -  161.3             = 12.3
B     177.6      -  167.0             = 10.6
C     171.0      -  159.3             = 11.7
D     175.0      -  160.3             = 14.7

By looking at the number, D has the largest difference between Male and Female in height and B has the smallest difference. Are they statistically significant? How do we test?

In “R”, there is a package for multcomp. In this package, there are several important features for this type of analysis.
Please read here for more details.

>library(multcomp) ## install multcomp package

Before start using “R”, let’s save the data above as “test.csv”. You need to add column name “Group”, “Sex” and “Measure” at the top of each column. Remember the directory you save the file (e.g. ./data).
Let’s set working directory and read  the test.csv file.

>setwd("./data")
>dat<-read.csv("./test.csv")

Then run ANOVA. Measure is height, Group is A~D and Sex is male or female.
Note that Group and Sex may interact each other, so you use * to run ANOVA. “-1” will remove intercept term.

>mod <-aov(Measure~Group*Sex-1,data=dat)

Print coefficients

>coef(mod)

GroupA          GroupB              GroupC           GroupD
161.3333333 167.0000000 159.3333333 160.3333333

SexMale       GroupB:SexMale     GroupC:SexMale   GroupD:SexMale
12.3333333 -1.6666667                -0.6666667              2.3333333

You may wonder what these numbers are….. But it is not hard.
First row is simply an average of female height for each Group.
SexMale (12.3333) is the difference height in Group A.
GroupB:SexMale (-1.6666) is the difference of the difference height B and A.
GroupC:SexMale (-0.6666) is the difference of the difference height C and A.
GroupD:SexMale (2.3333) is the difference of the difference height D and A.

As you can see, A is always used as reference to generate these numbers.
Now, to test difference in A and B is to test GroupB:SexMale=0
To test difference in A and C is to test GroupC:SexMale=0
To test difference in A and D is to test GroupD:SexMale=0

How about the rest of the comparisons?

To test difference in B and C is to test GroupB:SexMale -GroupC:SexMale=0
To test difference in B and Dis to test GroupB:SexMale -GroupD:SexMale=0
To test difference in C and D is to test GroupC:SexMale -GroupD:SexMale=0

The code for this is

>summary(glht(mod,linfct =
c("GroupB:SexMale = 0",
"GroupC:SexMale= 0",
"GroupD:SexMale= 0",
"GroupB:SexMale - GroupC:SexMale= 0",
"GroupB:SexMale - GroupD:SexMale= 0",
"GroupC:SexMale - GroupD:SexMale= 0")))

Simultaneous Tests for General Linear Hypotheses
Fit: aov(formula = Measure ~ Group * Sex – 1, data = dat)
Linear Hypotheses:

Estimate Std. Error t value Pr(>|t|)
GroupB:SexMale == 0                               -1.6667     6.6792     -0.250 0.994
GroupC:SexMale == 0                               -0.6667    6.6792     -0.100 1.000
GroupD:SexMale == 0                                2.3333    6.6792       0.349 0.985
GroupB:SexMale – GroupC:SexMale == 0 -1.0000    6.6792     -0.150 0.999
GroupB:SexMale – GroupD:SexMale == 0 -4.0000   6.6792     -0.599 0.931
GroupC:SexMale – GroupD:SexMale == 0 -3.0000   6.6792     -0.449 0.969
(Adjusted p values reported — single-step method)

Well, in this example none of the comparison ended up in significant p>0.05 (numbers on the right).
I think standard deviation of height was probably too large.
Please test with your own data to see if it works.

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