Multiple one-sample t Test I have a sample that can be divided into three groups. I now want to compare if any of the three groups differs from a given mean. 
I have thought about conducting multiple one-sample t Tests but I do not know if I need to correct for alpha? I am really not sure. On the one hand, it is not a pairwise comparison, but on the other, it is still multiple testing. 
What would you say? Is there maybe a more elegant way to it than to conduct multiple one-sample t Tests? 
Kind regards, 
Helena
 A: It may make sense to use an adjustment for alpha or for p values if multiple one-sample t tests are used.  This adjustment is employed dependent on the number of hypotheses being tested that are considered in a family.


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I think the following makes sense as way to combine several one-sample t tests into one model.  In this scenario we have three groups, and want to compare them to a given mean of 3.
Essentially, the given mean is subtracted from the data for each group, and then a general linear model is fit, with no intercept, and the groups dummy coded as independent variables.
A = c(1,2,3,3,3,3,4,5)
B = c(3,4,4,4,5,5,5,5)
C = c(1,1,1,2,2,2,2,3)

One-sample t tests
t.test(A, mu=3)
   ### t = 0, df = 7, p-value = 1

t.test(B, mu=3)
   ### t = 5.2271, df = 7, p-value = 0.001216

t.test(C, mu=3)
   ### t = -5, df = 7, p-value = 0.001565

Combine the data into a single data set.
Y     = c(A, B, C)
Group = c(rep("A", length(A)), rep("B", length(B)), rep("C", length(C)))

Mean0 is the given mean.  The syntax of the model is a little funky.  Y - Mean0 could be done separately, but I'll do it within the model.  0 indicates that no intercept should be fit.
Mean0 = 3

model = lm(I(Y - Mean0) ~ 0 + Group)

I wonder if the anova results can be considered an omnibus test: testing if the mean of at least one group is different than the given mean.
anova(model)

   ###           Df Sum Sq Mean Sq F value    Pr(>F)    
   ### Group      3 27.625  9.2083   11.13 0.0001393 ***
   ### Residuals 21 17.375  0.8274 

summary gives tests for each group. Here, the results are somewhat different than conducting individual t tests.  Also note that mean(B) = Estimate(GroupB) + Mean0.
summary(model)

   ### Coefficients:
   ###         Estimate Std. Error t value Pr(>|t|)    
   ### GroupA  2.355e-16  3.216e-01   0.000 1.000000    
   ### GroupB  1.375e+00  3.216e-01   4.276 0.000336 ***
   ### GroupC -1.250e+00  3.216e-01  -3.887 0.000851 ***

A: The natural extension of the t-test to more than two groups is called ANOVA, and is well-studied with many off-the-shelf implementations.
Note that ANOVA is a fairly weak tool when used against the standard null of "all the groups are equal."  Significance does not tell you very much.
