# Can I apply a t-test to normalized data?

I'm conducting biological experiments and have to normalize my raw data to the value of the untreated control in order to analyze them. This means that I have for the untreated sample something like {1,1,1,1,1} and for the treated sample something like {1.12,2.1,2.05,1.85,1.78}. How do I test if both sets are significantly different? I obviously cannot enter 1,1,1,1,1 into a t-test, can I?

In case I want to test for a significant difference in two treated samples, lets say treated with two different doses which have, on their own, also been normalized to the untreated control (Dataset A {1.12,2.1,2.05,1.85,1.78}, Dataset B {2.2,3.1,2.5,2.9,1.8}), how do I do this the right way?

Thanks a lot!

Actually, you can. In fact, entering all 1's for one group is equivalent to testing whether the treated group has a mean of 1. E.g. in R

#first, create two groups of people - treatment and control - here 10 in each
group <- c(rep('C', 10), rep('T',10))
#create some values for the continuous variable - all 1's for C, normal 1.5, .1 for T
value <- c(rep(1, 10), rnorm(10, 1.5, .1))
t.test(value~group) #two sample t-test, testing 'value' for two levels of group
t.test(value[group == 'T'], mu = 1) #one sample t test, testing value = 1 for just T group


the two t tests give identical results.

However, the second version seems, somehow, 'cleaner' - perhaps less likely to raise eyebrows or demand clarification.

• Thank you for your answer. Could you please explain a bit what you just did? I have used R maybe twice in my life and I don't understand what the variables group and value assigned to. I also don't understand the difference between the two t.test commands. I don't understand anything. :) – Eekhoorn Oct 31 '12 at 13:47
• I will edit the answer – Peter Flom - Reinstate Monica Oct 31 '12 at 13:50