# What is the best way to perform batch ajustment between two experiments?

I have duplicate drug efficacy experiments performed six months apart. I would like to know what is the right way to perform statistical analysis to understand fold changes after treatment with a drug.

Say I have

ctrl1       tube1       ctrl2       tube2
7,732637722 10,71639307 5,454318175 8,052899428
6,69630905  8,762916793 7,441582994 9,855106201
10,35624396 11,73716043 8,976524001 11,0975511
4,29150392  4,848632578 5,901132154 7,918630661


and the same experiment but 6 months after (numbers are slightly different)

Could I take the mean between samples divided by two can work out? If not - why?

I would like to have statistically significant values for futher analysis. Thanks.

• What do you want to show? Taking the mean is rarely a good move except in the final analysis
– M__
Commented May 14, 2022 at 2:53
• I want to adjust values between the same experiments, to be able to analyze them via t-test for example. It's just these two batches are 6-months different.
– Lara
Commented May 14, 2022 at 8:09

The answer is simply you use both sets of values in a one-way paired ANOVA. Note that certain criteria need to be in place for ANOVA, notably the Fmax test.

Looking at the data 2-way ANOVA might be needed and that is more complicated, or else 2 one-way ANOVAs: I don't understand 'ctl2' and 'tube2' data. Is this a single or multiple drugs?

Wilcoxon signed-rank test is the first choice test because there are no prior assumptions required, which replaces both the T-test and the 1-way ANOVA.

Whatever you do, taking the mean and performing a T-test is not a good idea. You asked why ... because the variation between the values is critical to the significance of the test and is simply demonstrated:

Tube 1 value

tube1 time X = 11
tube1 time y = 9
tube 1 mean = 10


Tube 2 value

tube 2 time x = 19
tube 2 time y = 1
tube 2 mean = 10


Thus both would appear to have no change - they are both 10 - and yet the variation between them means they observe very different behaviours. Thats why.