To combine or not to combine standard deviations?


I'm testing the effect of 115 Chinese herbs on bacterial biofilms.

I have been carrying out my experiment in microtiter plates and measuring the absorbance readings.

My test plate consists of bacterial culture + herb (six repeats of each herb)

While my background reading plate consists of media + herb (six repeats of each herb)

I have been subtracting the mean test reading from mean background reading to obtain the true mean reading.

However I am unsure of what to do with the standard deviations of the test reading and background reading. I need a solution because I have to include standard deviation on my graph for each herb.

Thanks. :)
Hey chiro,

the goal is to determine which herbs can disperse biofilm, hence by measuring the absorbances of the treatment, background reading and negative control (i.e bacterial biofilm + water), I can see which herbs have significantly reduced the biofilm growing on the microtiter plates.

Greater the dispersion, the lower the absorbance value.

For example, my setup consists of:
(herb 1 + biofilm)* = average treatment absorbance = t
(herb 1 + media)* = average background reading absorbance = b
(water + biofilm)* = average negative control absorbance = c

*six repeats

Therefore, t - b = x (true mean absorbance value) I am do this herbs have a strong colour, therefore I am removing the interference it is causing to the absorbance reading.

Using t-test, I am comparing x and c, to see if there is a significant difference between those two absorbance values.

Hope that you understood that :)

I already know I have to do a t-test, but what I don't know is the standard deviations (s.ds) of t and b. I have subtracted b from t, so do I simply just subtract s.d of t and the s.d of b to get a true s.d absorbance value?

I know I can't do that, what is the right way? Do I combine the two s.ds with a certain formula?

Thanks for your question, hope I haven't confused too much.
You usually have three kinds of t-tests: paired, pooled, and non-paired/non-pooled.

Paired tests are used when there is a relationship between each pair of data, pooled is when you have same variance and the other one assumes none of these.

The standard error of the total statistic is the sum of the individual standard errors and these individual errors are calculated using S_1^2/n1 and S_2^2/n2 where S_1 is the sample variance of the first sample and S_2 is the sample variance of the second sample with n1 being the number of observations in 1st sample and n2 being the number of observations in the 2nd sample.

The final standard error used is se = SQRT(S_1^2/n1 + S_2^2/n2) where you have [(x_bar - y_bar) - d]/se ~ t(n1+n2-2).