# Comparative Test - The right formula for calculating the number of samples needed?

M

#### Monica Lewis

Comparative test

Hi Don,

Thank you for the answers regarding the puschasing issues. Our Design and Development Manager would like to get some advice regarding this issue. Below is his letter to you and all the other members in this forum.

We do surface coating of medical devices for another company. The coating process itself links an organic molecule to the surface by a chemical bond. After coating we do quantitative analysis of the amount of the organic molecule found on the surface of the device, expressed as g/cm2

The company want to change supplier of the material and therefore want to know if there may be any difference in the amount of organic molecule found on the material from the two different suppliers.

We figure that we could do a simple unpaired comparative test to show no difference with regard to the amount of organic molecule after coating of material from the two different manufacturers (test and control). We figure that we run both test and control in the same batch and test three different batches from the potential new supplier. The argument for using unpaired comparative test rather than paired test is that the material comes from two different manufacturers.

What would be the right formula to use when calculating the number of samples required for testing the hypothesis?

The formula we suggest is: N = 2x(sd / D )2 x (Za + Zb)2

Where N is the number of samples required
sd is the estimated standard deviation
D is the maximum difference between the two means that is accepted
Za and Zb is the significant and power of the test

D

#### Don Winton

Monica,

I went into detail on sampling and sampling plans here:

http://Elsmar.com/ubb/Forum10/HTML/000027.html

Try that and if you have further questions, feel free to ask. The formula presented above may be a variation of the basic sampling equations, but I am not sure how it was derived.

As far as significance testing, I agree an unpaired t-test would probably be best, but you may want to look at ANOVA as well.

Regards,

Don

M

#### Monica Lewis

Our Design and Development Manager was very satisfied regarding your answer and he was very impressed over your sampling stuff at the Lair.

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