Sample size and power for two sample proportions

Question

I need to test if a change to my line will adversely affect yields but I am not sure if I am using the correct values for Proportion 2 and the Null Difference in Proportion in the Sample Size and Power calculator for Two Sample Proportions.

I am expecting the process change to have no effect on yield but want to design a test that would have high power of detecting a 1% drop.

For Alpha=0.05 and Power=0.80, which of the options below is correct?

Option A

Proportion 1: 0.94

Proportion 2: 0.94

Null Difference in Proportion: -0.01

Option B

Proportion 1: 0.94

Proportion 2: 0.93

Null Difference in Proportion: 0

Regards

S

jules · Accepted Answer

Hi swelish,

It seems as though option B is what you will want to use. Under the null hypothesis there would be no change (assuming your change to the line will have no effect on yields, the difference in the proportions will be 0). The difference between proportion 1 and 2 is what you are calculating your power to estimate -- in this case, you want high power to detect that 0.01 difference.

Option A represents a different type of test, one in which you are specifying a world in which the proportions are really the same, but under the null hypothesis one should expect that 0.01 difference. This might apply if, in the past, there has always been  0.01 difference in yields, and you want to determine power to detect that you have brought them in alignment.

I hope this helps!

julian

michael_jmp · Accepted Answer

You can read more about the two-sample proportion module here: One-Sample and Two-Sample Proportions

For more details about the computations in the power and sample size module, please see this white paper on jmp.com:

http://www.jmp.com/blind/whitepapers/wp_jmp_powersample_104887.pdf

Best,
Michael