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I have test results from 2 suppliers.

  • 20 samples from Supplier 1 resulted in 8 units passing a test and 12 units failing; a failure proportion of 0.6
  • 20 samples from Supplier 2 resulted in 2 units passing and 18 units failing; a failure proportion of 0.9

Minitab produces a Power Value of 0.719743 with inputs:

Alternative Hypothesis p1 < p2
Significance Level = 0.05
Each Sample Size = 20
p1=0.6
p2=0.9

I have two questions:

  1. Would you consider the following statement to be the proper interpretation of these results (i.e., true, relevant and clear), or can it be improved?

    The Null Hypothesis is that the Supplier 1 failure proportion is greater than the Supplier 2 failure proportion and based on the Minitab analysis results there is a 71.97% probability that we are correctly rejecting this Null Hypothesis, therefore accepting the Alternative Hypothesis is prudent. We are 1- alpha or 95% confident in this statement.

    Is there anything else that can be stated here that provides insight regarding the belief/degree that the population of product from Supplier 1 is likely to be superior to the population of product from Supplier 2?

  2. Why there is a slight difference in the computed power if I run the same analysis using the pss4 on-line calculator?

    I get a power value of 70.75% selecting the 1-sided option. In general, is one of these tools more accurate, true or appropriate for engineering calculations and decision making than the other?

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  • $\begingroup$ Hello experts, is there any additional information I can add to clarify this question ? $\endgroup$
    – Steve
    Oct 24, 2015 at 0:47
  • $\begingroup$ There is no reason to do power analysis after you've done the experiment. See this page. $\endgroup$
    – EdM
    Oct 24, 2015 at 15:34

1 Answer 1

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  1. The Null Hypothesis is that the Supplier 1 failure proportion is greater than the Supplier 2 failure proportion and based on the Minitab analysis results there is a 71.97% probability that we are correctly rejecting this Null Hypothesis, therefore accepting the Alternative Hypothesis is prudent. We are 1- alpha or 95% confident in this statement.

    That isn't the correct interpretation of a power analysis. You don't know if you are correct in concluding that p1 > p2, and you never will. If you want to make a decision while holding your long run type I error rate at alpha, you should conduct a hypothesis test (e.g., a z-test for difference of two independent proportions) using that alpha.

    A power analysis helps you think through what would happen in the future, if you ran a study where the truth was the two proportions were .6 and .9. The answer is that you would have a 72% probability of correctly rejecting the null.

  2. I don't know why there is a difference. The difference isn't very big ~1.25%. Be aware that there are different versions of the test for differences in proportions (e.g., to employ the continuity correction or not), and that there is a limit to the precision of the answer due to the numerical methods employed to compute it.

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