Sample size calculation - single mean method

John Scanlon

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Hi, Thanks you for sending this through! For the single mean test, should the difference in means be 86.1-83.5? Rather than 89.7-86.1? I want to show the sample size needed to show that the mean will be above 83.5 with the already published studies. A huge thank you again for your input!

• Kav10

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  You are correct. It should be 86.1-83.5. The difference of means between the null hypothesis and your sample data. I don’t think it makes a significant difference in the result, but yes that was a typo. I meant to write 86.1-83.5.

John Scanlon

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The standard deviation also uses the standard deviations from my sample and previous studies. Does the solution still work if one standard deviation was used (instead of SD1squared + SD2squared/2)

• Kav10

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  Yes, the formula I provided uses SD. When you are comparing two means, it will become a SD-p (called pooled standard deviation), which is a combination of the two SDs.

Kav10

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If comparing your sample against previous studies, you would use the SDs from both. If comparing with mean, you would use only the SD from your sample. Same formula.

• John Scanlon

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  Would you mind posting the solution using the single mean method? I am unsure how to convert solution 1 to use one mean and one standard deviation to show that the outcome will be above 83.5

Kav10

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Yes, I can do that for you.

• Kav10

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  Added as a new file (see end of the document).

John Scanlon

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Is it legitimate to use a Z score for samples with an n less than 30?

• Kav10

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  Yes, because population variance is known.

John Scanlon

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Thank you, I got you some coffees for the trouble. So is it correct to say that (using my sample data) the minimum sample required is 3 with an alpha of 0.05 and a power of 80% when 83.5 is considered for the null hypothesis?

• Kav10

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  Thanks. Like I said in the response, your question was/is not clear so I provided multiple approaches so you choose what best suits your problem. I can suggest a couple of useful links for you to take a look to better decided when to use each method. Also, remember, that in practice, %10-15 percent is added to the calculated sample size (educated guess) to account for missing/non-response in surveys. Sample size of 3 sounds to be too small, but that’s what your data and that approach says.

John Scanlon

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Apologies, I've included the Z beta in your initial equation and my minimum sample size required is 7 with an alpha of 0.05 a power of 80%. Is that correct?

• Kav10

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  When I get to my computer, I’ll send you some very good links to read about the tests and sample size calculations. I cannot see your calculations, but if you’ve used the correct formula and added correct variables, then it should be correct.

Kav10

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See these two links: https://bookdown.org/mandyyao98/bookdown-demo-master/lecture-4-inference-for-means-continued.html

Kav10

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https://bookdown.org/mandyyao98/bookdown-demo-master/lecture-5-sample-size-calculations-to-plan-for-hypothesis-tests-of-means.html

John Scanlon

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Thank you Kav10. I appreciate your patience and knowledge.

• Kav10

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  Of course! Thank you.