# Sample size calculation - single mean method

Hi,

The problem is to calculate the sample size needed to show that the intervention (that my sample and the previous study received) will result in an outcome score of 83.5 or more. I want to use the same method described in the attached paper.

Null hypothesis: Mean = 83.5 (PASS value equivalent from example)
Alternative hypothesis: Mean >(greater than or equals) 83.5

Data from previous studies: n=16, mean = 86.1, SD=12.6
(Data from my sample: n=19, mean=89.7, SD=5.8)

Is it possible to calculate a sample size with this information?

Answers can only be viewed under the following conditions:
1. The questioner was satisfied with and accepted the answer, or
2. The answer was evaluated as being 100% correct by the judge.

2 Attachments

Kav10
1.8K
• 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!

• 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.

• 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)

• 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.

• 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.

• 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

• Yes, I can do that for you.

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

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

• Yes, because population variance is known.

• 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?

• 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.

• 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?

• 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.

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

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

• Thank you Kav10. I appreciate your patience and knowledge.

• Of course! Thank you.