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Thread: Sample size calculation for Chi square Test

  1. #1
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    Sample size calculation for Chi square Test

    Hi, I have trouble determining the sample size for a simple Chi Square Test.
    My problem is the following:
    I tried to calculate the sample size for two samples whith P1=0.7 and P2=0.9. Unfortunately, the result was different when I used another software. I simulated the data and did the Chi Square test in SPSS and the results were not even close to 0.05 even though I set alpha to 0.05.
    My questions are now:
    - which software is the best fo sample size calculations?
    - what is the appropriate number of cases for this problem for each group?
    - how do you calculate the sample size for proportions of more than 2 groups (e.g. 2x3 table)

    Thanks so much for your help!

  2. #2
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    Re: Sample size calculation for Chi square Test


    as far as I understand, you want to determine an appropriate sample size N for the Chi^2 Test in order to detect a certain effect size w with a certain alpha, beta and DF-value? I always use G*Power, which is for free.

    Best regards

  3. #3
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    hlsmith's Avatar
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    Re: Sample size calculation for Chi square Test

    I always hear good things about GPower, but have never used it.

    Every program should provide its formula and they should all be comparable - so I don't think there is a best. You probably run into issues with the defaults settings and many options available, plus I am unsure if sample size calculations will be different between trying to power a likelihood ratio or Pearson chi-square. I just run those both and found a difference of 61 versus 62 subjects per group. Also you need to state a reference group many times.

    I ran your numbers in SAS and got the following:

    The POWER Procedure

    Pearson Chi-square Test for Two Proportions
    Fixed Scenario Elements Distribution Asymptotic normal Method Normal approximation Group 1 Proportion 0.7
    Group 2 Proportion 0.9
    Nominal Power 0.8
    Number of Sides 2
    Null Proportion Difference 0
    Alpha 0.05

    Group Actual Power 0.803
    N per Group 62

    I believe simulation could give you more variability in the number generates if the seed is not set - typically using the system clock. To be cautious, don't forget to add on an additional 10% or so if you have any doubts about the sample you may get in comparison to the numbers used to generate the calculations.

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