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Sample Size and Power for Two Sample Proportions
Jul 31, 2025 05:39 PM
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Use to interactively explore the relationships between Power, Sample Sizes, and Alternative Proportions in testing a hypothesis comparing two independent population proportions. See the Two Proportions Test and Confidence Interval guide to learn how to perform a statistical test comparing two population proportions.

Sample Size and Power - Two Sample Proportion

  1. Select DOE > Sample Size Explorers and choose Power >Power for Two Independent Sample Proportions.
  1. Choose the type of test: One-Sided or Two-Sided and choose Alpha (significance level for the test).
    The Null Hypothesis is that the two proportions are equal. Here we chose a two-sided alternative which is used to test that the two proportions are not equal.
    This null and alternative hypothesis can be written using notation as  H0: p1 = p2 vs. HA: p1 ≠ p2
  2. Enter values for the Group 1 and Group 2 Population Proportions under HA to base the analysis on.
    Here we consider the scenario where Proportion 1 is 0.50 and Proportion 2 is 0.75.
  3. Select parameter to solve for. Here we chose Total Sample Size.
  4. Enter a value for the Power. Here we entered 0.80.
    The solution of Total Sample Size of 110 (n1=55 and n2=55) is displayed.
  5. Use the interactive cross-hair tool (or type in values) for Power, Sample Sizes, and Assumed Proportions to study the relationship between these parameters solving for many different scenarios.

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The settings and solution for each analysis performed can be saved. The table of saved settings shows the results of five different analyses performed when testing the hypothesis H0: p1 = p2 vs. HA: p1 ≠ p2
1. What sample size is needed to achieve a power of 80% assuming p1=0.50 and p2=0.75?
Answer: 110 (n1 = 55 and n2 = 55)
2. What is the power with a sample size of 25 in each group assuming p1=0.50 and p2=0.75? Answer: Power = 47.2%
3. What sample size is needed to achieve a power of 80% assuming p1=0.50 and p2=0.65?
Answer: 335 (n1 = 167 and n2 = 168)
4. What difference from 0.50 for the proportion of group 2 can be detected with 80% power using a sample size of 100 in each group?
Answer: 0.69

 

Note: Determining sample size to achieve a desired margin of error in a Confidence Interval can be done using DOE > Sample Size Explorers > Confidence Intervals > Margin of Error for Two Independent Sample Proportions.


Visit Design of Experiments Guide > Sample Size Explorers in JMP Help to learn more.

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