Two Sample Proportion Test with SigmaXL

By Lean Sigma Corporation

What is the Two Sample Proportion Test with SigmaXL?

The two sample proportion test with SigmaXL is a hypothesis test to compare the proportions of one certain event occurring in two populations following the binomial distribution.

  • Null Hypothesis(H0): p1 = p2
  • Alternative Hypothesis(Ha): p1 ≠ p2

Two Sample Proportion Test Assumptions

  • The sample data drawn from the populations of interest are unbiased and representative.
  • There are only two possible outcomes in each trial for both populations: success/failure, yes/no, and defective/non-defective etc.
  • The underlying distributions of both populations are binomial distribution.
  • When np ≥ 5 and np(1 – p) ≥ 5, the binomial distribution can be approximated by the normal distribution.

When |Zcalc| is smaller than Zcrit, we fail to reject the null hypothesis.

Run a Two Sample Proportion Test with SigmaXL

Case study: We are interested in comparing the exam pass rates of a high school in March and April using a nonparametric (i.e. distribution-free) hypothesis test: two sample proportion test.
Data File: “Two Sample Proportion” tab in “Sample Data.xlsx”

  • Null Hypothesis (H0): pMarch = pApril
  • Alternative Hypothesis (Ha): pMarch ≠ pApril

Steps to run a two sample proportion test in SigmaXL:

  1. Click SigmaXL -> Statistical Tools -> 2 Proportions Test & Confidence Interval
  2. A new tab named “2 Proportions Test and CI” appears automatically.
  3. Enter “89” in the yellow box of “Number of Events” in Sample #1 column
  4. Enter “112” in the yellow box of “Sample Size in Sample #1 column.
  5. Enter “102” in the yellow box of “Number of Events” in Sample #2 column.
  6. Enter “130” in the yellow box of “Sample Size” in Sample #2 column.
  7. Select “Fisher’s Exact” as the testing method.
    Two Sample Proportion Test with SigmaXL

Model summary: The p-value of the two-sample proportion test is 0.8756, greater than the alpha level (0.05), and we fail to reject the null hypothesis. We conclude that the exam pass rates of the high school in March and April are not statistically different.

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About Lean Sigma Corporation

Lean Sigma Corporation is a trusted leader in Lean Six Sigma training and certification, boasting a rich history of providing high-quality educational resources. With a mission to honor and maintain the traditional Lean Six Sigma curriculum and certification standards, Lean Sigma Corporation has empowered thousands of professionals and organizations worldwide with over 5,300 certifications, solidifying its position and reputation as a go-to source for excellence through Lean Six Sigma methodologies.