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Basic Statistical Templates  2 Proportions Equivalence Test

Click SigmaXL > Templates & Calculators > Basic Statistical Templates >  2 Proportions Equivalence Test to access the 2 Proportions Equivalence Test (Two One-Sided Tests TOST) calculator. The template gives the following default example.

  1. Enter summarized Sample Data, Upper & Lower Equivalence Limits and Confidence Level in cells with yellow highlight. Do not modify any other part of this worksheet.
  2. Select Confidence Interval Method using drop-down.
    • Confidence intervals for difference in binomial proportions have an "oscillation" phenomenon
      where the coverage probability varies with n and p.
    • Newcombe-Wilson Score is recommended and has a mean coverage probability that is close to the
      specified confidence interval. (See Newcombe method 10).
    • Newcombe-Wilson Score (CC = Continuity Corrected) is conservative and will typically meet the
      specified confidence level as a minimum coverage probability, but results in wider intervals. (See
      Newcombe method 11).
    • Jeffreys-Perks is similar to Newcombe-Wilson, and included as an option because it is the preferred
      interval for some practitioners. (See Radhakrishna; Newcombe method 4).
    • Normal Approximation will match the P-Value calculations, but should only be used when minimum
      expected cell value, shown above, is >= 5.
    • Exact methods that are strictly conservative (like Clopper-Pearson for the one proportion case) are
      not included in this template because they are computationally intensive and slow.
  3. Null hypothesis for P1: Proportion Difference >= UEL; Null hypothesis for P2: Proportion
    Difference <= LEL. Both null hypotheses must be rejected to conclude that equivalence is true.
    The P-Values are based on the normal approximation unpooled method.
  4. LEL and UEL establish the zone or region of equivalence and are determined by what size
    proportion difference is considered practically significant.
  5. Since the confidence interval options use different methods than the hypothesis test (except
    for Normal option), it is possible that the conclusion from the Equivalence P-Value will be
    different from that of the confidence interval. In this case, we recommend using just the
    confidence interval method.
  6. Due to the complexity of calculations, this template uses VBA macros rather than Excel
    formulas. SigmaXL must be initialized and appear on the menu in order for this template to


1. Beal, S. L. (1987), Asymptotic confidence intervals for the difference between two binomial parameters for
use with small samples. Biometrics, 43, 941-950.

2. Newcombe, R. G. (1998b), Interval estimation for the difference between independent proportions:
Comparison of eleven methods. Statistics in Medicine, 17:873890.

3. Radhakrishna S., Murthy B.N., Nair N.G., Jayabal P., Jayasri R. (1992), Confidence intervals in medical
research. Indian J Med Res., Jun;96:199-205.

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