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Basic Statistical Templates – 2 Poisson Rates Equivalence Test

Click SigmaXL > Templates & Calculators > Basic Statistical Templates > 2 Poisson Rates Equivalence Test to access the 2 Poisson Rates Equivalence Test (Two One-Sided Tests TOST) calculator. The template gives the following default example. Notes
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. Sample Size (area of opportunity) can be a count, time, length or other unit that defines the area of opportunity for an occurrence.
3. Select Confidence Interval Method using drop-down.
• Confidence intervals for difference in Poisson rates have an "oscillation" phenomenon where the coverage probability varies with x and n.
• Jeffreys Hybrid is recommended and has a mean coverage probability that is close to the specified confidence interval. (See Li, 2011).
• Normal Approximation will match the P-Value calculations, but should only be used when the number of occurrences for each sample is greater than 10.
4. Null hypothesis for P1: Rate Difference >= UEL; Null hypothesis for P2: Rate 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.
5. LEL and UEL establish the zone or region of equivalence and are determined by what size rate difference is considered practically significant.
6. Since the Jeffreys Hybrid confidence interval option uses a different method than the normal based hypothesis test, 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.
7. 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 function.

## References:

Li, H.Q., Tang, M.L., Poon, W.Y. and Tang, N.S. (2011), Confidence intervals for difference between two Poisson rates, Comm. Stat. Simul. Comput. 40, pp. 1478–1491.

Przyborowski, J., Wilenski, H., (1940), Homogeneity of results in testing samples from Poisson series. Biometrika 31, 313–323.

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