Basic Statistical Templates 2 Proportions Test and Confidence Interval
Example
Click SigmaXL > Templates & Calculators > Basic
Statistical Templates >
2 Proportions Test and Confidence Interval to access the
template.
Notes
- Enter summarized Sample Data, Null Hypothesis and Confidence Level in cells with
yellow highlight. Do not modify any other part of this worksheet.
- Select Alternative Hypothesis and Methods using drop-down.
- Hypothesis Test Method:
- Fisher's Exact is recommended, but is only valid for H0: P1 - P2 = 0.
- Use Normal Approximation only when minimum expected cell value, shown above, is
>= 5. Unpooled is used if H0: P1 - P2 <> 0. Use pooled if H0: P1 - P2 =
0. (See Peltier).
- Confidence Interval Method:
- 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 is not recommended, but included here to validate hand
calculations. Use only 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.
- 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:
Beal, S. L. (1987), Asymptotic confidence intervals for the difference between two
binomial parameters for use with small samples. Biometrics, 43, 941-950.
Newcombe, R. G. (1998b), Interval estimation for the difference between independent
proportions: Comparison of eleven methods. Statistics in Medicine, 17:873890.
Peltier, C., Why Do We Pool for the Two-Proportion z-Test?, https://apcentral.collegeboard.com/apc/members/courses/teachers_corner/49013.html.
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.
