Confidence intervals for single, paired and independent proportions

Description

Computes confidence intervals for single proportions as well as for differences in dependent and independent proportions, the odds-ratio and the relative risk in a 2x2 table. Intervals are available for independent samples and matched pairs. The functions are partly written by assistants of Alan Agresti, see website http://www.stat.ufl.edu/~aa/cda/cda.html.

Details

Author(s)

Ralph Scherer

Maintainer: Ralph Scherer <shearer.ra76@gmail.com>

References

Agresti, A., Coull, B. (1998) Approximate is better than exact for interval estimation of binomial proportions. The American Statistician 52, 119–126.

Agresti, A., Caffo, B.(2000) Simple and effective confidence intervals for proportions and difference of proportions result from adding two successes and two failures. The American Statistician 54 (4), 280–288.

Agresti, A. (2002) Categorical Data Analysis. Wiley, 2nd Edition.

Agresti, A. and Min, Y. (2005) Simple improved confidence intervals for comparing matched proportions Statistics in Medicine 24 (5), 729–740.

Agresti, A., Gottard, A. (2005) Randomized confidence intervals and the mid-P approach, discussion of article by C. Geyer and G. Meeden, Statistical Science 20, 367–371.

Altman, D. G. (1999) Practical statistics for medical research. London, Chapman & Hall.

Blaker, H. (2000). Confidence curves and improved exact confidence intervals for discrete distributions, Canadian Journal of Statistics 28 (4), 783–798.

Clopper, C. and Pearson, E.S. (1934) The use of cenfidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404–413.

Koopman PAR. (1985) Confidence limits for the ratio of two binomial proportions. Biometrics 40, 513–517.

Mee, RW. (1984) Confidence bounds for the difference between two probabilities. Biometrics 40, 1175–1176.

Miettinen OS, Nurminen M. (1985) Comparative analysis of two rates. Statistics in Medicine 4, 213–226.

Nam, J. M. (1995) Confidence limits for the ratio of two binomial proportions based on likelihood scores: Non-iterative method. Biom. J. 37 (3), 375–379.

Nurminen, M. (1986) Analysis of trends in proportions with an ordinally scaled determinant. Biometrical J. 28, 965–974.

Olivier, J. and May, W. L. (2006) Weighted confidence interval construction for binomial parameters Statistical Methods in Medical Research 15 (1), 37–46.

Tango T. (1998) Equivalence test and confidence interval for the difference in proportions for the paired-sample design Statistics in Medicine 17, 891–908.

Wilson, E. B. (1927) Probable inference, the law of succession, and statistical inference. J. Amer. Stat. Assoc. 22, 209–212.

internal function

Description

computes the Blaker acceptability of p when x is observed and X is bin(n, p)

Agresti-Coull add-4 CI for a binomial proportion

Description

Agresti-Coull add-4 CI for a binomial proportion, based on adding 2 successes and 2 failures before computing the Wald CI. The CI is truncated, when it overshoots the boundary

Usage

add4ci(x, n, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Agresti, A., Coull, B. (1998) Approximate is better than exact for interval estimation of binomial proportions. The American Statistician 52, 119–126.

Agresti, A., Caffo, B.(2000) Simple and effective confidence intervals for proportions and difference of proportions result from adding two successes and two failures. The American Statistician 54 (4), 280–288.

Examples

add4ci(x = 15, n = 112, conf.level = 0.95)

Agresti-Coull CI for a binomial proportion based on adding z^2/2 successes and z^2/2 failures before computing the Wald CI

Description

Agresti-Coull CI for a binomial proportion based on adding z^2/2 successes and z^2/2 failures before computing the Wald CI. The CI is truncated, when it overshoots the boundary.

Usage

addz2ci(x, n, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Agresti, A., Coull, B. (1998): Approximate is better than exact for interval estimation of binomial proportions. The American Statistician 52, 119–126.

Examples

addz2ci(x = 15, n = 112, conf.level = 0.95)

Blaker's exact CI for a binomial proportion

Description

Blaker's exact CI for a binomial proportion

Usage

blakerci(x, n, conf.level, tolerance=1e-05)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Blaker, H. (2000). Confidence curves and improved exact confidence intervals for discrete distributions, Canadian Journal of Statistics 28 (4), 783–798

Bayesian confidence interval for different of independent proportions

Description

Approximate Bayesian confidence interval for different of proportions using simulation method

Usage

diffci.bayes(x1,n1,x2,n2,a,b,c,d,conf.level, nsim)

Arguments

Value

Confidence interval with given confidence level.

References

Agresti, A. (2002) Categorical Data Analysis. Wiley, 2nd Edition.

Bayesian HPD confidence interval for different of independent proportions

Description

Approximate Bayesian HPD confidence interval for different of proportions using independent priors

Usage

diffci.bayes.hpd(x1,n1,x2,n2,a,b,c,d,conf.level)

Arguments

Value

Confidence interval with given confidence level.

References

Agresti, A. (2002) Categorical Data Analysis. Wiley, 2nd Edition.

Wald interval for a difference of proportions with matched pairs

Description

Wald interval for a difference of proportions with matched pairs.

Usage

diffpropci.Wald.mp(b, c, n, conf.level)

Arguments

Details

The interval is truncated, when it overshoots the boundary

Value

A list with class '"htest"' containing the following components:

References

D. G. Altman (1999) Practical statistics for medical research. London, Chapman & Hall

Examples

diffpropci.Wald.mp(b = 3, c = 9, n = 32, conf.level = 0.95)

Adjusted Wald interval for a difference of proportions with matched pairs

Description

Adjusted Wald interval for a difference of proportions with matched pairs. This is the interval called Wald+2 in Agresti and Min (2005). Adds 0.5 to each cell before constructing the Wald CI

Usage

diffpropci.mp(b, c, n, conf.level)

Arguments

Details

The interval is truncated, when it overshoots the boundary

Value

A list with class '"htest"' containing the following components:

References

Agresti, A. and Min, Y. (2005) Simple improved confidence intervals for comparing matched proportions. Statistics in Medicine 24 (5), 729–740.

Examples

diffpropci.mp(b = 40, c = 20, n = 160, conf.level = 0.95)

Score interval for difference of proportions

Description

Score interval for difference of proportions and independent samples (p1 - p2)

Usage

diffscoreci(x1, n1, x2, n2, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Agresti, A. (2002) Categorical Data Analysis. Wiley, 2nd Edition.

Mee, RW. (1984) Confidence bounds for the difference between two probabilities. Biometrics 40, 1175–1176.

Miettinen OS, Nurminen M. (1985) Comparative analysis of two rates. Statistics in Medicine 4, 213–226.

Nurminen, M. (1986) Analysis of trends in proportions with an ordinally scaled determinant. Biometrical J. 28, 965–974

Clopper-Pearson exact CI

Description

Clopper-Pearson exact CI

Usage

exactci(x, n, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Clopper, C. and Pearson, E.S. (1934) The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404–413.

internal function

Description

internal function of orscoreci

mid-P confidence interval adaptation of the Clopper-Pearson interval

Description

mid-P confidence interval adaptation of the Clopper-Pearson interval

Usage

midPci(x, n, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Agresti, A., Gottard, A. (2005) Randomized confidence intervals and the mid-P approach, discussion of article by C. Geyer and G. Meeden, Statistical Science 20, 367–371.

Examples

midPci(x = 15, n = 112, conf.level = 0.95)
  

Adapted binomial score confidence interval for the subject-specific odds ratio with matched pairs

Description

Adapted binomial score confidence interval for the subject-specific odds ratio with matched pairs. This uses the Wilson score CI for a binomial parameter with the off-diagonal counts.

Usage

oddsratioci.mp(b, c, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

A. Agresti and Y. Min, (2005) Simple improved confidence intervals for comparing matched proportions. Statistics in Medicine 24 (5), 729–740.

Examples

oddsratioci.mp(b = 40, c = 20, conf.level = 0.95)

Bayesian tail confidence interval for an odds ratio

Description

Approximate Bayesian tail confidence interval for an odds ratio using simulation method

Usage

orci.bayes(x1,n1,x2,n2,a,b,c,d,conf.level, nsim)

Arguments

Value

Confidence interval for an odds ratio with given confidence level.

References

Agresti, A. (2002) Categorical Data Analysis. Wiley, 2nd Edition.

score confidence interval for an odds ratio in a 2x2 table [p1(1-p1)/(p2(1-p2))]

Description

score confidence interval for an odds ratio in a 2x2 table [p1(1-p1)/(p2(1-p2))]

Usage

orscoreci(x1, n1, x2, n2, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Cornfield, J. (1956) A statistical problem arising from retrospective studies. In Neyman J. (ed.), Proceedings of the third Berkeley Symposium on Mathematical Statistics and Probability 4, pp. 135–148.

Miettinen O. S., Nurminen M. (1985) Comparative analysis of two rates. Statistics in Medicine 4, 213–226.

Agresti, A. 2002. Categorical Data Analysis. Wiley, 2nd Edition.

score confidence interval for the relative risk in a 2x2 table

Description

score confidence interval for the relative risk in a 2x2 table

Usage

riskscoreci(x1, n1, x2, n2, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Nam, J. M. (1995) Confidence limits for the ratio of two binomial proportions based on likelihood scores: Non-iterative method. Biom. J. 37 (3), 375–379.

Koopman PAR. (1985) Confidence limits for the ratio of two binomial proportions. Biometrics 40, 513–517.

Miettinen OS, Nurminen M. (1985) Comparative analysis of two rates. Statistics in Medicine 4, 213–226.

Nurminen, M. (1986) Analysis of trends in proportions with an ordinally scaled determinant. Biometrical J 28, 965–974

Agresti, A. (2002) Categorical Data Analysis. Wiley, 2nd Edition.

Bayesian tail confidence interval for the relative risk

Description

Approximate Bayesian tail confidence interval for the relative risk using simulation method

Usage

rrci.bayes(x1,n1,x2,n2,a,b,c,d,conf.level, nsim)

Arguments

Value

Confidence interval for the relative risk with given confidence level.

References

Agresti, A. (2002) Categorical Data Analysis. Wiley, 2nd Edition.

Wilson's confidence interval for a single proportion

Description

Wilson's confidence interval for a single proportion. Score CI based on inverting the asymptotic normal test using the null standard error

Usage

scoreci(x, n, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Wilson, E.B. (1927) Probable inference, the law of succession, and statistical inference J. Amer. Stat. Assoc 22, 209–212

Tango's score confidence interval for a difference of proportions with matched pairs

Description

Tango's score confidence interval for a difference of proportions with matched pairs

Usage

scoreci.mp(b, c, n, conf.level)

Arguments

Value

A list with class '"htest"' containing the following components:

References

Agresti, A. and Min, Y. (2005) Simple improved confidence intervals for comparing matched proportions Statistics in Medicine 24 (5), 729–740.

Tango T. (1998) Equivalence test and confidence interval for the difference in proportions for the paired-sample design Statistics in Medicine 17, 891–908

Examples

scoreci.mp(b = 40, c = 20, n = 160, conf.level = 0.95)

Wald interval with the possibility to adjust according to Agresti, Caffo (2000) for difference in proportions and independent samples.

Description

Wald interval with the possibility to adjust according to Agresti, Caffo (2000) for difference in proportions and independent samples. The Agresti-Caffo interval adds 1 to x1 and x2 and adds 2 to n1 and n2.

Usage

wald2ci(x1, n1, x2, n2, conf.level, adjust)

Arguments

Details

If adjust=AC is chosen, the standard Wald interval is modified to the Agresti-Caffo adjusted CI (American Statistician, 2000)

Value

A list with class '"htest"' containing the following components:

References

Agresti, A. (2002) Categorical Data Analysis. Wiley, 2nd Edition. Agresti, A., Caffo, B.(2000) Simple and effective confidence intervals for proportions and difference of proportions result from adding two successes and two failures. The American Statistician 54 (4), 280–288.

internal function

Description

internal function of diffscoreci