Bonferroni confidence intervals for all pairwise proportion differences in a between-subjects design

Computes adjusted Wald confidence intervals for all pairwise differences of population proportions in a between-subjects design using a Bonferroni adjusted alpha level.

For more details, see Section 2.7 of Bonett (2021, Volume 3)

Usage

ci.pairs.prop.bs(alpha, f, n)

Arguments

alpha: alpha level for simultaneous 1-alpha confidence
f: vector of frequency counts of participants who have the attribute
n: vector of sample sizes

Value

Returns a matrix with the number of rows equal to the number of pairwise comparisons. The columns are:

Estimate - adjusted estimate of proportion difference
SE - adjusted standard error
z - z test statistic
p - two-sided p-value
LL - lower limit of the adjusted Wald confidence interval
UL - upper limit of the adjusted Wald confidence interval

References

Agresti A, Caffo B (2000). “Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures.” The American Statistician, 54(4), 280-288. ISSN 00031305, doi:10.2307/2685779 .

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

f <- c(111, 161, 132)
n <- c(200, 200, 200)
ci.pairs.prop.bs(.05, f, n)
#>        Estimate         SE       z       p          LL          UL
#>  1 2 -0.2475248 0.04482323 -5.5222 0.00000 -0.35483065 -0.14021885
#>  1 3 -0.1039604 0.04833562 -2.1508 0.03149 -0.21967489  0.01175409
#>  2 3  0.1435644 0.04358401  3.2940 0.00099  0.03922511  0.24790360

# Should return:
#        Estimate         SE       z       p          LL          UL
# 1 2  -0.2475248 0.04482323 -5.5222 0.00000 -0.35483065 -0.14021885
# 1 3  -0.1039604 0.04833562 -2.1508 0.03149 -0.21967489  0.01175409
# 2 3   0.1435644 0.04358401  3.2940 0.00099  0.03922511  0.24790360