ci.tukey: Tukey-Kramer confidence intervals for all pairwise mean...

In statpsych: Statistical Methods for Psychologists

Tukey-Kramer confidence intervals for all pairwise mean differences in a between-subjects design

Description

Computes heteroscedastic Tukey-Kramer (also known as Games-Howell) confidence intervals for all pairwise comparisons of population means using estimated means, estimated standard deviations, and samples sizes as input. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence intervals.

For more details, see Section 3.1 of Bonett (2021, Volume 1)

Usage

ci.tukey(alpha, m, sd, n)

Arguments

alpha	alpha level for simultaneous 1-alpha confidence
m	vector of estimated group means
sd	vector of estimated group standard deviations
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 - estimated mean difference

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided Tukey p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

\insertRef

Games1976statpsych

\insertRef

Bonett2021statpsych

Examples

m <- c(12.86, 17.57, 26.29, 30.21)
sd <- c(13.185, 12.995, 14.773, 15.145)
n <- c(20, 20, 20, 20)
ci.tukey(.05, m, sd, n)

# Should return:
#     Estimate       SE       t    df       p        LL         UL
# 1 2    -4.71 4.139530 -1.1378 37.99 0.66881 -15.83085  6.4108517
# 1 3   -13.43 4.427673 -3.0332 37.52 0.02177 -25.33172 -1.5282764
# 1 4   -17.35 4.490074 -3.8641 37.29 0.00233 -29.42281 -5.2771918
# 2 3    -8.72 4.399497 -1.9820 37.39 0.21291 -20.54783  3.1078269
# 2 4   -12.64 4.462292 -2.8326 37.14 0.03572 -24.64034 -0.6396589
# 3 4    -3.92 4.730817 -0.8286 37.98 0.84055 -16.62958  8.7895768

statpsych documentation built on Jan. 13, 2026, 1:07 a.m.