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

Source: R/statpsych1.R

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.

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 p-value

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Games PA, Howell JF (1976). “Pairwise multiple comparison procedures with unequal N's and/or variances: A Monte Carlo study.” Journal of Educational Statistics, 1(2), 113. ISSN 03629791, doi:10.2307/1164979 .

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)
#>      Estimate       SE          t       df           p        LL         UL
#>  1 2    -4.71 4.139530 -1.1378102 37.99200 0.668806358 -15.83085  6.4108517
#>  1 3   -13.43 4.427673 -3.0331960 37.51894 0.021765570 -25.33172 -1.5282764
#>  1 4   -17.35 4.490074 -3.8640790 37.29278 0.002333937 -29.42281 -5.2771918
#>  2 3    -8.72 4.399497 -1.9820446 37.39179 0.212906199 -20.54783  3.1078269
#>  2 4   -12.64 4.462292 -2.8326248 37.14275 0.035716267 -24.64034 -0.6396589
#>  3 4    -3.92 4.730817 -0.8286096 37.97652 0.840551420 -16.62958  8.7895768

# Should return:
#     Estimate       SE          t       df           p        LL         UL
# 1 2    -4.71 4.139530 -1.1378102 37.99200 0.668806358 -15.83085  6.4108517
# 1 3   -13.43 4.427673 -3.0331960 37.51894 0.021765570 -25.33172 -1.5282764
# 1 4   -17.35 4.490074 -3.8640790 37.29278 0.002333937 -29.42281 -5.2771918
# 2 3    -8.72 4.399497 -1.9820446 37.39179 0.212906199 -20.54783  3.1078269
# 2 4   -12.64 4.462292 -2.8326248 37.14275 0.035716267 -24.64034 -0.6396589
# 3 4    -3.92 4.730817 -0.8286096 37.97652 0.840551420 -16.62958  8.7895768