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

Source: R/statpsych1.R
ci.tukey.Rd

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

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 .

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

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 -1.1378 37.99 0.66881 -15.83088  6.4108781
#>  1 3   -13.43 4.427673 -3.0332 37.52 0.02177 -25.33171 -1.5282918
#>  1 4   -17.35 4.490074 -3.8641 37.29 0.00233 -29.42285 -5.2771504
#>  2 3    -8.72 4.399497 -1.9820 37.39 0.21292 -20.54785  3.1078528
#>  2 4   -12.64 4.462292 -2.8326 37.14 0.03572 -24.64038 -0.6396178
#>  3 4    -3.92 4.730817 -0.8286 37.98 0.84056 -16.62952  8.7895242

# 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