Computes confidence intervals of standardized effects in a 2x2 between-subjects design

Source: R/statpsych1.R

Computes confidence intervals for standardized linear contrasts of means (AB interaction, main effect of A, main effect of B, simple main effects of A, and simple main effects of B) in a 2x2 between-subjects design with a quantitative response variable. Equality of population variances is not assumed. An unweighted variance standardizer is used, which is the recommended standardizer when both factors are treatment factors.

ci.2x2.stdmean.bs(alpha, y11, y12, y21, y22)

Arguments

alpha

alpha level for 1-alpha confidence

y11

vector of scores at level 1 of A and level 1 of B

y12

vector of scores at level 1 of A and level 2 of B

y21

vector of scores at level 2 of A and level 1 of B

y22

vector of scores at level 2 of A and level 2 of B

Value

Returns a 7-row matrix (one row per effect). The columns are:

  • Estimate - estimate of standardized effect

  • adj Estimate - bias adjusted estimate of standardized effect

  • SE - standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Bonett DG (2008). “Confidence intervals for standardized linear contrasts of means.” Psychological Methods, 13(2), 99--109. ISSN 1939-1463, doi:10.1037/1082-989X.13.2.99 .

Examples

y11 <- c(14, 15, 11, 7, 16, 12, 15, 16, 10, 9)
y12 <- c(18, 24, 14, 18, 22, 21, 16, 17, 14, 13)
y21 <- c(16, 11, 10, 17, 13, 18, 12, 16, 6, 15)
y22 <- c(18, 17, 11, 9, 9, 13, 18, 15, 14, 11)
ci.2x2.stdmean.bs(.05, y11, y12, y21, y22)
#>             Estimate adj Estimate        SE         LL         UL
#> AB:      -1.44976487   -1.4193502 0.6885238 -2.7992468 -0.1002829
#> A:        0.46904158    0.4592015 0.3379520 -0.1933321  1.1314153
#> B:       -0.75330920   -0.7375055 0.3451209 -1.4297338 -0.0768846
#> A at b1: -0.25584086   -0.2504736 0.4640186 -1.1653006  0.6536189
#> A at b2:  1.19392401    1.1688767 0.5001423  0.2136630  2.1741850
#> B at a1: -1.47819163   -1.4471806 0.4928386 -2.4441376 -0.5122457
#> B at a2: -0.02842676   -0.0278304 0.4820369 -0.9732017  0.9163482

# Should return:
#             Estimate  adj Estimate        SE         LL         UL
# AB:      -1.44976487    -1.4193502 0.6885238 -2.7992468 -0.1002829
# A:        0.46904158     0.4592015 0.3379520 -0.1933321  1.1314153
# B:       -0.75330920    -0.7375055 0.3451209 -1.4297338 -0.0768846
# A at b1: -0.25584086    -0.2504736 0.4640186 -1.1653006  0.6536189
# A at b2:  1.19392401     1.1688767 0.5001423  0.2136630  2.1741850
# B at a1: -1.47819163    -1.4471806 0.4928386 -2.4441376 -0.5122457
# B at a2: -0.02842676    -0.0278304 0.4820369 -0.9732017  0.9163482