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Computes confidence intervals of effects in a 2x2 within-subjects design for medians

Source: R/statpsych1.R
ci.2x2.median.ws.Rd

Computes distribution-free confidence intervals for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 within-subjects factorial design. The effects are defined in terms of medians rather than means. Tied scores within each level combination are assumed to be rare.

Usage

ci.2x2.median.ws(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 effect

  • SE - standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2020). “Interval estimation for linear functions of medians in within-subjects and mixed designs.” British Journal of Mathematical and Statistical Psychology, 73(2), 333–346. ISSN 0007-1102, doi:10.1111/bmsp.12171 .

Examples

y11 <- c(222, 402, 333, 301, 284, 182, 281, 230, 290, 182, 133, 278)
y12 <- c(221, 371, 340, 288, 293, 150, 317, 211, 286, 161, 126, 234)
y21 <- c(219, 371, 314, 279, 284, 155, 278, 185, 296, 169, 118, 229)
y22 <- c(170, 332, 280, 273, 272, 160, 260, 204, 252, 153, 137, 223)
ci.2x2.median.ws(.05, y11, y12, y21, y22)
#>          Estimate        SE           LL       UL
#> AB:          3.50 21.050122 -37.75748155 44.75748
#> A:          24.25  9.603490   5.42750463 43.07250
#> B:          17.75  9.101881  -0.08935904 35.58936
#> A at b1:    26.00 11.813742   2.84549058 49.15451
#> A at b2:    22.50 16.323093  -9.49267494 54.49267
#> B at a1:    19.50 15.710347 -11.29171468 50.29171
#> B at a2:    16.00 11.850202  -7.22596953 39.22597

# Should return:
#          Estimate        SE           LL       UL
# AB:          3.50 21.050122 -37.75748155 44.75748
# A:          24.25  9.603490   5.42750463 43.07250
# B:          17.75  9.101881  -0.08935904 35.58936
# A at b1:    26.00 11.813742   2.84549058 49.15451
# A at b2:    22.50 16.323093  -9.49267494 54.49267
# B at a1:    19.50 15.710347 -11.29171468 50.29171
# B at a2:    16.00 11.850202  -7.22596953 39.22597