Computes tests and confidence intervals of effects in a 2x2 between-subjects design for medians

Source: R/statpsych1.R

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 between-subjects design with a quantitative response variable. The effects are defined in terms of medians rather than means. Tied scores are assumed to be rare.

ci.2x2.median.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 effect

  • SE - standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2002). “Statistical inference for a linear function of medians: Confidence intervals, hypothesis testing, and sample size requirements.” Psychological Methods, 7(3), 370--383. ISSN 1939-1463, doi:10.1037/1082-989X.7.3.370 .

Examples

y11 <- c(19.2, 21.1, 14.4, 13.3, 19.8, 15.9, 18.0, 19.1, 16.2, 14.6)
y12 <- c(21.3, 27.0, 19.1, 21.5, 25.2, 24.1, 19.8, 19.7, 17.5, 16.0)
y21 <- c(16.5, 11.3, 10.3, 17.7, 13.8, 18.2, 12.8, 16.2, 6.1, 15.2)
y22 <- c(18.7, 17.3, 11.4, 12.4, 13.6, 13.8, 18.3, 15.0, 14.4, 11.9)
ci.2x2.median.bs(.05, y11, y12, y21, y22)
#>          Estimate       SE        LL         UL
#> AB:        -3.850 2.951019 -9.633891  1.9338914
#> A:          4.525 1.475510  1.633054  7.4169457
#> B:         -1.525 1.475510 -4.416946  1.3669457
#> A at b1:    2.600 1.992028 -1.304302  6.5043022
#> A at b2:    6.450 2.177232  2.182703 10.7172971
#> B at a1:   -3.450 2.045086 -7.458294  0.5582944
#> B at a2:    0.400 2.127472 -3.769769  4.5697694

# Should return:
#          Estimate       SE        LL         UL
# AB:        -3.850 2.951019 -9.633891  1.9338914
# A:          4.525 1.475510  1.633054  7.4169457
# B:         -1.525 1.475510 -4.416946  1.3669457
# A at b1:    2.600 1.992028 -1.304302  6.5043022
# A at b2:    6.450 2.177232  2.182703 10.7172971
# B at a1:   -3.450 2.045086 -7.458294  0.5582944
# B at a2:    0.400 2.127472 -3.769769  4.5697694