Confidence interval for a standardized linear contrast of means in a within-subjects design

Computes confidence intervals for two types of population standardized linear contrast of means (unweighted standardizer and level 1 standardizer) in a within-subjects design. Equality of variances is not assumed, but the correlations among the repeated measures are assumed to be approximately equal.

For more details, see Section 4.7 of Bonett (2021, Volume 1)

Usage

ci.lc.stdmean.ws(alpha, m, sd, cor, n, q)

Arguments

alpha: alpha level for 1-alpha confidence
m: vector of estimated means for levels of within-subjects factor
sd: vector of estimated standard deviations for levels of within-subjects factor
cor: average estimated correlation of all measurement pairs
n: sample size
q: vector of within-subjects contrast coefficients

Value

Returns a 2-row matrix. The columns are:

Estimate - estimated standardized linear contrast
adj Estimate - bias adjusted standardized linear contrast estimate
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 .

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

Examples

m <- c(33.5, 37.9, 38.0, 44.1)
sd <- c(3.84, 3.84, 3.65, 4.98)
q <- c(.5, .5, -.5, -.5)
ci.lc.stdmean.ws(.05, m, sd, .672, 20, q)
#>                          Estimate adj Estimate      SE      LL      UL
#> Unweighted standardizer:  -1.3013      -1.2666 0.31479 -1.9182 -0.6843
#> Level 1 standardizer:     -1.3932      -1.3375 0.36618 -2.1109 -0.6755

# Should return:
#                          Estimate adj Estimate      SE      LL      UL
# Unweighted standardizer:  -1.3013      -1.2666 0.31479 -1.9182 -0.6843
# Level 1 standardizer:     -1.3932      -1.3375 0.36618 -2.1109 -0.6755