Scheffe confidence interval for a linear contrast of proportions in a between-subjects design

Computes an adjusted Wald confidence interval for a linear contrast of population proportions in a between-subjects design using a Scheffe critical value. A Scheffe p-value is computed for the test statistic. This function is useful in exploratory studies where the linear contrast of proportions was not planned but was suggested by the pattern of sample proportions. Use the ci.lc.prop.bs function with a Bonferroni adjusted alpha value to compute simultaneous confidence intervals for two or more planned linear contrasts of proportions.

For more details, see Section 2.9 of Bonett (2021, Volume 3)

Usage

ci.lc.prop.scheffe(alpha, f, n, v)

Arguments

alpha: alpha level for 1-alpha confidence
f: vector of frequency counts of participants who have the attribute
n: vector of sample sizes
v: vector of between-subjects contrast coefficients

Value

Returns a 1-row matrix. The columns are:

Estimate - adjusted estimate of proportion linear contrast
SE - adjusted standard error
z - z test statistic
p - two-sided Scheffe p-value
LL - lower limit of the Scheffe confidence interval
UL - upper limit of the Scheffe confidence interval

References

Price RM, Bonett DG (2004). “An improved confidence interval for a linear function of binomial proportions.” Computational Statistics & Data Analysis, 45(3), 449–456. ISSN 01679473, doi:10.1016/S0167-9473(03)00007-0 .

Marascuilo LA, McSweeney M (1977). Nonparametric and Distribution-Free Methods for the Social Sciences. Brooks/Cole.

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

Examples

f <- c(26, 24, 38)
n <- c(60, 60, 60)
v <- c(-.5, -.5, 1)
ci.lc.prop.scheffe(.05, f, n, v)
#>   Estimate         SE      z       p         LL        UL
#>  0.2119565 0.07602892 2.7878 0.02053 0.02585698 0.3980561

# Should return:
#  Estimate         SE      z       p         LL        UL
# 0.2119565 0.07602892 2.7878 0.02053 0.02585698 0.3980561