Computes Dunnett's (1955, 1964) simultaneous confidence intervals
for the \(a - 1\) comparisons of \(a - 1\) treatment means
against a single control mean, with family-wise coverage at the
specified conf_level. Returns the result in tidy long form.
Usage
ci_dunnett(
x,
group = NULL,
control = NULL,
alternative = c("two_sided", "less", "greater"),
conf_level = 0.95
)Arguments
- x
Either (a) a fitted
lmoraovobject with a one-way factor predictor, or (b) a numeric vector of observations, in which casegroupmust also be supplied.- group
When
xis a vector, a factor of group labels of the same length.- control
Character name of the control level (must be one of the factor levels). If
NULL(default), the first level is used.- alternative
One of
"two_sided"(default; the base-R spelling"two.sided"is accepted as an alias),"less", or"greater".- conf_level
Family-wise confidence level. Default
0.95.
Value
A data.frame with one row per non-control
level. Columns: contrast, mean_difference,
se, t_statistic, lower_limit,
upper_limit, p_adjusted.
Details
Critical value. The two-sided Dunnett critical value
\(d_{\alpha, a - 1, \nu}^{(2)}\) is obtained from the multivariate
t distribution with \(a - 1\) dimensions, common correlation
\(0.5\) (the Dunnett correlation under balanced n; the
function does not adjust for unequal n), and \(\nu\) error
degrees of freedom. The function uses the existing
cv_dunnett() critical value.
Adjusted p-values. Computed exactly from the same equicorrelated multivariate t distribution. The one common correlation \(1/2\) admits a one-factor representation, so the probability that all comparisons fall inside (or below) the observed statistic collapses to two nested one-dimensional integrals, evaluated by quadrature. The adjusted p-value is one minus that probability. The computation is deterministic (no Monte Carlo) and needs no additional package.
References
Dunnett, C. W. (1955). A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50(272), 1096–1121.
Dunnett, C. W. (1964). New tables for multiple comparisons with a control. Biometrics, 20(3), 482–491.
Hsu, J. C. (1996). Multiple comparisons: Theory and methods. Chapman & Hall.
See also
cv_dunnett, ci_tukey_kramer,
ci_scheffe
Other hypothesis tests:
adjusted_means(),
ancova(),
anova_within(),
ci_scheffe(),
ci_tukey_kramer(),
compare_cov_structures(),
contrast_test(),
correlations_test(),
equivalence_r(),
equivalence_smd(),
factorial_anova(),
manova_split_plot(),
mauchly_test(),
mixed_anova(),
obrien_test(),
pairwise_within(),
randomization_test(),
randomization_test_paired(),
regions_of_significance(),
simple_effects_AB(),
summary_t_test(),
welch_t()
Author
Ken Kelley kkelley@nd.edu
Examples
# 1. Compare the SSRI and placebo arms of the depression_bdi study
# against the wait list control:
fit <- lm(bdi_post ~ condition, data = depression_bdi)
ci_dunnett(fit, control = "wait_list")
#> contrast mean_difference se t_statistic lower_limit upper_limit
#> ssri - wait_list -6.7 2.81 -2.38 -13.3 -0.132
#> placebo - wait_list -1.8 2.81 -0.639 -8.37 4.77
#> p_adjusted
#> 0.0452
#> 0.7494
#>
#> Confidence level: 95%
# 2. One-sided: a treatment that works pulls the posttest BDI down,
# so the directional alternative is "less":
ci_dunnett(fit, control = "wait_list", alternative = "less")
#> contrast mean_difference se t_statistic lower_limit upper_limit
#> ssri - wait_list -6.7 2.81 -2.38 -Inf -1.08
#> placebo - wait_list -1.8 2.81 -0.639 -Inf 3.82
#> p_adjusted
#> 0.0226
#> 0.3973
#>
#> Confidence level: 95%