Provides a unified interface for several parametric post hoc tests following a significant ANOVA. The function computes pairwise comparisons of group means with different methods for controlling the family-wise error rate.
Usage
postHocTest(x, ...)
# S3 method for class 'aov'
postHocTest(
x,
which = NULL,
method = c("hsd", "bonferroni", "lsd", "scheffe", "newmankeuls", "duncan"),
conf.level = 0.95,
ordered = FALSE,
...
)
# S3 method for class 'matrix'
postHocTest(
x,
method = c("none", "fdr", "BH", "BY", "bonferroni", "holm", "hochberg", "hommel"),
conf.level = 0.95,
...
)
# S3 method for class 'table'
postHocTest(
x,
method = c("none", "fdr", "BH", "BY", "bonferroni", "holm", "hochberg", "hommel"),
conf.level = 0.95,
...
)
# S3 method for class 'PostHocTest'
print(x, digits = getOption("digits", 3), ...)Arguments
- x
an object of class
aov.- ...
further arguments, not used so far.
- which
a character vector listing terms in the fitted model for which the intervals should be calculated. Defaults to all the terms.
- method
one of
"hsd","bonferroni","lsd","scheffe","newmankeuls","duncan", defining the method for the pairwise comparisons (may be abbreviated).
For the post hoc test of tables the methods ofp.adjust()can be supplied. See the detail there.- conf.level
a numeric value between zero and one giving the family-wise confidence level to use. If this is set to NA, just a matrix with the p-values will be returned.
- ordered
a logical value indicating if the levels of the factor should be ordered according to increasing average in the sample before taking differences. If ordered is
TRUEthen the calculated differences in the means will all be positive. The significant differences will be those for which the lower end point is positive.
This argument will be ignored if method is not eitherhsdornewmankeuls.- digits
controls the number of fixed digits to print.
Value
An object of class "PostHocTest": a list of data frames
containing the mean difference, lower and upper confidence interval bounds,
and p-value when conf.level is not NA; otherwise, a list of
p-value matrices.
Details
Post hoc tests differ in how strongly they control type I error. Conservative methods reduce false positives but have lower power, while more liberal methods increase power at the cost of a higher false positive rate.
LSD (Fisher): No adjustment for multiple testing;
highest power but inflated type I error. Mainly suitable for a small
number of groups.
Bonferroni (Dunn's (Bonferroni) t-test): Adjusts p-values
by the number of comparisons;
simple and robust, but often overly conservative.
Tukey HSD: Controls the family-wise error rate for all
pairwise comparisons; widely used and generally recommended for balanced
designs.
Newman-Keuls: Stepwise procedure with more power than Tukey,
but weaker error control; may inflate type I error.
Duncan: Similar to Newman-Keuls but more liberal; provides
higher power at the cost of increased false positives.
Scheffé: Very conservative; suitable for both pairwise and
complex (contrast-based) comparisons.
Guidance
Tukey HSD is typically a good default for pairwise comparisons.
Bonferroni is useful when strict error control is required.
Scheffé is appropriate for more complex contrasts.
Tables
For tables pairwise chi-square tests can be performed,
either without correction or with correction for multiple testing following
the logic in p.adjust().
See also
TukeyHSD(), aov(),
pairwise.t.test(), scheffeTest()
Other test.posthoc:
conoverTest(),
dscfTest(),
dunnTest(),
dunnettTest(),
gamesHowellTest(),
nemenyiTest(),
plot.PostHocTest(),
scheffeTest(),
signifDiff(),
steelTest()
Examples
postHocTest(aov(breaks ~ tension, data = warpbreaks), method = "lsd")
#>
#> Posthoc multiple comparisons of means : Fisher LSD
#> 95% family-wise confidence level
#>
#> Fit: aov(formula = breaks ~ tension, data = warpbreaks)
#>
#> $tension
#> diff lci uci pval signif
#> M-L -10.000000 -17.95042 -2.049581 0.015 *
#> H-L -14.722222 -22.67264 -6.771803 < 0.001 ***
#> H-M -4.722222 -12.67264 3.228197 0.239
#>
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
postHocTest(aov(breaks ~ tension, data = warpbreaks), method = "hsd")
#>
#> Posthoc multiple comparisons of means : Tukey HSD
#> 95% family-wise confidence level
#>
#> Fit: aov(formula = breaks ~ tension, data = warpbreaks)
#>
#> $tension
#> diff lci uci pval signif
#> M-L -10.000000 -19.55982 -0.4401756 0.038 *
#> H-L -14.722222 -24.28205 -5.1623978 0.001 **
#> H-M -4.722222 -14.28205 4.8376022 0.463
#>
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
postHocTest(aov(breaks ~ tension, data = warpbreaks), method = "scheffe")
#>
#> Posthoc multiple comparisons of means : Scheffé
#> 95% family-wise confidence level
#>
#> Fit: aov(formula = breaks ~ tension, data = warpbreaks)
#>
#> $tension
#> diff lci uci pval signif
#> M-L -10.000000 -19.98534 -0.01465926 0.050 *
#> H-L -14.722222 -24.70756 -4.73688148 0.002 **
#> H-M -4.722222 -14.70756 5.26311852 0.496
#>
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
r.aov <- aov(breaks ~ tension, data = warpbreaks)
# compare p-values:
round(cbind(
lsd= postHocTest(r.aov, method="lsd")$tension[,"pval"]
, bonf=postHocTest(r.aov, method="bonf")$tension[,"pval"]
), 4)
#> lsd bonf
#> M-L 0.0147 0.0442
#> H-L 0.0005 0.0015
#> H-M 0.2386 0.7158
# only p-values by setting conf.level to NA
postHocTest(aov(breaks ~ tension, data = warpbreaks), method = "hsd",
conf.level=NA)
#>
#> Posthoc multiple comparisons of means : Tukey HSD
#>
#> Fit: aov(formula = breaks ~ tension, data = warpbreaks)
#>
#> $tension
#> L M
#> M 0.038 -
#> H 0.001 0.463
#>
#>