Compares treatment means after an analysis of variance and returns compact letter displays (means sharing a letter do not differ). Fisher's LSD, Duncan's multiple range test (DMRT), Tukey's HSD, Student-Newman-Keuls, Scheffe and Bonferroni are computed inside the package, so no extra package is needed. Dunnett's test against a control uses multcomp when it is installed.
Usage
perform_posthoc(
model,
data,
response,
treatment,
mse = NULL,
df_error = NULL,
posthoc = "lsd",
alpha = 0.05,
control = NULL,
verbose = TRUE
)Arguments
- model
A fitted
aovorlmmodel containing the treatment factor.- data
Data frame used to fit the model. Kept for compatibility; the model frame is used for the calculations.
- response
Name of the response variable (used to label output).
- treatment
Name of the treatment factor in the model.
- mse
Error mean square. Default
NULLtakes it from the model. Supply it to compare means against a different error term (for example the main-plot error of a split-plot design).- df_error
Error degrees of freedom matching
mse. DefaultNULLtakes it from the model.- posthoc
Method(s):
"lsd","duncan","tukey","snk","scheffe","bonferroni","dunnett", a vector of these, or"all".- alpha
Significance level. Default 0.05.
- control
Control level for Dunnett's test. Default
NULLuses the first level of the treatment factor.- verbose
Logical. If TRUE (default), prints the results.
Value
A list with one element per method. Each element contains
groups (means and letters, ordered from highest to lowest, with
treatments as row names), table (level, mean, SE, letter,
replications), comparisons (all pairwise differences with
their SE, p-value and significance), critical_range and
statistics. The Dunnett element is a data frame of comparisons
with the control.
Details
Means are least-squares means of the treatment factor averaged over the other factors in the model. With complete, balanced data they equal the arithmetic means. With missing plots or unequal replication every pair is tested with its own standard error of difference, so the letters stay exact (Tukey-Kramer form for the range tests).
Duncan's and the Student-Newman-Keuls tests use the studentized range for the number of means spanned by each pair, with the protection level \(1 - (1 - \alpha)^{p - 1}\) for Duncan's test, and apply the closure rule: two means are declared different only if every range of means containing them is also significant (Duncan, 1955). The p-value reported for a pair is the largest p-value of the ranges containing it, so it agrees with the letters.
Least-squares means that cannot be estimated (for example a level whose
cells are all empty in a model with interactions) are left out with a
warning. Dunnett's test averages differences over interacting factors
and uses mse and df_error when they are supplied.
Letters are assigned with the insert-and-absorb algorithm of Piepho (2004), which gives a valid display for any pattern of significant pairs. The group containing the highest mean gets the letter "a".
References
Duncan, D.B. (1955). Multiple range and multiple F tests. Biometrics, 11(1), 1-42. doi:10.2307/3001478
Piepho, H.-P. (2004). An algorithm for a letter-based representation of all-pairwise comparisons. Journal of Computational and Graphical Statistics, 13(2), 456-466. doi:10.1198/1061860043515
Kramer, C.Y. (1956). Extension of multiple range tests to group means with unequal numbers of replications. Biometrics, 12(3), 307-310. doi:10.2307/3001469
See also
compare_means for summary statistics,
anova_rbd.
Examples
data(mothbean_rbd)
fit <- aov(seed_yield ~ block + treatment, data = mothbean_rbd)
ph <- perform_posthoc(fit, mothbean_rbd, response = "seed_yield",
treatment = "treatment", posthoc = c("lsd", "duncan"))
#>
#> ======================================================================
#> POST-HOC COMPARISONS
#> ======================================================================
#>
#> Fisher's LSD (alpha = 0.05, error df = 21)
#> Critical difference: 45.884
#> level mean SE group n
#> T5 RDF+Rhizobium+PSB 705.00 15.601 a 4
#> T6 75% RDF+FYM 662.75 15.601 ab 4
#> T3 RDF+Rhizobium 650.75 15.601 bc 4
#> T8 RDF+Zn5 639.75 15.601 bcd 4
#> T4 RDF+PSB 632.25 15.601 bcd 4
#> T7 RDF+S20 610.75 15.601 cd 4
#> T2 RDF 604.75 15.601 d 4
#> T1 Control 516.25 15.601 e 4
#>
#> Duncan's MRT (alpha = 0.05, error df = 21)
#> Critical ranges: p=2 45.884, p=3 48.171, p=4 49.629, p=5 50.651, p=6 51.407, p=7 51.986, p=8 52.441
#> level mean SE group n
#> T5 RDF+Rhizobium+PSB 705.00 15.601 a 4
#> T6 75% RDF+FYM 662.75 15.601 ab 4
#> T3 RDF+Rhizobium 650.75 15.601 bc 4
#> T8 RDF+Zn5 639.75 15.601 bc 4
#> T4 RDF+PSB 632.25 15.601 bc 4
#> T7 RDF+S20 610.75 15.601 c 4
#> T2 RDF 604.75 15.601 c 4
#> T1 Control 516.25 15.601 d 4
#>
#> Means sharing a letter do not differ significantly.
ph$duncan$groups
#> seed_yield groups
#> T5 RDF+Rhizobium+PSB 705.00 a
#> T6 75% RDF+FYM 662.75 ab
#> T3 RDF+Rhizobium 650.75 bc
#> T8 RDF+Zn5 639.75 bc
#> T4 RDF+PSB 632.25 bc
#> T7 RDF+S20 610.75 c
#> T2 RDF 604.75 c
#> T1 Control 516.25 d