R: Least Significant Difference Test

lsdTest {PMCMRplus} | R Documentation

## Least Significant Difference Test

### Description

Performs the least significant difference all-pairs comparisons test for normally distributed data with equal group variances.

### Usage

    lsdTest(x, ...)

    ## Default S3 method:
    lsdTest(x, g, ...)

    ## S3 method for class 'formula'
    lsdTest(formula, data, subset, na.action, ...)

    ## S3 method for class 'aov'
    lsdTest(x, ...)

### Arguments

`x` | a numeric vector of data values, a list of numeric data vectors or a fitted model object, usually an aov fit.
`...` | further arguments to be passed to or from methods.
`g` | a vector or factor object giving the group for the corresponding elements of `"x"`. Ignored with a warning if `"x"` is a list.
`formula` | a formula of the form `response ~ group` where `response` gives the data values and `group` a vector or factor of the corresponding groups.
`data` | an optional matrix or data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`subset` | an optional vector specifying a subset of observations to be used.
`na.action` | a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`.

### Details

For all-pairs comparisons in an one-factorial layout with normally distributed residuals and equal variances the least signifiant difference test can be performed after a significant ANOVA F-test. Let X_{ij} denote a continuous random variable with the j-the realization (1 ≤ j ≤ n_i) in the i-th group (1 ≤ i ≤ k). Furthermore, the total sample size is N = ∑_{i=1}^k n_i. A total of m = k(k-1)/2 hypotheses can be tested: The null hypothesis is H_{ij}: μ_i = μ_j ~~ (i \ne j) is tested against the alternative A_{ij}: μ_i \ne μ_j (two-tailed). Fisher's LSD all-pairs test statistics are given by

SEE PDF

with s^2_{\mathrm{in}} the within-group ANOVA variance. The null hypothesis is rejected if |t_{ij}| > t_{vα/2}, with v = N - k degree of freedom. The p-values (two-tailed) are computed from the `TDist` distribution.

### Value

A list with class `"PMCMR"` containing the following components:

method

  a character string indicating what type of test was performed.

data.name

  a character string giving the name(s) of the data.

statistic

  lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

  lower-triangle matrix of the p-values for the pairwise tests.

alternative

  a character string describing the alternative hypothesis.

p.adjust.method

  a character string describing the method for p-value adjustment.

model

  a data frame of the input data.

dist

  a string that denotes the test distribution.

### Note

As there is no p-value adjustment included, this function is equivalent to Fisher's protected LSD test, provided that the LSD test is only applied after a significant one-way ANOVA F-test. If one is interested in other types of LSD test (i.e. with p-value adustment) see function `pairwise.t.test`.

### References

Sachs, L. (1997) Angewandte Statistik, New York: Springer.

### See Also

`TDist`, `pairwise.t.test`

### Examples

    fit <- aov(weight ~ feed, chickwts)
    shapiro.test(residuals(fit))
    bartlett.test(weight ~ feed, chickwts)
    anova(fit)

    ## also works with fitted objects of class aov
    res <- lsdTest(fit)
    summary(res)
    summaryGroup(res)

[Package PMCMRplus version 1.7.1 Index]