See pairwise for further description.
# S3 method for pairwise
summary(
object,
stat.table = TRUE,
test.type = c("dist", "VC", "DL", "var"),
angle.type = c("rad", "deg"),
confidence = 0.95,
show.vectors = FALSE,
...
)Object from pairwise
Logical argument for whether results should be returned in one table (if TRUE) or separate pairwise tables (if FALSE)
the type of statistic to test. See below should be used in the test.
If test.type = "VC", whether angle results are expressed in radians or degrees.
Confidence level to use for upper confidence limit; default = 0.95 (alpha = 0.05)
Logical value to indicate whether vectors should be printed.
Other arguments passed onto pairwise
Michael Collyer
The following summarize the test that can be performed:
#'
Vectors for LS means or slopes originate at the origin and point to some location, having both a magnitude and direction. A distance between two vectors is the inner-product of of the vector difference, i.e., the distance between their endpoints. For LS means, this distance is the difference between means. For multivariate slope vectors, this is the difference in location between estimated change for the dependent variables, per one-unit change of the covariate considered. For univariate slopes, this is the absolute difference between slopes.
If LS mean or slope vectors are scaled to unit size, the vector correlation is the inner-product of the scaled vectors. The arccosine (acos) of this value is the angle between vectors, which can be expressed in radians or degrees. Vector correlation indicates the similarity of vector orientation, independent of vector length.
If the length of a vector is an important attribute -- e.g., the amount of multivariate change per one-unit change in a covariate -- then the absolute value of the difference in vector lengths is a practical statistic to compare vector lengths. Let d1 and d2 be the distances (length) of vectors. Then |d1 - d2| is a statistic that compares their lengths.
Vectors of residuals from a linear model indicate can express the distances of observed values from fitted values. Mean squared distances of values (variance), by group, can be used to measure the amount of dispersion around estimated values for groups. Absolute differences between variances are used as test statistics to compare mean dispersion of values among groups. Variance degrees of freedom equal n, the group size, rather than n-1, as the purpose is to compare mean dispersion in the sample. (Additionally, tests with one subject in a group are possible, or at least not a hindrance to the analysis.)
The argument, test.type is used to select one of the tests
above. See pairwise for examples.
In previous versions of pairwise, summary.pairwise had three
test types: "dist", "VC", and "var". When one chose "dist", for LS mean
vectors, the statistic was the inner-product of the vector difference.
For slope vectors, "dist" returned the absolute value of the difference
between vector lengths, which is "DL" in 0.6.2 and subsequent versions. This
update uses the same calculation, irrespective of vector types. Generally,
"DL" is the same as a contrast in rates for slope vectors, but might not have
much meaning for LS means. Likewise, "dist" is the distance between vector
endpoints, which might make more sense for LS means than slope vectors.
Nevertheless, the user has more control over these decisions with version 0.6.2
and subsequent versions.