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R version 3.4.0 (2017-04-21) -- "You Stupid Darkness"
Copyright (C) 2017 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
Natural language support but running in an English locale
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> # Test data from:
> # Circular statistics in biology, Batschelet, E (1981)
> # ยง6.2, p99
> #
>
> suppressMessages(library("circular"))
> # ?watson.williams.test
>
> angles <- circular( c(rep(c(-20, -10, 0), c(1,7,2)), rep(c(-10, 0, 10, 20), c(3,3,3,1))), units="degrees", template="geographics")
> group <- factor(rep(c("exp", "control"), each=10))
>
> # expect this:
> # F = 8.7329, df1 = 1, df2 = 18, p-value = 0.003108
> # mean of control mean of exp
> # 1.988969 -9.000615
>
> # Test interfaces
> xn <- angles
> watson.williams.test(xn, group)
Watson-Williams test for homogeneity of means
data: xn by group
F = 8.7329, df1 = 1, df2 = 18, p-value = 0.008472
sample estimates:
Circular Data:
Type = angles
Units = degrees
Template = geographics
Modulo = asis
Zero = 1.570796
Rotation = clock
mean of control mean of exp
1.988969 -9.000615
>
> xl <- split(xn, group)
> watson.williams.test(xl)
Watson-Williams test for homogeneity of means
data: control and exp
F = 8.7329, df1 = 1, df2 = 18, p-value = 0.008472
sample estimates:
Circular Data:
Type = angles
Units = degrees
Template = geographics
Modulo = asis
Zero = 1.570796
Rotation = clock
mean of control mean of exp
1.988969 -9.000615
>
> xl <- split(xn, group)
> names(xl) <- NULL
> watson.williams.test(xl)
Watson-Williams test for homogeneity of means
data: 1 and 2
F = 8.7329, df1 = 1, df2 = 18, p-value = 0.008472
sample estimates:
Circular Data:
Type = angles
Units = degrees
Template = geographics
Modulo = asis
Zero = 1.570796
Rotation = clock
mean of 1 mean of 2
1.988969 -9.000615
>
> xd <- data.frame(group=group, angles=angles)
> watson.williams.test(angles ~ group, xd)
Watson-Williams test for homogeneity of means
data: angles by group
F = 8.7329, df1 = 1, df2 = 18, p-value = 0.008472
sample estimates:
Circular Data:
Type = angles
Units = degrees
Template = geographics
Modulo = asis
Zero = 1.570796
Rotation = clock
mean of control mean of exp
1.988969 -9.000615
>
> # Test the influence of ordering the groups
> id <- c(9, 8, 7, 4, 6, 5, 12, 18, 10, 17, 1, 19, 3, 20, 2, 16, 15, 14, 13, 11)
> angles <- angles[id]
> group <- group[id]
>
> xn <- angles
> watson.williams.test(xn, group)
Watson-Williams test for homogeneity of means
data: xn by group
F = 8.7329, df1 = 1, df2 = 18, p-value = 0.008472
sample estimates:
Circular Data:
Type = angles
Units = degrees
Template = geographics
Modulo = asis
Zero = 1.570796
Rotation = clock
mean of control mean of exp
1.988969 -9.000615
> xl <- split(xn, group)
> watson.williams.test(xl)
Watson-Williams test for homogeneity of means
data: control and exp
F = 8.7329, df1 = 1, df2 = 18, p-value = 0.008472
sample estimates:
Circular Data:
Type = angles
Units = degrees
Template = geographics
Modulo = asis
Zero = 1.570796
Rotation = clock
mean of control mean of exp
1.988969 -9.000615
> xd <- data.frame(group=group, angles=angles)
> watson.williams.test(angles ~ group, xd)
Watson-Williams test for homogeneity of means
data: angles by group
F = 8.7329, df1 = 1, df2 = 18, p-value = 0.008472
sample estimates:
Circular Data:
Type = angles
Units = degrees
Template = geographics
Modulo = asis
Zero = 1.570796
Rotation = clock
mean of control mean of exp
1.988969 -9.000615
>
> # Test NAs
> angles[length(angles)+1] <- NA
> levels(group) <- c("exp", "control", "bar")
> group[length(group)+1] <- "bar"
> xn <- angles
> watson.williams.test(xn, group)
Watson-Williams test for homogeneity of means
data: xn by group
F = 8.7329, df1 = 1, df2 = 18, p-value = 0.008472
sample estimates:
Circular Data:
Type = angles
Units = degrees
Template = geographics
Modulo = asis
Zero = 1.570796
Rotation = clock
mean of exp mean of control
1.988969 -9.000615
>
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