R Under development (unstable) (2024-08-28 r87069 ucrt) -- "Unsuffered Consequences"
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> # Test data from:
> #    Circular statistics in biology, Batschelet, E (1981)
> #    §6.2, 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 

> 
> proc.time()
   user  system elapsed 
   0.28    0.12    0.32