Test for common mean direction (vectorial)

Tests whether two or more groups of 3-D orientations share a common mean direction applicable to spherical data with multiple groups. The test compares the within-group mean vectors via a weighted sum of squared discrepancies and returns a conclusion statement, per-group vector statistics, the pooled test result, and an equal-area stereonet.

Usage

dir_aov_spher_vec(
  trd,
  plg,
  grp,
  data = NULL,
  conf.level = 0.95,
  type = c("line", "dir", "strike")
)

Arguments

trd

Numeric vector of trend values in degrees, or an unquoted column name when data is supplied. For lines: trend of the lineation. For planes: dip direction or strike depending on type.

plg

Numeric vector of plunge values in degrees, or an unquoted column name when data is supplied. For lines: plunge. For planes: dip angle.

grp

A vector (factor or character) of group labels, or an unquoted column name when data is supplied. Must be the same length as trd and plg.

data

A data frame (or tibble) containing the columns referenced by trd, plg, and grp. Default NULL (use vectors directly).

conf.level

Numeric. Confidence level for per-group and pooled mean direction confidence cones. Default 0.95.

type

Character. How to interpret the input orientations:

"line": (default) Trend and plunge of a lineation.
"dir": Dip direction and dip angle of a plane (pole used internally).
"strike": Strike (right-hand rule) and dip angle of a plane (pole used internally).

Value

A named list with four components:

statement: Character string summarising the test conclusion.
vector_g: Tibble with per-group statistics: group label, sample size N, resultant length R, mean resultant length Rbar, concentration parameter kappa, mean trend trd, mean plunge plg, and confidence cone half-width cone (degrees).
vector_res: Tibble with the test statistic Nr, degrees of freedom df, and p-value p.value. When the null hypothesis is not rejected, the pooled mean direction statistics are appended as additional columns.
stereoplot: A ggplot equal-area stereonet showing the data points, per-group mean directions (coloured triangles) with confidence cones, and—when the null is not rejected—the pooled mean direction (gold triangle) with its confidence cone.

Details

When the null hypothesis is not rejected (samples share a common mean), the pooled mean direction and its confidence cone are overlaid in gold on the stereonet. Per-group mean directions and their confidence cones are always shown in distinct colours.

References

Fisher, N. I., Lewis, T., & Embleton, B. J. J. (1987). Statistical analysis of spherical data. Cambridge University Press.

Examples

set.seed(123)
trds <- c(runif(10, 50, 70), runif(10, 70, 90))
plgs <- c(runif(10, 20, 40), runif(10, 30, 50))
grps <- rep(c("A","B"), each=10)
res <- dir_aov_spher_vec(trds, plgs, grps)
res$statement
#> [1] "Mean direction differs between samples"
res$vector_res
#> # A tibble: 1 × 3
#>      Nr    df  p.value
#>   <dbl> <dbl>    <dbl>
#> 1  54.0     2 1.87e-12
res$stereoplot


# From a data frame
csv_path <- system.file("spherical_data_vec_aov.csv", package = "GMisc")
df <- utils::read.csv(csv_path)
dir_aov_spher_vec(trend, plunge, type, data = df)
#> $statement
#> [1] "Samples come from a distribution with common mean direction"
#> 
#> $vector_g
#> # A tibble: 4 × 9
#>   grp       N     R  Rbar kappa   sigc   trd   plg  cone
#>   <chr> <int> <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl>
#> 1 A        36  35.7 0.992 115.  0.0218 17.3  -76.3  2.16
#> 2 B        39  38.8 0.994 162.  0.0176 10.4  -77.2  1.75
#> 3 C        16  15.7 0.981  48.7 0.0494 11.0  -75.1  4.91
#> 4 D        16  15.8 0.989  86.0 0.0371  7.62 -80.9  3.69
#> 
#> $vector_res
#> # A tibble: 1 × 16
#>      Nr    df p.value   trd   plg strike   dir   dip     R  Rbar kappa  cone
#>   <dbl> <dbl>   <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1  10.8     6  0.0956  12.7 -77.2   103.  193.  167.  106. 0.990  97.9  1.39
#> # ℹ 4 more variables: N <int>, x <dbl>, y <dbl>, z <dbl>
#> 
#> $stereoplot

#>