Type:	Package
Title:	Analysis of the Interpopulation Difference in Degree of Sexual Dimorphism Using Summary Statistics
Version:	0.5.8
Maintainer:	Bassam A. Abulnoor <bassam.abulnoor@gmail.com>
Description:	Offers a solution for the unavailability of raw data in most anthropological studies by facilitating the calculations of several sexual dimorphism related analyses using the published summary statistics of metric data (mean, standard deviation and sex specific sample size) as illustrated by the works of Relethford, J. H., & Hodges, D. C. (1985) <doi:10.1002/ajpa.1330660105>, Greene, D. L. (1989) <doi:10.1002/ajpa.1330790113> and Konigsberg, L. W. (1991) <doi:10.1002/ajpa.1330840110>.
License:	GPL-3
Depends:	R (≥ 3.5.0)
Suggests:	testthat (≥ 2.1.0), knitr, rmarkdown
VignetteBuilder:	knitr
Encoding:	UTF-8
Language:	en-US
LazyData:	true
RoxygenNote:	7.2.3
Imports:	corrplot, dplyr, ggplot2, Morpho, multcompView, stats, tidyr,tmvtnorm ,truncnorm ,utils
Date:	2023-11-17
NeedsCompilation:	no
Packaged:	2023-11-17 20:01:10 UTC; dell
Author:	Bassam A. Abulnoor [aut, cre], MennattAllah H. Attia [aut], Iain R. Konigsberg [aut], Lyle W. Konigsberg [aut]
Repository:	CRAN
Date/Publication:	2023-11-17 20:20:08 UTC

Australia

Description

Raw data from Joseph Birdsell's 1938 survey. The data is from two regions (B1 and B19), see Gilligan and Bulbeck (2007) for a map of the regions. Data downloaded from Dr. Peter Brown's website: https://www.peterbrown-palaeoanthropology.net/resource.html

Usage

Australia

Format

A data frame with 94 rows and 9 variables:

Pop

(Region) ("B1" = Southwest Australia, "B19" = Northeast Australia), see Gilligan and Bulbeck (2007)

Sex

Sex coded as "F" or "M"

Weight.kg

body weight in kilograms

Stature.mm

Standing height in millimeters

Hum.Lgth

Humeral length in millimeters

Rad.Lgth

Radius length in millimeters

Fem.Lgth

Femoral length in millimeters

Tib.Lgth

Tibial length in millimeters

Bi.illiac

Bi-illiac breadth in millimeters

References

Gilligan, I., & Bulbeck, D. (2007). Environment and morphology in Australian Aborigines: A re-analysis of the Birdsell database. American Journal of Physical Anthropology, 134(1), 75-91.

Measurements from calcined postcranial materials.

Description

Part of Table 3 from Cavazzuti et al. (2019).

Usage

Cremains_measurements

Format

A data frame with 22 rows and 8 variables:

Trait

Measured feature

M.mu

Means of males

F.mu

Means of females

m

Male sample sizes

f

Female sample sizes

M.sdev

Standard deviations for males

F.sdev

Standard deviations for females

D

published value for Chakraborty and Majumder's (1982) measure of sexual dimorphism.

References

Cavazzuti, Claudio, et al. (2019) "Towards a new osteometric method for sexing ancient cremated human remains. Analysis of Late Bronze Age and Iron Age samples from Italy with gendered grave goods." PloS one 14.1: e0209423.

Chakraborty, R., & Majumder, P. P. (1982). On Bennett's measure of sex dimorphism. American journal of physical anthropology, 59(3), 295-298.

Dissimilarity index

Description

Visual and statistical computation of the area of non-overlap in the trait distribution between two sex groups.

Usage

D_index(
  x,
  plot = FALSE,
  fill = "female",
  Trait = 1,
  B = NULL,
  verbose = FALSE,
  CI = 0.95,
  rand = TRUE,
  digits = 4
)

Arguments

Details

Chakraborty and Majumder's (1982) D index. The calculations are done using Inman and Bradley's (1989) equations, and the relationship that D = 1 - OVL where OVL is the overlap coefficient described in Inman and Bradley. A parametric bootstrap was used assuming normal distributions. The method is known as the "bias-corrected percentile method" (Efron, 1981) or the "bias-corrected percentile interval" (Tibshirani, 1984)

Value

a table and a graphical representation of the selected traits and their corresponding dissimilarity indices, confidence intervals and significance tests.

References

Chakraborty, Ranajit, and Partha P. Majumder.(1982) "On Bennett's measure of sex dimorphism." American Journal of Physical Anthropology 59.3 : 295-298.

Inman, Henry F., and Edwin L. Bradley Jr.(1989) "The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities." Communications in Statistics-Theory and Methods 18.10:3851-3874.

Efron, B. (1981). Nonparametric standard errors and confidence intervals. Canadian Journal of Statistics, 9(2), 139-158.

Tibshirani, R. J. (1984). Bootstrap confidence intervals. Technical Report No. 3, Laboratory for Computational Statistics, Department of Statistics, Stanford University.

Examples

# plot and calculation of D
run.D <- function() {
  print(D_index(Cremains_measurements[1, ], plot = TRUE))
  cat("Published D value: ", Cremains_measurements[1, 8], "\n")
}
run.D()

## Not run: 
# confidence interval with bootstrapping
D_index(Cremains_measurements[1, ], rand = FALSE, B = 1000)

## End(Not run)

Heuristic data

Description

Heuristic data from Fidler and Thompson (2001)

Usage

FT

Format

A data frame with 24 rows and 3 variables:

Sex

'M' for male and 'F' for female

Pop

Populations' names

x

Dependent variable

References

Fidler, Fiona, and Bruce Thompson. "Computing correct confidence intervals for ANOVA fixed-and random-effects effect sizes." Educational and Psychological Measurement 61.4 (2001): 575-604.

Hedges' g

Description

quantifies the size of difference between sexes in measured traits.

Usage

Hedges_g(
  x,
  Trait = 1,
  CI = 0.95,
  B = NULL,
  verbose = FALSE,
  rand = TRUE,
  digits = 4
)

Arguments

Details

Calculates Hedges' (1981) g and its confidence intervals using the pooled standard deviation and correcting for bias. See Goulet-Pelletier and Cousineau (2018) for details of the calculations and D_index for description of the bootstrap.

Value

a table of Hedge's g values with confidence interval for different traits.

References

Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107-128.

Goulet-Pelletier, J.-C., & Cousineau, D. (2018). A review of effect sizes and their confidence intervals, part I: The Cohen's d family. The Quantitative Methods for Psychology, 14(4), 242-265.

Examples

library(TestDimorph)
data("Cremains_measurements")
# Confidence intervals with non-central t distribution
Hedges_g(Cremains_measurements[1, ])
## Not run: 
# confidence interval with bootstrapping
Hedges_g(Cremains_measurements[1, ], rand = FALSE, B = 1000)

## End(Not run)

The Howells' craniometric data

Description

A subset of a dataset that consists of 82 craniometric measurements taken from approximately two thousands and half human crania from 28 geographically diverse populations. The full data set can be found in https://rdrr.io/github/geanes/bioanth/man/howell.html

Usage

Howells

Format

A data frame with 441 rows and 10 variables:

Sex

'M' for male and 'F' for female

Pop

Populations' names

GOL

Glabello occipital length

NOL

Nasio occipital length

BNL

Bastion nasion length

BBH

Basion bregma height

XCB

Maximum cranial breadth

XFB

Maximum frontal breadth

ZYB

Bizygomatic breadth

AUB

Biauricular breadth

References

Howells WW. (1989). Skull Shapes and the Map. Craniometric Analyses in the Dispersion of Modern Homo. Papers of the Peabody Museum of Archaeology and Ethnology, vol. 79, pp. 189. Cambridge, Mass.: Peabody Museum.

Howells WW. (1995). Who's Who in Skulls. Ethnic Identification of Crania from Measurements. Papers of the Peabody Museum of Archaeology and Ethnology, vol. 82, pp. 108. Cambridge, Mass.: Peabody Museum.

Howells, W. W. (1973). Cranial Variation in Man: A Study by Multivariate Analysis of Patterns of Difference Among Recent Human Populations (Vol. 67). Cambridge, MA: Peabody Museum of Archaeology and Ethnology.

Howells, W. W. (1996). Notes and Comments: Howells' craniometric data on the internet. American Journal of Physical Anthropology, 101(3), 441-442

Pooled within group correlation matrix for Howells' data

Description

Pooled within group correlation matrix for Howells' data

Usage

Howells_R

Format

A 8*8 numerical matrix

Pooled within-group variance-covariance matrix for Howells' data

Description

Pooled within-group variance-covariance matrix for Howells' data

Usage

Howells_V

Format

A 8*8 numerical matrix

See Also

Howells

Summary of the Howells' craniometric data

Description

Summary statistics of the Howells' data subset.

Usage

Howells_summary

Format

A data frame with 32 rows and 8 variables:

Trait

Measured feature

Pop

Population name

M.mu

Means of males

F.mu

Means of females

m

Male sample sizes

f

Female sample sizes

M.sdev

Standard deviations for males

F.sdev

Standard deviations for females

References

Howells

List format of Howells_summary for multivariate analysis

Description

List format of Howells_summary for multivariate analysis

Usage

Howells_summary_list

Format

A list of 5 matrices (R.res, M.mu, F.mu, M.sdev, and F.sdev) and two vectors (m and f) with structure similar to baboon.parms_list

Mixture Index ("MI")

Description

Ipina and Durand's (2010) mixture intersection (MI) measure of sexual dimorphism. This measure is an overlap coefficient where the sum of the frequency of males and the frequency of females equals 1.0. Ipina and Durand (2010) also define a normal intersection (NI) measure which is the overlap coefficient of two normal distributions (each integrating to 1.0), equivalent to Inman and Bradley's (1989) "overlap coefficient." As a result of this rescaling, the "MI" and "NI" plots will appear identical save for the scale on the y-axis.

Usage

MI_index(
  x,
  plot = FALSE,
  Trait = 1,
  B = NULL,
  verbose = FALSE,
  CI = 0.95,
  p.f = 0,
  index_type = "MI",
  rand = TRUE,
  digits = 4
)

Arguments

Details

see D_index for bootstrap method.

Value

returns a table of Ipina and Durand's (2010) mixture index ("MI") for different traits with graphical representation.

References

Inman, H. F., & Bradley Jr, E. L. (1989). The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities. Communications in Statistics-Theory and Methods, 18(10), 3851-3874.

Ipina, S. L., & Durand, A. I. (2010). Assessment of sexual dimorphism: a critical discussion in a (paleo-) anthropological context. Human Biology, 82(2), 199-220.

Examples

# plot and calculation of MI
MI_index(Cremains_measurements[1, ], plot = TRUE)
#' #NI index
MI_index(Cremains_measurements[1, ], index_type = "NI")
1 - D_index(Cremains_measurements[1, ])$D

## Not run: 
# confidence interval with bootstrapping
MI_index(Cremains_measurements[1, ], rand = FALSE, B = 1000)

## End(Not run)

NHANES 1999

Description

Raw data from 1999-2000 NHANES (National Health and Nutrition Examination Survey). Centers for Disease Control and Prevention (CDC). National Center for Health Statistics (NCHS). National Health and Nutrition Examination Survey Data. Hyattsville, MD: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, 2020, https://www.cdc.gov/nchs/nhanes/index.htm

Usage

NHANES_1999

Format

A data frame with 1430 rows and 5 variables:

Sex

(RIAGENDR) Sex coded as "F" or "M"

Pop

(RIDRETH1) Self-reported race, coded as "Black" = Non-Hispanic Black, "Mex.Am" = Mexican American, or "White" = Non-Hispanic White

BMXWT

Body weight in kilograms

BMXHT

Standing height in centimeters

BMXARML

Upper arm length in centimeters

Note

This is not the complete dataset. It is selected so that age in years is greater than or equal to 20 and less than or equal to 40

Hypothetical set of unbalanced data

Description

Example data set from Shaw and Mitchell-Olds (1993)

Usage

SMO

Format

A data frame with 11 rows and 3 variables:

Sex

'M' for male and 'F' for female

Pop

Populations' names

x

Dependent variable

References

Shaw, Ruth G., and Thomas Mitchell-Olds. "ANOVA for unbalanced data: an overview. " Ecology 74.6 (1993): 1638-1645.

Sex Specific One way ANOVA From Summary statistics

Description

Calculates sex specific one way ANOVA from summary statistics.

Usage

aov_ss(
  x,
  Pop = 1,
  pairwise = TRUE,
  letters = FALSE,
  es_anova = "none",
  digits = 4,
  CI = 0.95
)

Arguments

Details

Data is entered as a data frame of summary statistics where the column containing population names is chosen by position (first by default), other columns of summary data should have specific names (case sensitive) similar to baboon.parms_df

Value

Sex specific ANOVA tables and pairwise comparisons in tidy format.

References

#For the femur head diameter data

F. Curate, C. Umbelino, A. Perinha, C. Nogueira, A.M. Silva, E. Cunha, Sex determination from the femur in Portuguese populations with classical and machinelearning classifiers, J. Forensic Leg. Med. (2017) , doi:http://dx.doi.org/10.1016/j. jflm.2017.08.011.

O. Gulhan, Skeletal Sexing Standards of Human Remains in Turkey (PhD thesis), Cranfield University, 2017 [Dataset].

P. Timonov, A. Fasova, D. Radoinova, A.Alexandrov, D. Delev, A study of sexual dimorphism in the femur among contemporary Bulgarian population, Euras. J. Anthropol. 5 (2014) 46–53.

E.F. Kranioti, N. Vorniotakis, C. Galiatsou, M.Y. Iscan , M. Michalodimitrakis, Sex identification and software development using digital femoral head radiographs, Forensic Sci. Int. 189 (2009) 113.e1–7.

Examples

# Comparisons of femur head diameter in four populations
df <- data.frame(
  Pop = c("Turkish", "Bulgarian", "Greek", "Portuguese"),
  m = c(150.00, 82.00, 36.00, 34.00),
  f = c(150.00, 58.00, 34.00, 24.00),
  M.mu = c(49.39, 48.33, 46.99, 45.20),
  F.mu = c(42.91, 42.89, 42.44, 40.90),
  M.sdev = c(3.01, 2.53, 2.47, 2.00),
  F.sdev = c(2.90, 2.84, 2.26, 2.90)
)
aov_ss(x = df)

Pooled within group correlation matrix for baboon data

Description

Pooled within group correlation matrix for baboon data

Usage

baboon.parms_R

Format

A 4*4 numerical matrix

See Also

baboon.parms_list

data frame format for the baboon.parms_df for multivariate analysis

Description

A dataset containing summary statistics for low density lipoprotein (LDL) and apolipoprotein B (apo B) levels in 604 baboons measured on two different diets: a basal diet and a high cholesterol, saturated fat diet. The baboons were classified into one of two subspecies and a hybrid of the two subspecies (Papio hamadryas anubis, P.h. cynocephalus, or hybrid). Each animal was measured on each of the two diets.

Usage

baboon.parms_df

Format

A data frame with 12 rows and 8 variables

Trait

Apolipoprotein B and LDL on two diets

Sub

Sub-species or hybrid

M.mu

Means of LDL and apo B in different sub-species for males

F.mu

Means of LDL and apo B in different sub-species for females

m

Male sample sizes

f

Female sample sizes

M.sdev

Standard deviations for males

F.sdev

Standard deviations for females

Note

The baboon data collection were supported by NIH grant HL28972 and NIH contract HV53030 to the Southwest Foundation for Biomedical Research (Now: Texas Biomedical Research Institute), and funds from the Southwest Foundation for Biomedical Research

References

Konigsberg LW (1991). An historical note on the t-test for differences in sexual dimorphism between populations. American journal of physical anthropology, 84(1), 93–96.

List format for the baboon.parms_df for multivariate analysis

Description

List format for the baboon.parms_df for multivariate analysis

Usage

baboon.parms_list

Format

A list of 5 matrices (R.res, M.mu, F.mu, M.sdev, and F.sdev) and two vectors (m and f)

R.res

pooled within group correlation matrix

M.mu

Means of LDL and apo B in different sub-species for males

F.mu

Means of LDL and apo B in different sub-species for females

m

Male sample sizes

f

Female sample sizes

M.sdev

Standard deviations for males

F.sdev

Standard deviations for females

See Also

baboon.parms_df

Summary Statistics Extraction

Description

Extract summary data needed for other functions from raw data.

Usage

extract_sum(x, Sex = 1, Pop = 2, firstX = 3, test = "tg", run = TRUE, ...)

Arguments

Details

Raw data is entered in a wide format data frame similar to Howells data set. The first two columns contain sex 'Sex' (‘M' for male and 'F' for female) (Default: '1') and populations’ names 'Pop' (Default:'2'). Starting from 'firstX' column (Default: '3'), measured parameters are entered each in a separate column.

Value

Input for other functions.

Examples

# for multivariate test
## Not run: 
extract_sum(Howells, test = "multi")
# for univariate test on a specific parameter
extract_sum(Howells, test = "uni", firstX = 4)

## End(Not run)

Multivariate Analysis Of Sexual Dimorphism

Description

Multivariate extension of Greene t test t_greene

Usage

multivariate(
  x,
  R.res = NULL,
  Trait = 1,
  Pop = 2,
  type_manova = "II",
  manova_test_statistic = "W",
  interact_manova = TRUE,
  es_manova = "none",
  univariate = FALSE,
  padjust = "none",
  ...,
  lower.tail = FALSE,
  CI = 0.95,
  digits = 4
)

Arguments

Details

Data can be entered either as a data frame of summary statistics as in baboon.parms_df. In that case the pooled within correlation matrix 'R.res' should be entered as a separate argument as in baboon.parms_R. Another acceptable format is is a named list of matrices and vectors containing different summary statistics as well as the correlation matrix as in baboon.parms_list. By setting the option 'univariate' to 'TRUE', multiple 'ANOVA's can be run on each parameter independently.

Value

MANOVA table. When the term is followed by '(E)' an exact f-value is calculated.

See Also

baboon.parms_df

Examples

# x is a data frame with separate correlation matrix
multivariate(baboon.parms_df, R.res = baboon.parms_R)
# x is a list with the correlation matrix included
multivariate(baboon.parms_list, univariate = TRUE)
# reproduces results from Konigsberg (1991)
multivariate(baboon.parms_df, R.res = baboon.parms_R)[3, ]
multivariate(baboon.parms_df, R.res = baboon.parms_R, interact_manova = FALSE)

Raw Data Generation By Normal Or Truncated Normal Distribution

Description

Generates raw data from summary statistics using uni/multivariate truncated normal distribution

Usage

raw_gen(
  x,
  Trait = 1,
  Pop = 2,
  R.res = NULL,
  lower = -Inf,
  upper = Inf,
  verbose = FALSE
)

Arguments

Details

If data generation is desired using multivariate distribution data is entered in the form of a list of summary statistics and pooled within correlation matrix as in baboon.parms_list, or the summary statistics are entered separately in the form of a data frame as in baboon.parms_df with a separate correlation matrix as in baboon.parms_R. If data frame is entered without a correlation matrix, data generation is carried out using univariate distribution.

Value

a data frame of raw data

Examples

# Data generation using univariate distributions
raw_gen(baboon.parms_df, lower = 0)

# another univariate example
library(dplyr)
data <- Cremains_measurements[1, ] %>% mutate(Pop=c("A")) %>%
relocate(Pop,.after=1)
raw_gen(data)[, -2]

# Data generation using multivariate distribution
raw_gen(baboon.parms_list, lower = 0)

Greene t test of Sexual Dimorphism

Description

Calculation and visualization of the differences in degree sexual dimorphism between two populations using summary statistics as input.

Usage

t_greene(
  x,
  Pop = 1,
  plot = FALSE,
  colors = c("#DD5129", "#985F51", "#536D79", "#0F7BA2", "#208D98", "#319F8E", "#43B284",
    "#7FB274", "#BCB264", "#FAB255"),
  alternative = c("two.sided", "less", "greater"),
  padjust = "none",
  letters = FALSE,
  digits = 4,
  CI = 0.95
)

Arguments

Details

The input is a data frame of summary statistics where the column containing population names is chosen by position (first by default), other columns of summary data should have specific names (case sensitive) similar to baboon.parms_df.For the visualization of pairwise comparisons using the corrplot, the rounder the image in the plot grid the lower the p-value (see the color scale for similar information). The default colors used in the corrplot are from the "MetBrewer" "Egypt" palette which is listed under the "colorblind_palettes". Different colors palettes can be selected from "RColorBrewer" package.

Value

data frame of t.test results

References

# for the t-test

Greene, David Lee. "Comparison of t-tests for differences in sexual dimorphism between populations." American Journal of Physical Anthropology 79.1 (1989): 121-125.

Relethford, John H., and Denise C. Hodges. "A statistical test for differences in sexual dimorphism between populations." American Journal of Physical Anthropology 66.1 (1985): 55-61.

#For the femur head diameter data

F. Curate, C. Umbelino, A. Perinha, C. Nogueira, A.M. Silva, E. Cunha, Sex determination from the femur in Portuguese populations with classical and machinelearning classifiers, J. Forensic Leg. Med. (2017) , doi:http://dx.doi.org/10.1016/j. jflm.2017.08.011.

O. Gulhan, Skeletal Sexing Standards of Human Remains in Turkey (PhD thesis), Cranfield University, 2017 [Dataset].

P. Timonov, A. Fasova, D. Radoinova, A.Alexandrov, D. Delev, A study of sexual dimorphism in the femur among contemporary Bulgarian population, Euras. J. Anthropol. 5 (2014) 46–53.

E.F. Kranioti, N. Vorniotakis, C. Galiatsou, M.Y. Iscan , M. Michalodimitrakis, Sex identification and software development using digital femoral head radiographs, Forensic Sci. Int. 189 (2009) 113.e1–7.

Examples

# Comparisons of femur head diameter in four populations
df <- data.frame(
  Pop = c("Turkish", "Bulgarian", "Greek", "Portuguese"),
  m = c(150.00, 82.00, 36.00, 34.00),
  f = c(150.00, 58.00, 34.00, 24.00),
  M.mu = c(49.39, 48.33, 46.99, 45.20),
  F.mu = c(42.91, 42.89, 42.44, 40.90),
  M.sdev = c(3.01, 2.53, 2.47, 2.00),
  F.sdev = c(2.90, 2.84, 2.26, 2.90)
)
t_greene(
  df,
  plot = TRUE,
  padjust = "none"
)

Univariate Analysis Of Sexual Dimorphism

Description

Calculation and visualization of the differences in degree sexual dimorphism between multiple populations using a modified one way ANOVA and summary statistics as input

Usage

univariate(
  x,
  Pop = 1,
  type_anova = "II",
  interact_anova = TRUE,
  es_anova = "none",
  pairwise = FALSE,
  padjust = "none",
  ...,
  lower.tail = FALSE,
  CI = 0.95,
  digits = 4
)

Arguments

Details

Data is entered as a data frame of summary statistics where the column containing population names is chosen by position (first by default), other columns of summary data should have specific names (case sensitive) similar to baboon.parms_df

Value

ANOVA table.

References

Hector, Andy, Stefanie Von Felten, and Bernhard Schmid. "Analysis of variance with unbalanced data: an update for ecology & evolution." Journal of animal ecology 79.2 (2010): 308-316.

Examples

#'
# See Tables 6 and 8 and from Fidler and Thompson (2001).
# The “eta2” and “omega2” CIs match those in Table 8.
# See “FT” dataset for Fidler and Thompson (2001) reference

# acquiring summary data
FT_sum <- extract_sum(FT, test = "uni", run = FALSE)
# univariate analysis on summary data
univariate(FT_sum, CI = 0.90, es_anova = "eta2", digits = 5)
univariate(FT_sum, CI = 0.90, es_anova = "omega2", digits = 5)


# Reproduces Table 2 from Shaw and Mitchell-Olds (1993) using their Table 1.
# See “SMO” dataset for Shaw and Mitchell-Olds (1993) reference
# Note that Table 2 residual df is incorrectly given as 6,
# but is correctly given as 7 in Hector et al. (2010)

# acquiring summary data
univ_SMO <- extract_sum(SMO, test = "uni", run = FALSE)
# univariate analysis on summary data
print(univariate(univ_SMO, type_anova = "I")[[1]])
print(univariate(univ_SMO, type_anova = "II"))
univariate(univ_SMO, type_anova = "III")

Graphical and statistical representation of dimorphism differences.

Description

Provides testing for differences in patterning of sexual dimorphism between populations, as well as for evolutionary trends that may characterize other species. The test is based on the computation of the first q canonical variates (q=2 by default) or multiple discriminant functions to develop various tests of sexual dimorphism in any two populations A and B.

Usage

van_vark(
  x,
  W = NULL,
  q = 2,
  Trait = 1,
  Pop = 2,
  plot = TRUE,
  lower.tail = FALSE,
  digits = 4
)

Arguments

Details

Input is a data frame of means and sample sizes similar to Howells_summary with the same naming conventions used throughout the functions but with the standard deviation columns removed.

Value

The output includes a two-dimensional plot that illustrate the existing differences between tested populations and a statistical test of significance for the difference in dimorphism using chi square distribution.

Note

For plot labels to be fully visualized, maximizing image size is advised.

References

Van Vark, G. N., et al. "Some multivariate tests for differences in sexual dimorphism between human populations." Annals of human biology 16.4 (1989): 301-310.

Examples

# selecting means and sample sizes
van_vark_data <- Howells_summary[!endsWith(
  x = names(Howells_summary),
  suffix = "dev"
)]
# running the function
van_vark(van_vark_data, Howells_V)