Author: Bassam A. Abulnoor, MennattAllah H. Attia, Iain R. Konigsberg, and Lyle W. Konigsberg
Date: 2022-08-22

# TestDimorph examples

#### Bassam A. Abulnoor, MennattAllah H. Attia, Iain R. Konigsberg, and Lyle W. Konigsberg

#### August 22, 2022

#### Table 1 Description of the main functions of the TestDimorph R package.

Function | Description | Notes
--- | --- | ---
aov_ss | Calculates sex specific one-way ANOVA from summary statistics and performs pairwise comparisons | Uses the summary statistics
D_index | Dissimilarity index (Chakraborty and Majumder 1982) for statistical computation and visualization of the area of non-overlap in the trait distribution between the sexes. | Provides a table and a graphical representation of the selected traits and their corresponding dissimilarity indices. Also provides confidence intervals via a bias-corrected parametric bootstrap.
extract_sum | Extract summary statistics needed for the other functions from uploaded raw data directly without need to go to a third-party package. | Can also run the aov_ss, multivariate, t_greene, univariate, or van_vark functions after extracting the summary statistics.
Hedges_g | Calculates Hedges’ (1981) for effect size between the sexes for a single trait. The confidence interval is found using a method described in Goulet-Pelletier and Cousineau (2018). | Can also find the confidence interval using a bias-corrected parametric bootstrap.
MI_index | Mixture Index is the mixture intersection measure of sexual dimorphism (Ipiña and Durand 2010). Ipiña and Durand (2010) also define a normal intersection NI measure which is the overlap coefficient of two normal distributions, equivalent to Inman and Bradley’s (1989) overlap coefficient. | Can produce confidence intervals using a bias-corrected parametric bootstrap.
multivariate | An extension of the univariate analysis of sexual dimorphism between different samples. MANOVA test is used to analyze the interaction effects and main effects. | Type of MANOVA test employed can be “I”, “II” or “III” sum of squares and cross products. The test statistics can be Wilks’ lambda, Pillai’s trace, Hotelling-Lawley’s trace or Roy’s largest root. If univariate argument is TRUE, the function conducts ANOVAs on each variable.
raw_gen | Raw data generation from summary statistics using univariate or multivariate normal distributions (with truncation as an option). |
t_greene | Relethford and Hodges’ (1985) and Greene’s (1989) t-test of sexual dimorphism. | A plot of p-values for differences in sexual dimorphism across all pairs of samples can be produced with plot=TRUE
univariate | Univariate analysis of sexual dimorphism using two-way ANOVA. | Type of sums of squares can type type “I”, “II”, or “III.”
van_vark | Provides testing for differences in sexual dimorphism between samples using van Vark et al.’s (1989) method. |

#### This is Table 2. The R script extracts summary statistics for body mass from the 1999-2000 NHANES raw data and stores it in NHANES_univariate. The “populations” are self-reported race, coded as “Black” = Non-Hispanic Black, “Mex.Am” = Mexican American, or “White” = Non-Hispanic White, and the data are restricted to ages 20-40 years (inclusive). The output are an ANOVA (type II sums of squares by default) with eta-squared values and a table of pairwise comparisons. For more information on the NHANES studies see https://www.cdc.gov/nchs/nhanes/index.htm

    Table.02=function ()
    {
    library(TestDimorph)
    options(width=100) # This option just for output from Rmarkdown
    NHANES_univariate<<-extract_sum(NHANES_1999,test='uni',run=FALSE) # BMXWT (Body mass)
    univariate(NHANES_univariate,es_anova = "eta2",pairwise = TRUE)
    }

    Table.02()

    The parameter used is BMXWT

    $univariate
           term   df    sumsq  meansq statistic p.value signif   eta2 lower.eta2 upper.eta2
    1       Sex    1  25378.2 25378.2   63.8746  0.0000    *** 0.0429     0.0247     0.0652
    2       Pop    2  20970.0 10485.0   26.3898  0.0000    *** 0.0357     0.0186     0.0558
    3   Sex*Pop    2   4141.8  2070.9    5.2123  0.0056     ** 0.0073     0.0007     0.0177
    4 Residuals 1424 565773.3   397.3        NA      NA   <NA>     NA         NA         NA

    $pairwise
       populations   df mean.diff conf.low conf.high statistic p.value signif
    1 Black-Mex.Am  764   -5.9980 -11.8657   -0.1304   -2.0067  0.0451      *
    2  Black-White  965   -8.9769 -14.8397   -3.1142   -3.0048  0.0027     **
    3 Mex.Am-White 1119   -2.9789  -7.4263    1.4685   -1.3142  0.1890     ns

#### This is Table 3. The R script extracts summary statistics for body mass, standing height, and upper arm length from the 1999-2000 NHANES raw data and stores it in NHANES_multivariate. The “populations” are self-reported race, coded as “Black” = Non-Hispanic Black, “Mex.Am” = Mexican American, or “White” = Non-Hispanic White, and the data are restricted to ages 20-40 years (inclusive). The output is a MANOVA table (type II sums of squares and cross products by default) using Wilk’s lambda (the default).

    Table.03=function()
    {
    library(TestDimorph)
    NHANES_multivariate<<-extract_sum(NHANES_1999,test='multi',run=FALSE)
    multivariate(NHANES_multivariate)
    }

    Table.03()

    The parameters used are BMXWT,BMXHT,BMXARML

            term df  Wilks approx.f num.df den.df p.value signif
    1     Sex(E)  1 0.5223 433.5580      3   1422  0.0000    ***
    2     Pop(E)  2 0.7637  68.4009      6   2844  0.0000    ***
    3 Sex*Pop(E)  2 0.9851   3.5834      6   2844  0.0015     **

#### This is Table 4. The R script uses NHANES_univariate and does an ANOVA with type III sums of squares. It then applies t_greene to do Relethford and Hodges’ (1985) and Greene’s (1989) t-test for all pairs, adjusts the p-values using the false discovery rate, and finally returns a “corrplot” view (https://cran.r-project.org/package=corrplot) of the p-values.

    Table.04=function()
    {
    library(TestDimorph)
    print(univariate(NHANES_univariate, type_anova='III'))
    t_greene(NHANES_univariate,plot = TRUE,padjust ="fdr")
    }

    Table.04()

           term   df    sumsq  meansq statistic p.value signif
    1       Sex    1  17356.4 17356.4   43.6845  0.0000    ***
    2       Pop    2  18902.3  9451.2   23.7877  0.0000    ***
    3   Sex*Pop    2   4141.8  2070.9    5.2123  0.0056     **
    4 Residuals 1424 565773.3   397.3        NA      NA   <NA>

       populations   df mean.diff conf.low conf.high statistic p.value signif
    1 Black-Mex.Am  764   -5.9980 -11.8657   -0.1304   -2.0067 0.06765     ns
    2  Black-White  965   -8.9769 -14.8397   -3.1142   -3.0048 0.00810     **
    3 Mex.Am-White 1119   -2.9789  -7.4263    1.4685   -1.3142 0.18900     ns

#### This is Table 5. The R script extracts summary statistics on eight variables from four samples in the W.W. Howells’(1973, 1989, 1995, 1996) dataset. The full data set can be found in https://rdrr.io/github/geanes/bioanth/man/howell.html. The script then runs van Vark et al.’s (1989) analysis.

    Table.05=function()
    {
    library(TestDimorph)
    to_van_Vark=extract_sum(Howells,test='van',run=F)
    van_vark(to_van_Vark)
    }

    Table.05()

    The parameters used are GOL,NOL,BNL,BBH,XCB,XFB,ZYB,AUB

    The maximum possible value of q is (7).

      populations statistic df p.value signif
    1 NORSE-EGYPT    1.2809  2  0.5271     ns
    2 NORSE-TOLAI    8.8981  2  0.0117      *
    3  NORSE-PERU    0.4268  2  0.8078     ns
    4 EGYPT-TOLAI    5.2097  2  0.0739     ns
    5  EGYPT-PERU    0.7477  2  0.6881     ns
    6  TOLAI-PERU    5.4584  2  0.0653     ns

#### This is Table 6. The R script writes summary statistics on femur head diameters for males and females from four samples (Curate et al. 2017; Gulhan 2017; Kranioti et al. 2009; Timonov et al. 2014) to the object df. It then uses aov_ss to do ANOVA within males and within females across the four samples with each ANOVA followed by post-hoc pairwise comparisons.

    Table.06=function ()
    {
    # Comparisons of femur head diameter in four populations
    library(TestDimorph)
    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)
    )
    print(aov_ss(x = df, CI=0.95),digits=6)
    }

    Table.06()

    $`Male model`
             term  df    sumsq   meansq statistic p.value signif
    1 Populations   3  566.214 188.7379   25.4042       0    ***
    2   Residuals 298 2213.959   7.4294        NA      NA   <NA>

    $`Male posthoc`
               populations mean.diff conf.low conf.high p.value signif
    1      Greek-Bulgarian     -1.34  -2.7479    0.0679  0.0686     ns
    2 Portuguese-Bulgarian     -3.13  -4.5664   -1.6936  0.0000    ***
    3    Turkish-Bulgarian      1.06   0.0929    2.0271  0.0254      *
    4     Portuguese-Greek     -1.79  -3.4741   -0.1059  0.0323      *
    5        Turkish-Greek      2.40   1.0930    3.7070  0.0000    ***
    6   Turkish-Portuguese      4.19   2.8524    5.5276  0.0000    ***

    $`Female model`
             term  df     sumsq  meansq statistic p.value signif
    1 Populations   3   88.4265 29.4755    3.7221   0.012      *
    2   Residuals 262 2074.8100  7.9191        NA      NA   <NA>

    $`Female posthoc`
               populations mean.diff conf.low conf.high p.value signif
    1      Greek-Bulgarian     -0.45  -2.0216    1.1216  0.8807     ns
    2 Portuguese-Bulgarian     -1.99  -3.7560   -0.2240  0.0202      *
    3    Turkish-Bulgarian      0.02  -1.1050    1.1450  1.0000     ns
    4     Portuguese-Greek     -1.54  -3.4798    0.3998  0.1716     ns
    5        Turkish-Greek      0.47  -0.9120    1.8520  0.8156     ns
    6   Turkish-Portuguese      2.01   0.4104    3.6096  0.0071     **

#### This is Table 7. The R script uses the maximum width of the patella from Cavazzuti et al. (2019). Calculated values are the mixture index (MI) and normal intersection (NI) (Ipiña and Durand 2010), the D index (Chakraborty and Majumder 1982), and Hedges’ g (Hedges 1981). For each statistic the bias-corrected parametric bootstrap (Efron 1981; Tibshirani 1984) is run 1,000 starting from a set.seed value of 42.

    Table.07=function (i.which=13)
    {
    library(TestDimorph)
    print(MI_index(Cremains_measurements[i.which,],B=1000,rand=F,verbose=F,plot=T))
    print(MI_index(Cremains_measurements[i.which,],index_type='NI',
       B=1000,rand=F,plot=T,verbose=F))
    print(D_index(Cremains_measurements[i.which,],B=1000,rand=F,verbose=F,plot=T))
    print(Hedges_g(Cremains_measurements[i.which,],B=1000,rand=F,verbose=F))
    }

    Table.07()

       Trait lower     MI upper
    1 PA-MXW 0.025 0.1108 0.231

       Trait  lower     NI upper
    1 PA-MXW 0.0544 0.2496 0.521

       Trait  lower      D  upper
    1 PA-MXW 0.4788 0.7504 0.9454
       Trait  lower      g  upper
    1 PA-MXW 1.2094 2.2429 3.7713

### References

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