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. |

```
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
```

```
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 **
```

```
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
```

```
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
```

```
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 **
```

```
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
```

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