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Introduction

Our sibling analysis provides an overview of family size, examining the number of children a mother has and its relationship with the number of sibling each individual has. This tells us the number of first degree relatives each individual has, helping to predict the probability that an individual will be detected in the forensic database.

Data Exploration

Here, we are trying to create frequency tables for each race to show the number of children born, the number of mother who has “chborn_num” children, the number of sibling, and the number of individuals who has “n_sib” siblings.

\[ n_{sib} = chborn_{num} - 1 \]

\[ \text{freq}_{n_{\text{sib}}} = \text{freq}_{\text{mother}} \cdot \text{chborn}_{\text{num}} \]

For example, suppose 10 mothers (generation 0) have 7 children, then there will be 70 children (generation 1) in total who each have 6 siblings.

1.Frequency Table of Number of Children & Siblings of Black/African American Population

Table 1

Frequency of Number of Children & Siblings of Black/African American Population

RACE

YEAR

chborn_num

freq_mother

n_sib

freq_n_sib

Black/African American

1,960

0

6,697

0

0

Black/African American

1,960

1

4,698

0

4,698

Black/African American

1,960

2

3,411

1

6,822

Black/African American

1,960

3

2,445

2

7,335

Black/African American

1,960

4

1,949

3

7,796

Black/African American

1,960

5

1,361

4

6,805

Black/African American

1,960

6

1,162

5

6,972

Black/African American

1,960

7

932

6

6,524

Black/African American

1,960

8

810

7

6,480

Black/African American

1,960

9

588

8

5,292

Black/African American

1,960

10

549

9

5,490

Black/African American

1,960

11

326

10

3,586

Black/African American

1,960

12

821

11

9,852

Black/African American

1,970

0

16,490

0

0

Black/African American

1,970

1

11,686

0

11,686

Black/African American

1,970

2

9,275

1

18,550

Black/African American

1,970

3

7,161

2

21,483

Black/African American

1,970

4

5,659

3

22,636

Black/African American

1,970

5

4,147

4

20,735

Black/African American

1,970

6

3,147

5

18,882

Black/African American

1,970

7

2,542

6

17,794

Black/African American

1,970

8

2,012

7

16,096

Black/African American

1,970

9

1,473

8

13,257

Black/African American

1,970

10

1,194

9

11,940

Black/African American

1,970

11

784

10

8,624

Black/African American

1,970

12

1,682

11

20,184

Black/African American

1,980

0

8,417

0

0

Black/African American

1,980

1

6,383

0

6,383

Black/African American

1,980

2

5,681

1

11,362

Black/African American

1,980

3

4,797

2

14,391

Black/African American

1,980

4

3,732

3

14,928

Black/African American

1,980

5

2,870

4

14,350

Black/African American

1,980

6

2,264

5

13,584

Black/African American

1,980

7

1,782

6

12,474

Black/African American

1,980

8

1,310

7

10,480

Black/African American

1,980

9

943

8

8,487

Black/African American

1,980

10

717

9

7,170

Black/African American

1,980

11

452

10

4,972

Black/African American

1,980

12

870

11

10,440

Black/African American

1,990

0

7,193

0

0

Black/African American

1,990

1

6,635

0

6,635

Black/African American

1,990

2

7,485

1

14,970

Black/African American

1,990

3

6,161

2

18,483

Black/African American

1,990

4

4,673

3

18,692

Black/African American

1,990

5

3,333

4

16,665

Black/African American

1,990

6

2,445

5

14,670

Black/African American

1,990

7

1,752

6

12,264

Black/African American

1,990

8

1,263

7

10,104

Black/African American

1,990

9

853

8

7,677

Black/African American

1,990

10

590

9

5,900

Black/African American

1,990

11

348

10

3,828

Black/African American

1,990

12

772

11

9,264

2.Frequency of Number of Children & Siblings of White Population by Census Year

Table 2

Frequency of Number of Children & Siblings of White Population

RACE

YEAR

chborn_num

freq_mother

n_sib

freq_n_sib

White

1,960

0

46,202

0

0

White

1,960

1

47,433

0

47,433

White

1,960

2

60,732

1

121,464

White

1,960

3

41,272

2

123,816

White

1,960

4

25,666

3

102,664

White

1,960

5

15,327

4

76,635

White

1,960

6

9,697

5

58,182

White

1,960

7

6,347

6

44,429

White

1,960

8

4,518

7

36,144

White

1,960

9

2,990

8

26,910

White

1,960

10

2,148

9

21,480

White

1,960

11

1,280

10

14,080

White

1,960

12

1,747

11

20,964

White

1,970

0

133,940

0

0

White

1,970

1

106,663

0

106,663

White

1,970

2

157,405

1

314,810

White

1,970

3

112,397

2

337,191

White

1,970

4

68,603

3

274,412

White

1,970

5

38,000

4

190,000

White

1,970

6

22,023

5

132,138

White

1,970

7

12,927

6

90,489

White

1,970

8

8,534

7

68,272

White

1,970

9

5,342

8

48,078

White

1,970

10

3,593

9

35,930

White

1,970

11

2,082

10

22,902

White

1,970

12

2,858

11

34,296

White

1,980

0

61,909

0

0

White

1,980

1

51,856

0

51,856

White

1,980

2

89,551

1

179,102

White

1,980

3

70,716

2

212,148

White

1,980

4

43,190

3

172,760

White

1,980

5

23,170

4

115,850

White

1,980

6

12,556

5

75,336

White

1,980

7

6,589

6

46,123

White

1,980

8

3,874

7

30,992

White

1,980

9

2,254

8

20,286

White

1,980

10

1,368

9

13,680

White

1,980

11

757

10

8,327

White

1,980

12

1,073

11

12,876

White

1,990

0

62,471

0

0

White

1,990

1

56,647

0

56,647

White

1,990

2

119,054

1

238,108

White

1,990

3

90,170

2

270,510

White

1,990

4

51,511

3

206,044

White

1,990

5

25,385

4

126,925

White

1,990

6

12,698

5

76,188

White

1,990

7

6,292

6

44,044

White

1,990

8

3,479

7

27,832

White

1,990

9

1,876

8

16,884

White

1,990

10

1,132

9

11,320

White

1,990

11

623

10

6,853

White

1,990

12

828

11

9,936

3.Summary Statistics of Number of Siblings of Black/African American Population

`summarise()` has grouped output by 'RACE'. You can override using the
`.groups` argument.

Table 3

Summary Statistics of Number of Siblings of Black/African American Population

RACE

YEAR

Mean

Variance

Std_Dev

Black/African American

1,960

3.02

9.69

3.11

Black/African American

1,970

3.00

8.86

2.98

Black/African American

1,980

3.21

8.66

2.94

Black/African American

1,990

3.20

7.62

2.76

4.Summary Statistics of Number of Siblings of White Population

Table 4

Summary Statistics of Number of Siblings of White Population

RACE

YEAR

Mean

Variance

Std_Dev

White

1,960

2.62

5.39

2.32

White

1,970

2.45

4.51

2.12

White

1,980

2.55

4.08

2.02

White

1,990

2.53

3.59

1.89

Data Visualization

1.Distribution of Number of Children by Census Year for each Race

Version Author Date
fbdfcf1 Tina Lasisi 2024-07-23
7e507f5 linmatch 2024-07-02
cc5fc63 linmatch 2024-06-26
bce5e2e hcvw 2024-05-27

2.Distribution of Number of Sibling by Census Year for each Race

`summarise()` has grouped output by 'RACE', 'nsib'. You can override using the
`.groups` argument.

Version Author Date
fbdfcf1 Tina Lasisi 2024-07-23
32ce10e linmatch 2024-07-18
635de08 Tina Lasisi 2024-07-18
2c460cf linmatch 2024-07-03
7e507f5 linmatch 2024-07-02
19aab99 linmatch 2024-06-26

3.Distribution of Number of Children/Siblings by Census Year (Black/African American)

Version Author Date
fbdfcf1 Tina Lasisi 2024-07-23
32ce10e linmatch 2024-07-18
7e507f5 linmatch 2024-07-02

4.Distribution of Number of Children/Siblings by Census Year (Black/African American)

Version Author Date
fbdfcf1 Tina Lasisi 2024-07-23
32ce10e linmatch 2024-07-18
635de08 Tina Lasisi 2024-07-18
99618c9 linmatch 2024-07-12

5.Distribution of Number of Children/Siblings by Age (Balck/African American)

Version Author Date
fbdfcf1 Tina Lasisi 2024-07-23
32ce10e linmatch 2024-07-18

6.Distribution of Number of Children/Siblings by Age (White)

Version Author Date
fbdfcf1 Tina Lasisi 2024-07-23
32ce10e linmatch 2024-07-18

7.Distribution of Number of Children by Age and Year(Balck/African American)

Version Author Date
bdc3293 linmatch 2024-07-29 

R version 4.3.2 (2023-10-31)
Platform: x86_64-apple-darwin20 (64-bit)
Running under: macOS Monterey 12.7.4

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/New_York
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] rempsyc_0.1.8     scales_1.3.0      knitr_1.45        viridis_0.6.5    
 [5] viridisLite_0.4.2 lubridate_1.9.3   forcats_1.0.0     stringr_1.5.1    
 [9] dplyr_1.1.4       purrr_1.0.2       tidyr_1.3.1       tibble_3.2.1     
[13] ggplot2_3.4.4     tidyverse_2.0.0   readr_2.1.5       workflowr_1.7.1  

loaded via a namespace (and not attached):
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[10] gfonts_0.2.0            ellipsis_0.3.2          processx_3.8.3         
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[22] labeling_0.4.3          curl_5.2.0              xml2_1.3.6             
[25] httpcode_0.3.0          withr_3.0.0             grid_4.3.2             
[28] fansi_1.0.6             git2r_0.33.0            gdtools_0.3.7          
[31] xtable_1.8-4            colorspace_2.1-0        crul_1.4.2             
[34] cli_3.6.2               rmarkdown_2.25          crayon_1.5.2           
[37] ragg_1.2.7              generics_0.1.3          rstudioapi_0.15.0      
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[46] callr_3.7.3             hms_1.1.3               systemfonts_1.0.5      
[49] jquerylib_0.1.4         glue_1.7.0              ps_1.7.6               
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[55] later_1.3.2             munsell_0.5.0           pillar_1.9.0           
[58] htmltools_0.5.7         openssl_2.1.1           R6_2.5.1               
[61] textshaping_0.3.7       rprojroot_2.0.4         evaluate_0.23          
[64] shiny_1.8.0             highr_0.10              httpuv_1.6.14          
[67] fontLiberation_0.1.0    bslib_0.6.1             Rcpp_1.0.12            
[70] zip_2.3.1               uuid_1.2-0              gridExtra_2.3          
[73] officer_0.6.6           whisker_0.4.1           xfun_0.41              
[76] fs_1.6.3                getPass_0.2-4           pkgconfig_2.0.3