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Table 3 Results of the mixed-effects regression analyses for change in running speed in female half-marathoners across years

From: Male and female Ethiopian and Kenyan runners are the fastest and the youngest in both half and full marathon

Parameter

Estimate

SE

DF

T

p value

95 % CI

Upper

Lower

Ethiopia

       

 Constant term

293.167388

371.574985

43.863

0.789

0.434

−455.758951

1042.093726

 Year

−0.140332

0.184932

43.873

−0.759

0.452

−0.513068

0.232405

 Cage

−0.173148

0.135294

36.958

−1.280

0.209

−0.447291

0.100995

 Cage2

−0.004387

0.006022

27.717

−0.728

0.472

−0.016727

0.007954

Kenya

       

 Constant term

−21.426837

150.844832

36.330

−.0142

0.888

−327.257984

284.404310

 Year

0.017207

0.075087

36.326

0.229

0.820

−0.135029

0.169443

 Cage

−0.144332

0.060829

27.148

−2.373

0.025

−0.269111

−0.019552

 Cage2

−0.003215

0.003653

30.133

−0.880

0.386

−0.010674

0.004243

Austria

       

 Constant term

31.578045

29.443671

597.888

1.072

0.284

−26.247547

89.403637

 Year

−0.011598

0.014658

597.871

−0.791

0.429

−0.040386

0.017190

 Cage

−0.028602

0.006916

600.177

−4.136

0.000

−0.042184

−0.015021

 Cage2

0.000663

0.000536

608.882

1.237

0.217

−0.000390

0.001716

Canada

       

 Constant term

−125.514888

73.115253

155.945

−1.717

0.088

−269.938931

18.909154

 Year

0.066249

0.036396

155.933

1.820

0.071

−0.005644

0.138143

 Cage

−0.020679

0.014519

170.268

−1.424

0.156

−0.049340

0.007982

 Cage2

7.822872E−5

0.001161

162.137

0.067

0.946

−0.002214

0.002370

Czech Republic

 Constant term

−220.270108

155.839548

40.611

−1.413

0.165

−535.086061

94.545845

 Year

0.113694

0.077609

40.610

1.465

0.151

−0.043086

0.270474

 Cage

−0.080535

0.051903

45.473

−1.552

0.128

−0.185044

0.023974

 Cage2

0.003476

0.004529

46.743

0.768

0.447

−0.005637

0.012589

Denmark

       

 Constant term

−144.099673

142.620810

55.173

−1.010

0.317

−429.897999

141.698652

 Year

0.076052

0.070989

55.174

1.071

0.289

−0.066203

0.218308

 Cage

−.012618

0.030636

58.407

−0.412

0.682

−0.073934

0.048697

 Cage2

−.000446

0.002495

59.214

−0.179

0.859

−0.005439

0.004546

Spain

       

 Constant term

−5.366288

67.028907

141.702

−0.080

0.936

−137.872163

127.139587

 Year

0.007615

0.033366

141.702

0.228

0.820

−0.058344

0.073574

 Cage

0.001968

0.014710

129.823

0.134

0.894

−0.027134

0.031069

 Cage2

−0.000865

0.001169

144.790

−0.740

0.461

−0.003175

0.001445

France

       

 Constant term

51.171466

15.295732

4653.214

3.345

0.001

21.184581

81.158350

 Year

−0.020670

0.007613

4653.140

−2.715

0.007

−0.035595

−0.005744

 Cage

−0.023120

0.003408

4755.183

−6.783

0.000

−0.029801

−0.016438

 Cage2

−0.000602

0.000252

4810.855

−2.392

0.017

−0.001095

−0.000109

Great Britain

 Constant term

28.901729

42.017402

749.113

0.688

0.492

−53.584137

111.387595

 Year

−0.009779

0.020917

749.099

−0.468

0.640

−0.050842

0.031283

 Cage

0.009513

0.009652

844.541

0.986

0.325

−0.009432

0.028457

 Cage2

−0.001723

0.000775

871.578

−2.222

0.027

−0.003245

−0.000201

Germany

       

 Constant term

15.158368

14.956731

4456.047

1.013

0.311

−14.164251

44.480986

 Year

−0.003244

0.007446

4455.945

−0.436

0.663

−0.017841

0.011353

 Cage

−0.023479

0.002955

3893.061

−7.946

0.000

−0.029272

−0.017686

 Cage2

−0.000163

0.000198

3910.190

−0.822

0.411

−0.000551

0.000225

Italy

       

 Constant term

55.277603

39.067728

844.859

1.415

0.157

−21.403589

131.958795

 Year

−0.022114

0.019449

844.831

−1.137

0.256

−0.060287

0.016060

 Cage

−0.049367

0.010292

954.174

−4.797

0.000

−0.069565

−0.029169

 Cage2

−0.001914

0.000776

961.174

−2.467

0.014

−0.003436

−0.000391

Japan

       

 Constant term

70.707877

63.986213

101.377

1.105

0.272

−56.217842

197.633596

 Year

−0.031946

0.031855

101.405

−1.003

0.318

−.0095133

0.031242

 Cage

−0.047542

0.017703

159.965

−2.685

0.008

−0.082504

−0.012579

 Cage2

0.001527

0.000930

166.855

1.641

0.103

−0.000310

0.003363

Principality of Liechtenstein

 Constant term

10.483455

64.869741

255.178

0.162

0.872

−117.264786

138.231696

 Year

0.000233

0.032291

255.155

0.007

0.994

−0.063358

0.063823

 Cage

−0.012747

0.013132

275.553

−0.971

0.333

−0.038598

0.013105

 Cage2

−0.001544

0.001094

290.811

−1.411

0.159

−0.003697

0.000610

Luxembourg

 Constant term

−47.666634

97.322485

48.909

−0.490

0.626

−243.252737

147.919469

 Year

0.027753

0.048451

48.906

0.573

0.569

−0.069617

0.125123

 Cage

−0.023725

0.013396

31.814

−1.771

0.086

−0.051017

0.003567

 Cage2

0.001603

0.001046

30.499

1.533

0.136

−0.000532

0.003737

Netherlands

 Constant term

133.938661

125.455169

149.777

1.068

0.287

−113.951882

381.829205

 Year

−0.062003

0.062457

149.769

−0.993

0.322

−0.185413

0.061407

 Cage

−0.011427

0.021283

105.363

−0.537

0.592

−0.053626

0.030771

 Cage2

0.000320

0.001177

84.597

0.272

0.786

−0.002020

0.002660

Norway

       

 Constant term

−487.272616

173.193914

54.820

−2.813

0.007

−834.386566

−140.158666

 Year

0.247478

0.086290

54.821

2.868

0.006

0.074537

0.420419

 Cage

−0.115170

0.020554

36.162

−5.603

0.000

−0.156850

−0.073491

 Cage2

0.002664

0.001240

33.459

2.150

0.039

0.000144

0.005185

Portugal

       

 Constant term

−474.101901

231.004145

55.403

−2.052

0.045

−936.968950

−11.234851

 Year

0.241610

0.114974

55.397

2.101

0.040

0.011234

0.471987

 Cage

−0.006509

0.059010

54.339

−0.110

0.913

−0.124800

0.111783

 Cage2

0.004436

0.005816

53.398

0.763

0.449

−0.007227

0.016100

Switzerland

 Constant term

17.415465

3.082751

85,158.813

5.649

0.000

11.373300

23.457631

 Year

−0.003429

0.001535

85,155.422

−2.235

0.025

−0.006437

−0.000422

 Cage

−0.010236

0.000499

71,948.591

−20.518

0.000

−0.011214

−0.009259

 Cage2

−0.000417

3.413093E−5

70,505.318

−12.217

0.000

−0.000484

−0.000350

United States of America

 Constant term

−102.180938

71.308524

295.142

−1.433

0.153

−242.518553

38.156677

 Year

0.055053

0.035488

295.135

1.551

0.122

−0.014789

0.124895

 Cage

−0.011404

0.012867

301.169

−0.886

0.376

−0.036725

0.013917

 Cage2

0.001037

0.000928

305.711

1.118

0.265

−0.000789

0.002863

Australia

 Constant term

535.990276

98.301322

13.686

5.453

0.000

324.700562

747.279990

 Year

−0.262740

0.048925

13.688

−5.370

0.000

−0.367899

−0.157580

 Cage

0.063641

0.055873

47.462

1.139

0.260

−0.048733

0.176014

 Cage2

−0.002360

0.002842

46.702

−0.830

0.411

−0.008078

0.003358

Belgium

 Constant term

7.038611

107.628613

165.205

0.065

0.948

−205.466290

219.543511

 Year

0.000697

0.053552

165.225

0.013

0.990

−0.105038

0.106433

 Cage

0.000626

0.015637

117.693

0.040

0.968

−0.030341

0.031593

 Cage2

0.000700

0.001032

108.364

0.678

0.499

−0.001345

0.002745

Hungary

 Constant term

−275.257629

154.694094

51.000

−1.779

0.081

−585.818982

35.303724

 Year

0.142544

0.076947

51.000

1.853

0.070

−0.011933

0.297021

 Cage

−0.083478

0.047940

51.000

−1.741

0.088

−0.179721

0.012765

 Cage2

0.000717

0.002086

51.000

0.344

0.732

−0.003470

0.004904

Ireland

       

 Constant term

−33.859940

165.743508

57.989

−0.204

0.839

−365.633001

297.913121

 Year

0.021718

0.082524

57.993

0.263

0.793

−0.143473

0.186909

 Cage

−0.036636

0.037101

37.244

−0.987

0.330

−0.111793

0.038521

 Cage2

−0.000562

0.003459

32.491

−0.162

0.872

−0.007603

0.006480

Poland

       

 Constant term

−72.726997

104.051935

60.961

−0.699

0.487

−280.794379

135.340384

 Year

0.040347

0.051798

60.974

0.779

0.439

−0.063230

0.143924

 Cage

−0.053476

0.023476

65.801

−2.278

0.026

−0.100351

−0.006601

 Cage2

−0.001860

0.001865

69.955

−0.997

0.322

−0.005579

0.001859

Russia

       

 Constant term

−106.441127

155.565229

42.567

−0.684

0.498

−420.260572

207.378318

 Year

0.057206

0.077443

42.538

0.739

0.464

−0.099022

0.213434

 Cage

−0.072584

0.042398

55.257

−1.712

0.093

−0.157542

0.012374

 Cage2

0.004846

0.003169

47.538

1.529

0.133

−0.001528

0.011219

Sweden

       

 Constant term

75.820147

143.966277

104.839

0.527

0.600

−209.643494

361.283787

 Year

−0.033856

0.071641

104.838

−0.473

0.637

−0.175909

0.108197

 Cage

−0.016537

0.020415

67.482

−0.810

0.421

−0.057279

0.024206

 Cage2

0.001067

0.001713

108.162

0.623

0.535

−0.002328

0.004462

Finland

       

 Constant term

−46.926724

100.378904

55.066

−0.467

0.642

−248.085146

154.231697

 Year

0.027006

0.049943

55.068

0.541

0.591

−0.073079

0.127091

 Cage

−0.053711

0.015750

46.121

−3.410

0.001

−0.085411

−0.022011

 Cage2

0.001208

0.001076

44.445

1.123

0.268

−0.000960

0.003376

Greece

       

 Constant term

−105.607974

339.956176

18.425

−0.311

0.760

−818.651669

607.435721

 Year

0.056703

0.169175

18.428

0.335

0.741

−0.298130

0.411535

 Cage

0.011301

0.080214

18.335

0.141

0.889

−0.157002

0.179604

 Cage2

0.005226

0.004315

20.000

1.211

0.240

−0.003776

0.014227

Republic of South Africa

 Constant term

195.281269

261.100120

30.776

0.748

0.460

−337.393318

727.955856

 Year

−0.093079

0.130031

30.771

−0.716

0.479

−0.358359

0.172201

 Cage

−0.033597

0.065427

31.996

−0.514

0.611

−0.166869

0.099674

 Cage2

0.000214

0.003268

27.237

0.066

0.948

−0.006488

0.006916

Brazil

       

 Constant term

178.944876

212.772674

32.077

0.841

0.407

−254.418110

612.307863

 Year

−0.084760

0.105910

32.083

−0.800

0.429

−0.300469

0.130949

 Cage

−0.054561

0.036085

32.952

−1.512

0.140

−0.127981

0.018860

 Cage2

0.003708

0.002066

37.833

1.795

0.081

−0.000475

0.007891

Mexico

       

 Constant term

−208.359308

343.548300

13.049

−0.606

0.555

−950.268215

533.549600

 Year

0.108288

0.170848

13.048

0.634

0.537

−0.260670

0.477246

 Cage

0.017053

0.033477

1.149

0.509

0.691

−0.297964

0.332070

 Cage2

−0.004284

0.002132

1.006

−2.009

0.293

−0.031003

0.022435

Argentina

       

 Constant term

171.161142

449.529264

12.527

0.381

0.710

−803.726404

1146.048688

 Year

−0.080710

0.223646

12.527

−0.361

0.724

−0.565727

0.404306

 Cage

−0.121342

0.107487

7.809

−1.129

0.292

−0.370266

0.127582

 Cage2

0.004002

0.011220

5.403

0.357

0.735

−0.024206

0.032210

India

       

 Constant term

−180.991329

118.481416

23.000

−1.528

0.140

−426.088812

64.106153

 Year

0.095159

0.058967

23.000

1.614

0.120

−0.026822

0.217141

 Cage

0.034212

0.026224

23.000

1.305

0.205

−0.020037

0.088460

 Cage2

0.002970

0.002305

23.000

1.288

0.210

−0.001798

0.007737

Israel

       

 Constant term

1791.341424

749.677965

4.526

2.389

0.068

−198.063460

3780.746308

 Year

−0.884457

0.372205

4.522

−2.376

0.069

−1.872464

0.103550

 Cage

−0.130351

0.107475

8.468

−1.213

0.258

−0.375823

0.115121

 Cage2

−0.026869

0.011891

11.589

−2.260

0.044

−0.052880

−0.000858

Slovenia

       

 Constant term

−31.714993

134.226844

13.547

−0.236

0.817

−320.508524

257.078539

 Year

0.020363

0.066884

13.547

0.304

0.765

−0.123540

0.164266

 Cage

−0.084123

0.046744

8.409

−1.800

0.108

−0.191009

0.022763

 Cage2

−0.001050

0.002818

9.076

−0.373

0.718

−0.007416

0.005317

  1. Data for Non-African runners are sorted in order of the number of finishers of each country
  2. Cage centered age, Cage 2 centered age squared