tables statistiques1

APPENDIX B

Statistical Tables

433

Table B-1 Normal Curve Areas

Source: Abridged from Table 1 of Statistical Tables and Formulas, by A. Hald, John Wiley & Sons,1952. Reproduced by permission of John Wiley & Sons.

434

Table B-2 Percentage Points of the �2-Distribution

Source: ‘‘Tables of the Percentage Points of the ��-Distribution,’’ by Catherine M. Thompson,Biometrika, Vol. 32, pp. 188—189 (1941). Reproduced by permission of the editor of Biometrika.

435

Table

B-3

5%Pointsof

the

F-D

istribution

436

437

Table

B-3

2.5%

Pointsof

the

F-D

istribution

438

439

Table

B-3

1%Pointsof

the

F-D

istribution

440

441

Table

B-3

0.5%

Pointsof

the

F-D

istribution

442

Sour

ce:‘‘TablesofPercentage

Points

oftheInverted

Beta

(F)Distribution,’’

byMaxineMerringtonandCatherineM.Thom

pson,

Bio

met

rika,Vol.3 3,p p.7 3

—88

(1943).Reprodu

cedbyperm

ission

oftheeditor

ofB

iom

etrika

.

443

Table B-4 Upper Tail Probabilities for the Null Distribution of the Kruskal--Wallis HStatistic: k � 3, n1� 1(1)5, n2 � n1(1)5, 2� n3 � n2(1)5

444

Table B-4 (continued)

445

Table B-4 (continued)

446

Table B-4 (continued)

447

Table B-4 (continued)

448

Table B-4 (continued)

449

Table B-4 (continued)

450

Table B-4 (continued)

451

Table B-4 (continued)

452

Table B-4 (continued)

453

Table B-4 (continued)

454

Table B-4 (continued)

455

Table B-4 (continued)

456

Table B-4 (continued)

457

Table B-4 (continued)

Source: Table F of A Nonparametric Introduction to Statistics, by C. H. Kraft and C van Eedan,Macmillan, New York, 1968. Reproduced by permission of the Macmillan Publishing Company.

458

Table B-5 Selected Critical Values for All Treatments: Multiple Comparisons Based onKruskal--Wallis Rank Sums

Source: ‘‘Rank Sum Multiple Comparisons in One- and Two-Way Classification,’’ by B. J.McDonald and W. A. Thompson, Biometrika, Vol. 54, pp. 487—497 (1967). Reproduced bypermission of the editor of Biometrika. The starred values are from ‘‘Distribution-Free MultipleComparisons,’’ Ph.D. thesis (1963), P. Nemenyi, Princeton University, with permission of theauthor. 459

Table B-6 Selected Critical Values for the Range of k Independent N(0, 1) Variables:k � 2(1)20(2)40(10)100

For a given k and �, the tabled entry is q(�, k, �).

Source: ‘‘Table of Range and Studentized Range,’’ by H. L. Harter, Ann. Math. Statist., Vol. 31, pp.1122—1147 (1960). Reproduced by permission of the editor of the Annals of MathematicalStatistics.

460

Table B-7 Percentage Points of the t-Distribution

Source: ‘‘Table of Percentage Points of the t-Distribution,’’ by Maxine Merrington, Biometrika,Vol. 32, p. 300 (1941). Reproduced by permission of the editor of Biometrika.

461

Table B-8 Coefficients (ai and bi) of the Best Estimates of the Mean (�) and StandardDeviation (�) in Censored Samples Up to n � 20 from A Normal Population

462

Table B-8 (continued)

463

Table B-8 (continued)

464

Tab

leB-8

(con

tinu

ed)

465

Tab

leB-8

(con

tinu

ed)

466

467

Tab

leB-8

(con

tinu

ed)

468

469

Tab

leB-8

(con

tinu

ed)

470

471

Table

B-8

(con

tinu

ed)

Sour

ce:‘‘E

stimationofLocationandScaleParam

etersby

Order

St atisticsfrom

SinglyandDoubly

CensoredSam

ples,PartsIa ndII,’’byA.E.

Sa rha n

a ndB.G.Gr ee nb er g,

Ann

.M

ath.

Stat

ist.,

Vol.27,pp.427—451

(1956 ).Reproducedby

permissionoftheeditorofthe

Ann

als

ofM

athe

mat

ical

Sta

tist

ics.

472

Table

B-9

Variances

andCovariances

oftheBestLinearEstim

ates

oftheMean(��)

andStanda

rdDeviation

(��)

for

CensoredSa

mples

Upto

Size

20from

aNormal

Population

473

Table

B-9

(con

tinu

ed)

Sour

ce:Upto

n�

15ofthistableisreproducedfrom

A.E

.Sarhan

andB.G

.Greenberg,‘‘E

stimationofLocationandScaleParam

etersbyOrder

Statistics

from

SinglyandCensoredSam

ples,P

artsIandII,’’

Ann

.Mat

h.Sta

tist.,Vol.27,pp.427

—451

(1956),and

Vo l.29 ,pp .7 9

—105

(1958),w

ithperm

ission

ofthe

editorofthe

Ann

alsof

Mat

hem

atic

alSt

atistics.T

herestofthetableisproducedfrom

A.E

.Sarhan

andB.G

.Greenberg,‘‘E

stimationofLocationandScale

Param

etersby

Order

Statisticsfrom

SinglyandDoublyCensoredSamples,PartIII,’’Tech.Rep.4-OOR,Project1597,U.S.Arm

yResearchOffice.

474

Table B-10 1/(1� R) and �� for the Estimation of the Parameters of the GammaDistribution When There Are No Censored Observations

Source: ‘‘Estimation of Parameters of the Gamma Distribution Using Order Statistics,’’ by M. B.Wilk, R. Gnanadesikan, and Marilyn J. Huyett, Biometrika, Vol. 49, pp. 525—545 (1962).Reproduced by permission of the editor of Biometrika.

475

Table B-11 �� (P,S) and �� (P, S) for Various Values of n/r: n/r � 1.0

For P� 0.52 read S from the left-hand margin, and for P � 0.56 read S from the right-handmargin. Note that the figures in region 2 are printed in bold roman type and those in region 3 inbold italic type; the remainder of the table (outside of regions 2 and 3) is region 1.

476

Table B-11 (continued)

477

Table B-11 (continued)

478

Table B-11 (continued)

479

Table B-11 (continued)

480

Table B-11 (continued)

481

Table B-11 (continued)

482

Table B-11 (continued)

483

Table B-11 (continued)

484

Table B-11 (continued)

Source: ‘‘Estimation of Parameters of the Gamma Distribution Using Order Statistics,’’ by M. B.Wilk, R. Gnanadesikan, and Marilyn J. Huyett, Biometrika, Vol. 49, pp. 525—545 (1962).Reproduced by permission of the editor of Biometrika.

485

Table B-12 Percentage Points l� Such That P(�� 1/�� 2 � l�)� 1��

Source: ‘‘Two Sample Test in the Weibull Distribution,’’ by D. R. Thoman and L. J. Bain,Technometrics, Vol. 11, pp. 805—815 (1969). Reproduced by permission of the editor of Techno-metrics.

486

Table B-13 Percentage Points z� Such That P(G� z�)� 1��

Source: ‘‘Two Sample Test in the Weibull Distribution,’’ by D. R. Thoman and L. J. Bain,Technometrics, Vol. 11, pp. 805—815 (1969). Reproduced by permission of the editor of Techno-metrics.

487

References

Aaronson, K. D., Schwartz, J. S., Chen, T. M., Wong, K. L., Goin, J. E, and Mancini,D.M. (1997). Development and Prospective Validation of a Clinical Index to PredictSurvival in Ambulatory Patients Referred for Cardiac Transplant Evaluation.Circulation, 95, 2660—2667.

Abramowitz, M., and Stegun, I. A. (1964). Handbook of Mathematical Functions withFormulas, Graphs, and Mathematical Tables. Applied Mathematics Series 55.National Bureau of Standards, Washington, DC.

Afifi, A. A., and Clark, V. (1990). Computer-Aided Multivariate Analysis, 2nd ed.Lifetime Learning Publications, Belmont, CA.

Agresti, A. (1990). Categorical Data Analysis. Wiley, New York.

Aitchison, J. (1970). Statistical Problems of Treatment Allocation. Journal of the RoyalStatistical Society, Series A, 133, 206—238

Aitchison, J., and Brown, J. A. C. (1957). The Lognormal Distribution. CambridgeUniversity Press, Cambridge.

Aitchison, J., and Silvey, S. D. (1957). The Generalization of Probit Analysis to the Caseof Multiple Responses. Biometrika, 44, 131—140.

Aitkin, M., Laird, N., and Francis, B. (1983). A Reanalysis of the Stanford HeartTransplant Data (with discussion). Journal of the American Statistical Association,78, 264—292.

Akaike, H. (1969). Fitting Autoregressive Models for Prediction. Annals of the Instituteof Statistical Mathematics, 21, 243—247.

Akaike, H. (1974). A New Look at the Statistical Model Identification. IEEE Transac-tions on Automatic Control, AC-19, 716—723.

Albert, I. J. (2000). The Use of Frailty Models in Genetic Studies: Application to theRelationship between End-Stage Renal Failure and Mutation Type in AlportSyndrome. European Community Alport Syndrome Concerted Action Group(ECASCA). Journal of Epidemiology and Biostatistics, 5(3), 169—175.

Albertson, P. C., Hanley, J. A., Gleason, D. F., and Barry, M. J. (1998). Competing RiskAnalysis of Men Aged 55 to 74 Years at Diagnosis Managed Conservatively forClinically Localized Prostate Cancer. Journal of the American Medical Association,280(11), 975—980.

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