Statistical Tables t Distribution

1 APPENDIXS tatistical TablesTable 1 Standard NormalCurve AreasTable 2 Percentage Pointsof Student stDistributionTable 3tTest Type IIError CurvesTable 4 Percentage Pointsof Sign Test:C ,nTable 5 Percentage Pointsof Wilcoxon RankSum Test:TLandTUTable 6 Percentage Pointsof WilcoxonSigned-Rank TestTable 7 Percentage Pointsof Chi-SquareDistribution: 2 table 8 Percentage PointsofFDistribution:F table 9 Values of2 Arcsin table 10 Percentage Pointsof StudentizedRange Distribution :q (t,v) table 11 Percentage Pointsfor Dunnett s Test:d (k,v) table 12 Percentage Pointsfor Hartley sFmaxTest:Fmax, table 13 Random NumbersTable 14 FTest PowerCurves for AOVT able 15 PoissonProbabilities:Pr(Y y)1090P1: FNTPB164-OTT6346F-OTTF ebruary 28, 200214:21 Appendix1091 Shaded area = Pr(Z z)0zTABLE 1 Standard normal curve : Computed by M.

2 Longnecker using : FNTPB164-OTT6346F-OTTF ebruary 28, 200214:211092 AppendixTABLE 1 Standard normal curve area = t , 0 table 2 Percentage points of Student stdistributiondf/ . : Computed by M. Longnecker using 3 Probability of Type IIerror curves for .01(one-sided) (d)Probability of Type II error997449392919148432 Source: Computed by M. Longnecker using 3 Probability of Type IIerror curves for .05(one-sided) (d)Probability of Type II error997449392919148432 Source: Computed by M. Longnecker using 3 Probability of Type IIerror curves for .01(two-sided) (d)Probability of Type II error997449392919148432 Source: Computed by M. Longnecker using 3 Probability of Type IIerror curves for .05(two-sided) (d)Probability of Type II error997449392919148432 Source: Computed by M.

3 Longnecker using 4 Percentage points for confidence intervals on the median and the sign test:C ,n (2). (2). (1). (1). ** * * 26 98766 5 42** * * 27 98776 5 53** * * 28109876 6 540** * * 29109877 6 5500**301010987666000**3111109877671000* *32111098876811000**3312111098879211000* 3412111099871021100 0 0 35131211109 8 81122110 0 0 36131211109 9 812 3 2 2 1 1 0 0 37 1413121010 9 813 3 3 2 1 1 1 0 38 1413121110 9 914 4 3 2 2 1 1 1 39 1513121111 10 915 4 3 3 2 2 1 1 40 1514131211 10 916 4 4 3 2 2 2 1 41 1514131211 11 1017 5 4 4 3 2 2 1 42 1615141312 11 1018 5 5 4 3 3 2 2 43 1615141312 11 1119 6 5 4 4 3 3 2 44 1716151313 12 1120 6 5 5 4 3 3 2 45 1716151413 12 1121 7 6 5 4 4 3 3 46 1816151413 13 1222 7 6 5 5 4 4 3 47 1817161514 13 1223 7 7 6 5 4 4 3 48

4 1917161514 13 1224 8 7 6 5 5 4 4 49 1918171515 14 1325 8 7 7 6 5 5 4 50 1918171615 14 13 Note: An * means that no test or confidence interval of this level : Computed by M. Longnecker using 5 Critical values ofTLandTUfor the Wilcoxon rank sum test: independent samples. Test statistic is rank sum associatedwith smaller sample (if equal sample sizes, either rank sum can be used).a..025 one-tailed; .05 two-tailedn1n2345678 9 10 TLTUTLTUTLTUTLTUTLTUTLTUTLTUTLTU35166186 2172372682883193346181125122812321335143 8154116445621122818371941204521492253245 6672312321941265228562961316532707726133 5204528563768397341784383882814382149296 1397349875193549898311541225331654178519 36310866114109 33164424563270438354986611479131b..05 one-tailed; .10 two-tailedn1n2345678 9 10 TLTUTLTUTLTUTLTUTLTUTLTUTLTUTLTU3615 717 720 822 924 92710 2911 3147171224132714301533163617391842572013 2719362040224324462550265468221430204028 5030543258336335677924153322433054396641 7143764680892716362446325841715284549057 9591029173925503363437654906610569111101 131184226543567468057956911183127 Source: From F.

5 Wilcoxon and R. A. Wilcox,Some Rapid Approximate Statistical Procedures(Pearl River, Laboratories, 1964), pp. 20 23. Reproduced with the permission of American Cyanamid 6 Critical values for theWilcoxon signed-rank test[n 5(1)54]One-SidedTwo-Sidedn 5n 6n 7n 8n 9p .1p .2235810p .05p .102358p .025p .050235p .01p .02013p .005p .0101p .0025p .0050p .001p .002 One-SidedTwo-Sidedn 15n 16n 17n 18n 19p .1p .23642485562p .05p .13035414753p .025p .052529344046p .01p .021923273237p .005p .011519232732p .0025p .0051215192327p .001p .002811141821 One-SidedTwo-Sidedn 25n 26n 27n 28n 29p .1p .2113124134145157p .05p .1100110119130140p .025p .058998107116126p .01p .02768492101110p .005p .0168758391100p .0025p .0056067748290p .001p .0025158647179 One-SidedTwo-Sidedn 35n 36n 37n 38n 39p .1p .2235250265281297p .05p .1213227241256271p.

6 025p .05195208221235249p .01p .02173185198211224p .005p .01159171182194207p .0025p .005146157168180192p .001p .002131141151162173 One-SidedTwo-Sidedn 45n 46n 47n 48n 49p .1p .2402422441462482p .05p .1371389407426446p .025p .05343361378396415p .01p .02312328345362379p .005p .01291307322339355p .0025p .005272287302318334p .001p .002249263277292307 Source: Computed by P. J. 6(continued)One-SidedTwo-Sidedn 10n 11n 12n 13n 14p .1p .21417212631p .05p .11013172125p .025p .05810131721p .01p .025791215p .005p .01357912p .0025p .00513579p .001p .00201246 One-SidedTwo-Sidedn 20n 21n 22n 23n 24p .1p .269778694104p .05p .16067758391p .025p .055258657381p .01p .024349556269p .005p .013742485461p .0025p .0053237424854p .001p .0022630354045 One-SidedTwo-Sidedn 30n 31n 32n 33n 34p .1p .2169181194207221p .05p .1151163175187200p.

7 025p .05137147159170182p .01p .02120130140151162p .005p .01109118128138148p .0025p .00598107116126136p .001p .0028694103112121 One-SidedTwo-Sidedn 40n 41n 42n 43n 44p .1p .2313330348365384p .05p .1286302319336353p .025p .05264279294310327p .01p .02238252266281296p .005p .01220233247261276p .0025p .005204217230244258p .001p .002185197209222235 One-SidedTwo-Sidedn 50n 51n 52n 53n 54p .1p .2503525547569592p .05p .1466486507529550p .025p .05434453473494514p .01p .02397416434454473p .005p .01373390408427445p .0025p .005350367384402420p .001p .0023233393553723891100 Appendix 2 table 7 Percentage points of the chi-square distributiondf . 7(continued) . : Computed by P. J. table 8 Percentage points of theFdistribution (df2between 1 and 6)df1df2 8(continued)df112152024304060120240inf. table 8 Percentage points of theFdistribution (df2between 7 and 12)df1df2 8(continued)df112152024304060120240inf.

8 table 8 Percentage points of theFdistribution (df2between 13 and 18)df1df2 1 2 3 8(continued)df112152024304060120240inf. table 8 Percentage points of theFdistribution (df2between 19 and 24)df1df2 1 2 8(continued)df112152024304060120240inf. table 8 Percentage points of theFdistribution (df2between 25 and 30)df1df2 1 8(continued)df112152024304060120240inf. table 8 Percentage points of theFdistribution (df2at least 40)df1df2 1 8(continued)df112152024304060120240inf. : Computed by P. J. 9 Values of 2 arcsin .001 .. Design: Procedures for the Behavioral Sciences,byRoger E. Kirk. Copyright 1968 by Wadsworth Publishing Company, by permission of the publisher, Brooks/Cole, Pacific Grove, 10 Percentage points of the Studentized ranget Number of Treatment MeansErrordf.

9 table is abridged from E. S. Pearson and H. O. Hartley, eds.,Biometrika Tables for Statisti-cians,2d ed., Vol 1 (New York: Cambridge University Press, 1958), table 29. Reproduced with thepermission of the editors and the trustees 10(continued)t Number of Treatment MeansErrordf121314151617181920 11 Percentage points for Dunnett s test:d (k, ) (one-sided) k C. W. Dunnett (1955), A Multiple Comparison Procedure for Comparing Several Treatments with a Con-trol, Journal of the American Statistical Association50, 1112 1118. Reprinted with permission fromJournal ofthe American Statistical 1955 by the American Statistical Association. All rights W. Dunnett (1964), New Tables for Multiple Comparisons with a Control, Biometrics20, 482 491. Also addi-tional Tables produced by C. W. Dunnett in 11 Percentage points for Dunnett s test:d (k, ) (one-sided) k 11 Percentage points for Dunnett s test:d (k, )(continued) (two-sided) k 11 Percentage points for Dunnett s test:d (k, )(continued) (two-sided) k 12 Percentage points ofFmax s2max/s2minUpper 5% 1% (6)24(9)28(1)31(0)33(7)36(1) the largest ands2minthe smallest in a set oftindependent mean squares, each based on df2 n 1 degrees of free-dom.

10 Values in the columnt 2 and in the rows df2 2 and are exact. Elsewhere, the third digit may be in error by afew units for the 5%points and several units for the 1%points. The third-digit figures in parentheses for df2 3 are themost uncertain. FromBiometrika Tables for Statisticians,3rd ed., Vol. 1, edited by E. S. Pearson and H. O. Hartley (NewYork: Cambridge University Press, 1966), table , p. 202. Reproduced by permission of theBiometrika 13 Random numbersLine/Col.(1)(2)(3)(4)(5)(6)(7)(8) (9)(10)(11)(12)(13)(14)11048015011015360 2011816479164669179141946259036207209699 9570912919070022236846573255958539330995 8919827982534029396534095526661917439615 9950532413048360225279726576393648091517 9248304934032081306801965563348586294421 6793093062436168007856163763944053537713 4157004008497491797758163795375703997581 8371665606121917826046881305496846067214 1100692701263546136779210690711008427512 7756534981860270659906551505321916818254 4394428807995627290556420699949887231016 7119418738440134884063213210691063412952 8963019197705463079721887620922945955686 9690146004518425849034250832307989579143 4263661102811745318103577408437825331125 6658678449470558556941108547536857533425 3988530605953338867623000815817983164391 1458185936495211289186957888231332767099 7799365686505859901063159501547855909161 0781881263553409614823503427496266944518 6637269552180208471223490511337039032213 0942993969526369273788974334883632017617 3001508272841152715630613749521410365611 2987529856894823752267676899339401511263 5885104202852997589868150711997336710480 8178772331391647564810569773585977293727 4461285519070716510851276551821512597745 2163086075692144494425390070960639907560 1407191702368213825240460268893681988555 3224481901188652556483544919059445515718 0101154092333629490431273041461859429852 7158585030511320191592747649511952162539 1646369585862321614513831499873623495643 5094738177523515635749200705697628337870 9998426980669176988136025185146104889161 9509256255810421486639124585828143460917 2301689022904734591932217830421616669990 4328122254164584922242174103470702530676 4682638458151066462152415227969094459223 3263932363055972420013363380059434228728 3580606912170126416118296228512429334270 0187637873085873100256458341539846557411 3510367076843618818510250248833062288340 7351197319242060952612805000167658325868 66795072094953 Abridged from William H.