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.

3 Longnecker using 3 Probability of Type IIerror curves for .05(two-sided) (d)Probability of Type II error997449392919148432 Source: Computed by M. 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

4 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 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.

5 05 one-tailed; .10 two-tailedn1n2345678 9 10 TLTUTLTUTLTUTLTUTLTUTLTUTLTUTLTU3615 717 720 822 924 92710 2911 3147171224132714301533163617391842572013 2719362040224324462550265468221430204028 5030543258336335677924153322433054396641 7143764680892716362446325841715284549057 9591029173925503363437654906610569111101 131184226543567468057956911183127 Source: From F. 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.

6 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 .025p .05195208221235249p .01p .02173185198211224p .005p .01159171182194207p .0025p .005146157168180192p .001p .002131141151162173 One-SidedTwo-Sidedn 45n 46n 47n 48n 49p .1p .2402422441462482p.

7 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 .025p .05137147159170182p .01p .02120130140151162p .005p.

8 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.

9 table 8 Percentage points of theFdistribution (df2between 7 and 12)df1df2 8(continued)df112152024304060120240inf. 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.

10 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 . 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.