TESTS FOR HOMOGENEITY OF VARIANCES 357 Table 5.For Normal and(Normal)2 Distributions,Proportion of Times the Null Hypothesis of Equal Variance Was Rejected by the Various Tests,Under the Null Hypothesis(test size and(in parentheses Under the Alternative Hypothesis(power )ata=.05 Normal Distribution:Symmetric (Normal)2:Asymmetric Special n=(5,5,5,5) (10,10,10,10) (20,20,20,20) (5,5,20,20) Study (10,10,10,10) (5,5,20,20) TABLE 1 TESTS N-P .103(.455) 069 .662) .812 (.826 .663 N-P:med 814 759 ,674 (.865 .115 454 .081 .662 .750 .687 ,830) ,669 ,864 Bar .033 .298) .051 .600 .060 .796 .049 .646 .032 .614 .788 .567 ,797 Bar:med .034 .2991 .052 596 64 .798 Coch .040 ,356 .045 ,602 .04 .791 98 629 .795 577 .798 .480 .563】 .576 ,768 Coch:med .041 .353】 .042 .604 .045 .792 .151 .684 223 .493 .6691 ,592 ,762 Hart .028 .231 055 554 ,052 .774 ,739 .604 Hart med 02g 235 .772 .720 ,882 .058 552 ,776 .720 .034 …613 (.777) .725 .879 Bar3 .303 ,051 .600 .060 ,796 .049 .648 .040 .614 .788 .570 .799 Bar3:med .037 .306 ,053 .597 ,064 .798 046 Sam 022 269 587 794 008 .796 .579 .799 ,781 .538 .764 Sam med 019 .274 ,048 .582 .795 594 .006 .616 90 547 Leh .094 .377 .618 med .615 8 .854 Leh2 .665 .761 .745 .697 .837 673 ,873 Leh2:med .198 .515) ,106 .665 .087 .8071 .112 .750 748 .717 .844 680 .870 TABLE 2 TESTS Barl .273（.612 .154 (.709) ,105 .822 123 .729) ,121 545 med .435 087 .638 :82 .414 132 Bar2 med .007 ,039 383 .249 083 .206 .281 .033 .696 .710 649 锅 9 090 .706 med .630 605 Sch2 ,112 .419 .063 ,720 ,645 Sch2: med .056 .136 .048 .322 .049 682 577 TABLE 3 TESTS Levl .083 (.303) .064 .543) 058 .768 .583 Levl:med .002 .065 732 52 ,293 489 927 235 .043 (.142 ,774 .456 .163 .107 Lev2 med .080 .015 .749 Lev3 069 Lev4 091 89 9 060 070 Lev4:med .000 .004 .037 .383 .034 659 Mill 030 134 .040 435 054 .752 89 .254 172 (.324 TABLE 4 TESTS Mood 3 .070 *247 .069 .472 .060 71 066 862) Mood F .091 .296 .077 Mood:med .002 874 827 837 .577 Mood:med 61 .009 2085 ,036 .506 48 .595 389 8器 F-A-8 .070 ,193 058 F-A-B F .094 .240 ,068 ,803 F-A-B:med 2 000 解 8 :8a8 .811 .486 ,033 F-A-B:med .000 9 .566 395 .550 .340 .643 (.000 .030 .575 043 .504 .065 ,418 .572 .357 660 Klotz .057 .265) Klotz F .078 .311 :88 med x2 032 强 841 ,678 802 855 .011 .704 .078 815 ,734 ,033 .472 Klotz:med .05 (.104) .039 .424) .036 .7401 .033 ,490 969 3粥 S-R 2 .060 248 .062 S-R F ,093 296 :88 .613 770 589 789 .630 783 e .000 .015 .658 .491 .054 .003 .038 .029 .353 ,035 .026 .654j .032 .509 092 ,119 .364 F-K 04.4 248 043 F-K F .061 776 .050 528 7 .422 623 361 576 ,782 .054 .544 .174 .442 646 F-K:med x2 004 .746) .030 ,470 034 F-K:med F .009 (.081 .020 .436 033 .751 032 .489 .054 218 (.235 .057 .211 T-G X2 068 203 .536 ,058 525 .305 .610 .753 608 8n9 T-G F ,643 .065 .540 T-G:med .418 .770 (.000 .027 .268 .025 .564 .035 .472 T-G:med F .000 (.000 .033 .288 .026 (.573 .038 .390 .491 .413 .189 .458 TECHNOMETRICS©，VOL. 23,N0. 4,NOVEMBER 1981 This content downloaded from 61.190.7.73 on Mon,30 Sep 2013 22:38:50 PM All use subject to JSTOR Terms and ConditionsTESTS FOR HOMOGENEITY OF VARIANCES Table 5. For Normal and (Normal)2 Distributions, Proportion of Times the Null Hypothesis of Equal Variance Was Rejected by VNull the Hypothesis (test size) and (in parentheses) Under the Alternative Hypothesis (power), at a = .05 Normal Distribution: Symmetric n=(5,5,5,5) (10,10,10,10) TABLE 1 TESTS .103 (.455) .115 (.454) .033 (.298) .034 (.299) .040 (.356) .041 (.353) .028 (.231) .029 (.235) .034 (.303) .037 (.306) .022 (.269) .019 (.274) .094 (.377) .104 (.381) .179 (.514) .198 (.515) .069 (.662) .081 (.662) .051 (.600) .052 (.596) .045 (.602) .042 (.604) .055 (.554) .058 (.552) .051 (.600) .053 (.597) .046 (.587) .048 (.582) .082 (.618) .085 (.615) .108 (.665) .106 (.665) (20,20,20,20) .071 (.812) .077 (.814) .060 (.796) .064 (.798) .043 (.791) .045 (.792) .052 (.774) .056 (.776) .060 (.796) .064 (.798) .058 (.794) .064 (.795) .069 (.792) .078 (.794) .079 (.806) .087 (.807) (Normal)2: Asymmetric (5,5,20,20) .104 (.759) .098 (.750) .049 (.646) .049 (.630) .138 (.706) .151 (.684) .218 (.739) .213 (.720) .049 (.648) .049 (.633) .045 (.607) .054 (.594) .102 (.731) .099 (.722) .119 (.761) .112 (.750) Special Study .625 .639 .032 .034 .234 .223 .625 .627 .040 .046 .008 .006 .498 .511 .745 .748 (10,10,10,10) .674 (.826) .687 (.830) .614 (.788) .629 (.795) .480 (.663) .493 (.669) .604 (.772) .613 (.777) .614 (.788) .629 (.796) .606 (.781) .616 (.790) .664 (.814) .676 (.819) .697 (.837) .717 (.844) (5,5,20,20) .663 (.865) .669 (.864) .567 (.797) .577 (.798) .576 (.768) .592 (.762) .720 (.882) .725 (.879) .570 (.799) .579 (.799) .538 (.764) .547 (.766) .634 (.858) .648 (.854) .673 (.873) .680 (.870) TABLE 2 TESTS .273 (.612) .121 (.435) .047 (.132) .007 (.039) .272 (.603) .170 (.477) .112 (.242) .056 (.136) .154 (.709) .087 (.638) .053 (.383) .024 (.281) .163 (.710) .114 (.649) .079 (.419) .048 (.322) .105 (.822) .082 (.807) .051 (.734) .033 (.696) .119 (.819) .090 (.802) .063 (.720) .049 (.682) .123 (.729) .092 (.667) .048 (.505) .029 (.431) .176 (.790) .140 (.737) .103 (.645) .072 (.577) .648 .397 .050 .014 .808 .722 .510 .402 .487 (.689) .365 (.549) .143 (.249) .043 (.100) .558 (.742) .443 (.630) .247 (.380) .137 (.228) .301 (.545) .182 (.414) .083 (.206) .021 (.090) .421 (.706) .321 (.605) .206 (.447) .122 (.312) TABLE 3 TESTS .083 (.303) .064 (.543) .002 (.065) .025 (.437) .057 (.235) .047 (.489) .011 (.080) .015 (.388) .069 (.192) .062 (.337) .091 (.283) .069 (.493) .000 (.004) .037 (.383) .030 (.134) .040 (.435) .058 (.768) .039 (.732) .048 (.774) .033 (.749) .057 (.554) .060 (.716) .034 (.659) .054 (.752) .060 (.583) .032 (.521) .055 (.456) .035 (.383) .069 (.461) .070 (.571) .049 (.552) .077 (.550) .263 .057 .163 .048 .403 .372 .020 .349 (.561) .293 (.489) .054 (.184) .043 (.142) .097 (.208) .116 (.107) .014 (.061) .044 (.029) .461 (.637) .471 (.699) .491 (.688) .477 (.710) .144 (.297) .104 (.337) .153 (.254) .172 (.324) TABLE 4 TESTS Mood X2 .070 (.247) Mood F .091 (.296) Mood:med X2 .002 (.033) Mood:med F .009 (.063) F-A-B X2 .070 (.193) F-A-B F .094 (.240) F-A-B:med X2 .000 (.000) F-A-B:med F .000 (.000) Klotz X2 .057 (.265) Klotz F .078 (.311) Klotz:med X2 .011 (.078) Klotz:med F .015 (.104) S-R X2 .060 (.248) S-R F .093 (.296) S-R:med X2 .000 (.015) S-R:med F .003 (.038) F-K X2 .044 (.248) F-K F .061 (.296) F-K:med X2 .004 (.058) F-K:med F .009 (.081) T-G X2 .068 (.203) T-G F .089 (.247) T-G:med X2 .000 (.000) T-G:med F .000 (.000) TECHNOMETRICS ?, VOL. 23, NO. 4, NOVEMBER 1981 N-P N-P:med Bar Bar:med Coch Coch:med Hart Hart: med Bar3 Bar3 :med Sam Sam:med Lehl Lehl :med Leh2 Leh2: med Barl Barl:med Bar2 Bar2 :med Schl Schl:med Sch2 Sch2:med Levl Levl:med Lev2 Lev2:med Lev3 Lev4 Lev4:med Mill .069 (.472) .077 (.494) .036 (.342) .041 (.367) .058 (.395) .068 (.415) .034 (.276) .037 (.294) .053 (.526) .064 (.547) .031 (.407) .039 (.424) .062 (.474) .074 (.494) .023 (.332) .029 (.353) .043 (.521) .052 (.540) .018 (.413) .020 (.436) .058 (.397) .067 (.420) .027 (.268) .033 (.288) .060 (.711) .063 (.716) .038 (.657) .038 (.663) .056 (.634) .058 (.643) .029 (.566) .030 (.575) .058 (.772) .062 (.777) .034 (.734) .036 (.740) .057 (.709) .059 (.714) .032 (.658) .035 (.664) .051 (.776) .053 (.782) .033 (.746) .033 (.751) .056 (.636) .059 (.643) .025 (.564) .026 (.573) .066 (.562) .076 (.578) .032 (.491) .036 (.506) .060 (.516) .065 (.532) .040 (.486) .043 (.504) .062 (.538) .072 (.551) .033 (.472) .033 (.490) .060 (.566) .068 (.586) .026 (.491) .032 (.509) .050 (.528) .054 (.544) .030 (.470) .032 (.489) .058 (.525) .065 (.540) .035 (.472) .038 (.491) .215 .317 .059 .094 .269 .380 .033 .065 .152 .222 .050 .084 .228 .322 .054 .092 .127 .174 .034 .054 .305 .418 .027 .053 .752 (.862) .768 (.874) .410 (.577) .433 (.595) .728 (.838) .741 (.852) .395 (.550) .418 (.572) .713 (.841) .741 (.855) .352 (.554) .387 (.574) .613 (.770) .630 (.783) .171 (.322) .183 (.340) .422 (.623) .442 (.646) .066 (.218) .084 (.235) .610 (.753) .621 (.770) .256 (.390) .272 (.413) .684 (.827) .702 (.837) .370 (.623) .381 (.636) .638 (.803) .648 (.811) .340 (.643) .357 (.660) .678 (.802) .704 (.815) .328 (.570) .348 (.588) .589 (.789) .611 (.802) .105 (.347) .119 (.364) .361 (.576) .383 (.596) .052 (.197) .057 (.211) .608 (.809) .623 (.818) .172 (.444) .189 (.458) 357 This content downloaded from 61.190.7.73 on Mon, 30 Sep 2013 22:38:50 PM All use subject to JSTOR Terms and Conditions