appendix tables.pdf

16
227 APPENDIX TABLE A-1 Random numbers A-2 Binomial probabilities A-3 Poisson probabilities A-4a Normal distribution A-4b Laplace function A-5 Values of chi-square A-6 Values of the Student t-distribution A-7 Values of the F-distribution: 10%, 5%, and 1% levels. A-8 Critical values for Duncan's multiple range test A-9a Critical values t (, k - 1, df) to compare control against each of k - 1 other treatments in one-sided Dunnett's tests. A-9b Critical values t (, k - 1, df) to compare control against each of k - 1 other treatments in two-sided Dunnett's tests. A-10 Orthogonal coefficient for trend comparisons A-11 Critical values of correlation coefficient for certain levels (.1, .05, .01 and .001) of significance.

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Page 1: APPENDIX TABLES.pdf

227

APPENDIX TABLE

A-1 Random numbers

A-2 Binomial probabilities

A-3 Poisson probabilities

A-4a Normal distribution

A-4b Laplace function

A-5 Values of chi-square

A-6 Values of the Student t-distribution

A-7 Values of the F-distribution: 10%, 5%, and 1% levels.

A-8 Critical values for Duncan's multiple range test

A-9a Critical values t (, k - 1, df) to compare control against

each of k - 1 other treatments in one-sided Dunnett's tests.

A-9b Critical values t (, k - 1, df) to compare control against

each of k - 1 other treatments in two-sided Dunnett's tests.

A-10 Orthogonal coefficient for trend comparisons

A-11 Critical values of correlation coefficient for certain levels

(.1, .05, .01 and .001) of significance.

Page 2: APPENDIX TABLES.pdf

228

'Table A-1 Random numbers

8 6 6 1 8 4 2 5 3 4 2 5 8 1 4 4 8 9 0 1 5 7 8 0

0 9 4 9 2 7 6 9 3 3 4 8 5 5 9 8 6 6 2 9 4 6 7 2

9 4 5 4 4 9 7 1 7 0 5 6 4 3 5 5 9 7 3 7 2 2 8 3

3 5 2 0 6 7 5 1 3 0 2 8 9 9 3 3 5 9 8 8 7 1 4 5

8 4 7 4 7 1 2 7 2 0 2 2 2 8 3 4 3 4 8 6 7 0 0 1

0 5 0 7 8 0 5 6 7 6 8 5 3 9 9 1 4 0 6 4 5 5 7 5

2 7 9 3 0 2 6 6 2 6 0 8 3 6 6 0 9 6 0 3 3 7 8 3

8 1 0 8 0 2 7 2 8 9 7 4 6 9 4 9 0 5 6 4 4 5 3 7

7 7 2 8 6 0 8 7 8 1 4 4 1 7 1 3 5 9 6 1 6 4 4 1

1 9 6 8 1 2 6 8 3 9 3 5 5 2 8 7 0 9 9 1 1 7 2 2

6 1 8 9 1 7 7 9 4 2 4 5 0 5 6 6 1 2 2 8 8 9 1 2

6 6 3 6 9 2 0 8 9 0 1 9 4 6 1 1 7 8 7 3 5 3 8 9

0 4 7 2 3 1 4 1 6 0 1 9 1 7 5 2 5 1 6 3 3 9 4 3

0 4 0 7 6 9 6 1 0 2 3 0 9 0 4 0 1 2 2 7 4 6 9 9

7 3 5 3 3 7 6 0 1 9 3 0 7 6 0 4 5 3 1 0 8 1 3 1

9 7 7 7 0 9 2 2 0 3 8 4 7 3 3 2 0 9 5 4 8 0 5 1

2 0 6 0 3 5 5 7 4 1 4 6 1 3 0 2 3 3 0 5 1 6 8 5

1 0 3 6 2 6 7 8 5 6 6 6 7 2 5 5 7 0 8 4 3 3 4 0

8 9 2 5 4 5 9 2 7 1 6 3 2 4 7 5 1 2 4 6 7 9 2 7

8 7 2 3 8 5 3 4 4 6 0 7 0 6 6 3 4 2 8 5 1 4 8 9

1 5 2 8 6 6 4 6 3 6 9 0 5 6 2 2 9 2 6 0 2 6 8 0

4 4 8 9 3 9 2 5 5 4 5 9 6 7 8 0 9 8 2 7 8 7 2 7

6 4 2 4 8 9 8 6 3 6 7 2 5 2 0 2 7 3 6 7 0 7 2 5

5 1 6 7 5 6 8 8 7 6 0 0 7 5 7 8 9 8 2 4 6 8 2 4

7 4 1 5 7 8 4 0 8 1 4 8 0 8 9 6 8 6 0 8 3 4 2 6

4 3 4 4 2 3 3 9 8 3 0 9 6 5 0 7 2 8 0 6 5 7 2 4

2 4 4 4 1 4 9 3 6 9 2 8 9 4 4 5 1 5 1 9 6 7 5 7

0 9 5 6 3 5 2 1 0 4 5 8 7 4 0 6 8 4 0 7 6 5 0 5

2 8 4 6 8 7 5 3 4 1 9 4 5 1 5 1 8 8 2 1 0 6 8 7

3 6 7 3 1 9 8 5 1 8 6 0 0 5 5 3 2 4 9 6 6 0 1 2

4 4 5 2 6 1 6 9 6 6 1 7 7 9 3 5 3 8 3 3 7 4 9 3

4 8 4 9 1 1 6 2 7 7 7 3 0 1 7 1 1 5 0 0 8 4 4 2

2 1 6 7 1 2 9 6 3 5 0 6 0 7 7 9 6 3 4 7 7 4 7 9

4 3 0 4 0 5 5 9 0 5 6 4 9 1 3 2 0 3 3 6 4 0 6 5

8 1 4 0 0 7 1 5 9 9 9 8 7 5 0 9 2 9 6 4 8 4 3 8

6 6 5 5 9 5 3 9 6 1 4 0 5 6 0 1 1 8 8 5 0 7 9 3

1 1 0 3 0 9 1 5 1 8 6 1 9 1 6 4 3 0 0 9 8 3 7 5

8 9 6 4 7 6 5 7 1 7 4 0 4 5 6 1 7 5 5 2 8 4 5 7

8 9 7 0 0 2 2 4 4 6 4 8 4 0 9 3 3 7 8 7 7 2 3 6

0 4 4 4 4 0 5 3 3 0 7 4 6 1 3 7 6 8 3 9 7 6 5 6

Page 3: APPENDIX TABLES.pdf

229

'Table A-2 Binomial probabilities [P(r) for values of r]: each value in the table

represents the probability of r occurrences in n trials with single

occurrence probability equal to p.

p

n r .05 .10 .15 .20 .25 .30 .35 .40 .45 .50

1 0 .950 .900 .850 .800 .750 .700 .650 .600 .550 .500

1 1 .050 .100 .150 .200 .250 .300 .350 .400 .450 .500

2 0 .903 .810 .723 .640 .563 .490 .423 .360 .303 .250

2 1 .095 .180 .255 .320 .375 .420 .455 .480 .495 .500

2 2 .003 .010 .023 .040 .063 .090 .123 .160 .203 .250

3 0 .857 .729 .614 .512 .422 .343 .275 .216 .166 .125

3 1 .135 .243 .325 .384 .422 .441 .444 .432 .408 .375

3 2 .007 .027 .057 .096 .141 .189 .239 .288 .334 .375

3 3 .000 .001 .003 .008 .016 .027 .043 .064 .091 .125

4 0 .815 .656 .522 .410 .316 .240 .179 .130 .092 .063

4 1 .171 .292 .368 .410 .422 .412 .384 .346 .299 .250

4 2 .014 .049 .098 .154 .211 .265 .311 .346 .368 .375

4 3 .000 .004 .011 .026 .047 .076 .111 .154 .200 .250

4 4 .000 .000 .001 .002 .004 .008 .015 .026 .041 .063

5 0 .774 .590 .444 .328 .237 .168 .116 .078 .050 .031

5 1 .204 .328 .392 .410 .396 .360 .312 .259 .206 .156

5 2 .021 .073 .138 .205 .264 .309 .336 .346 .337 .313

5 3 .001 .008 .024 .051 .088 .132 .181 .230 .276 .313

5 4 .000 .000 .002 .006 .015 .028 .049 .077 .113 .156

5 5 .000 .000 .000 .000 .001 .002 .005 .010 .018 .031

6 0 .735 .531 .377 .262 .178 .118 .075 .047 .028 .016

6 1 .232 .354 .399 .393 .356 .303 .244 .187 .136 .094

6 2 .031 .098 .176 .246 .297 .324 .328 .311 .278 .234

6 3 .002 .015 .041 .082 .132 .185 .235 .276 .303 .313

6 4 .000 .001 .005 .015 .033 .060 .095 .138 .186 .234

6 5 .000 .000 .000 .002 .004 .010 .020 .037 .061 .094

6 6 .000 .000 .000 .000 .000 .001 .002 .004 .008 .016

7 0 .698 .478 .321 .210 .133 .082 .049 .028 .015 .008

7 1 .257 .372 .396 .367 .311 .247 .185 .131 .087 .055

7 2 .041 .124 .210 .275 .311 .318 .298 .261 .214 .164

7 3 .004 .023 .062 .115 .173 .227 .268 .290 .292 .273

Page 4: APPENDIX TABLES.pdf

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Table A-2 (continued)

p

n r .05 .10 .15 .20 .25 .30 .35 .40 .45 .50

7 4 .000 .003 .011 .029 .058 .097 .144 .194 .239 .273

7 5 .000 .000 .001 .004 .012 .025 .047 .077 .117 .164

7 6 .000 .000 .000 .000 .001 .004 .008 .017 .032 .055

7 7 .000 .000 .000 .000 .000 .000 .001 .002 .004 .008

8 0 .663 .430 .272 .168 .100 .058 .032 .017 .008 .004

8 1 .279 .383 .385 .336 .267 .198 .137 .090 .055 .031

8 2 .051 .149 .238 .294 .311 .296 .259 .209 .157 .109

8 3 .005 .033 .084 .147 .208 .254 .279 .279 .257 .219

8 4 .000 .005 .018 .046 .087 .136 .188 .232 .263 .273

8 5 .000 .000 .003 .009 .023 .047 .081 .124 .172 .219

8 6 .000 .000 .000 .001 .004 .010 .022 .041 .070 .109

8 7 .000 .000 .000 .000 .000 .001 .003 .008 .016 .031

8 8 .000 .000 .000 .000 .000 .000 .000 .001 .002 .004

9 0 .630 .387 .232 .134 .075 .040 .021 .010 .005 .002

9 1 .299 .387 .368 .302 .225 .156 .100 .060 .034 .018

9 2 .063 .172 .260 .302 .300 .267 .216 .161 .111 .070

9 3 .008 .045 .107 .176 .234 .267 .272 .251 .212 .164

9 4 .001 .007 .028 .066 .117 .172 .219 .251 .260 .246

9 5 .000 .001 .005 .017 .039 .074 .118 .167 .213 .246

9 6 .000 .000 .001 .003 .009 .021 .042 .074 .116 .164

9 7 .000 .000 .000 .000 .001 .004 .010 .021 .041 .070

9 8 .000 .000 .000 .000 .000 .000 .001 .004 .008 .018

9 9 .000 .000 .000 .000 .000 .000 .000 .000 .001 .002

10 0 .599 .349 .197 .107 .056 .028 .013 .006 .003 .001

10 1 .315 .387 .347 .268 .188 .121 .072 .040 .021 .010

10 2 .075 .194 .276 .302 .282 .233 .176 .121 .076 .044

10 3 .010 .057 .130 .201 .250 .267 .252 .215 .166 .117

10 4 .001 .011 .040 .088 .146 .200 .238 .251 .238 .205

10 5 .000 .001 .008 .026 .058 .103 .154 .201 .234 .246

10 6 .000 .000 .001 .006 .016 .037 .069 .111 .160 .205

10 7 .000 .000 .000 .001 .003 .009 .021 .042 .075 .117

10 8 .000 .000 .000 .000 .000 .001 .004 .011 .023 .044

10 9 .000 .000 .000 .000 .000 .000 .001 .002 .004 .010

10 10 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001

Page 5: APPENDIX TABLES.pdf

231

Table A-2 (continued)

p n r .05 .10 .15 .20 .25 .30 .35 .40 .45 .50

11 0 .569 .314 .167 .086 .042 .020 .009 .004 .001 .000

11 1 .329 .384 .325 .236 .155 .093 .052 .027 .013 .005

11 2 .087 .213 .287 .295 .258 .200 .140 .089 .051 .027

11 3 .014 .071 .152 .221 .258 .257 .225 .177 .126 .081

11 4 .001 .016 .054 .111 .172 .220 .243 .236 .206 .161

11 5 .000 .002 .013 .039 .080 .132 .183 .221 .236 .226

11 6 .000 .000 .002 .010 .027 .057 .099 .147 .193 .226

11 7 .000 .000 .000 .002 .006 .017 .038 .070 .113 .161

11 8 .000 .000 .000 .000 .001 .004 .010 .023 .046 .081

11 9 .000 .000 .000 .000 .000 .001 .002 .005 .013 .027

11 10 .000 .000 .000 .000 .000 .000 .000 .001 .002 .005

11 11 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

12 0 .540 .282 .142 .069 .032 .014 .006 .002 .001 .000

12 1 .341 .377 .301 .206 .127 .071 .037 .017 .008 .003

12 2 .099 .230 .292 .283 .232 .168 .109 .064 .034 .016

12 3 .017 .085 .172 .236 .258 .240 .195 .142 .092 .054

12 4 .002 .021 .068 .133 .194 .231 .237 .213 .170 .121

12 5 .000 .004 .019 .053 .103 .158 .204 .227 .222 .193

12 6 .000 .000 .004 .016 .040 .079 .128 .177 .212 .226

12 7 .000 .000 .001 .003 .011 .029 .059 .101 .149 .193

12 8 .000 .000 .000 .001 .002 .008 .020 .042 .076 .121

12 9 .000 .000 .000 .000 .000 .001 .005 .012 .028 .054

12 10 .000 .000 .000 .000 .000 .000 .001 .002 .007 .016

12 11 .000 .000 .000 .000 .000 .000 .000 .000 .001 .003

12 12 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

13 0 .513 .254 .121 .055 .024 .010 .004 .001 .000 .000

13 1 .351 .367 .277 .179 .103 .054 .026 .011 .004 .002

13 2 .111 .245 .294 .268 .206 .139 .084 .045 .022 .010

13 3 .021 .100 .190 .246 .252 .218 .165 .111 .066 .035

13 4 .003 .028 .084 .154 .210 .234 .222 .184 .135 .087

13 5 .000 .006 .027 .069 .126 .180 .215 .221 .199 .157

13 6 .000 .001 .006 .023 .056 .103 .155 .197 .217 .209

13 7 .000 .000 .001 .006 .019 .044 .083 .131 .177 .209

13 8 .000 .000 .000 .001 .005 .014 .034 .066 .109 .157

13 9 .000 .000 .000 .000 .001 .003 .010 .024 .050 .087

13 10 .000 .000 .000 .000 .000 .001 .002 .006 .016 .035

Page 6: APPENDIX TABLES.pdf

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Table A-2 (continued)

p n r .05 .10 .15 .20 .25 .30 .35 .40 .45 .50

13 11 .000 .000 .000 .000 .000 .000 .000 .001 .004 .010

13 12 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002

13 13 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

14 0 .488 .229 .103 .044 .018 .007 .002 .001 .000 .000

14 1 .359 .356 .254 .154 .083 .041 .018 .007 .003 .001

14 2 .123 .257 .291 .250 .180 .113 .063 .032 .014 .006

14 3 .026 .114 .206 .250 .240 .194 .137 .085 .046 .022

14 4 .004 .035 .100 .172 .220 .229 .202 .155 .104 .061

14 5 .000 .008 .035 .086 .147 .196 .218 .207 .170 .122

14 6 .000 .001 .009 .032 .073 .126 .176 .207 .209 .183

14 7 .000 .000 .002 .009 .028 .062 .108 .157 .195 .209

14 8 .000 .000 .000 .002 .008 .023 .051 .092 .140 .183

14 9 .000 .000 .000 .000 .002 .007 .018 .041 .076 .122

14 10 .000 .000 .000 .000 .000 .001 .005 .014 .031 .061

14 11 .000 .000 .000 .000 .000 .000 .001 .003 .009 .022

14 12 .000 .000 .000 .000 .000 .000 .000 .001 .002 .006

14 13 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001

14 14 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

15 0 .463 .206 .087 .035 .013 .005 .002 .000 .000 .000

15 1 .366 .343 .231 .132 .067 .031 .013 .005 .002 .000

15 2 .135 .267 .286 .231 .156 .092 .048 .022 .009 .003

15 3 .031 .129 .218 .250 .225 .170 .111 .063 .032 .014

15 4 .005 .043 .116 .188 .225 .219 .179 .127 .078 .042

15 5 .001 .010 .045 .103 .165 .206 .212 .186 .140 .092

15 6 .000 .002 .013 .043 .092 .147 .191 .207 .191 .153

15 7 .000 .000 .003 .014 .039 .081 .132 .177 .201 .196

15 8 .000 .000 .001 .003 .013 .035 .071 .118 .165 .196

15 9 .000 .000 .000 .001 .003 .012 .030 .061 .105 .153

15 10 .000 .000 .000 .000 .001 .003 .010 .024 .051 .092

15 11 .000 .000 .000 .000 .000 .001 .002 .007 .019 .042

15 12 .000 .000 .000 .000 .000 .000 .000 .002 .005 .014

15 13 .000 .000 .000 .000 .000 .000 .000 .000 .001 .003

15 14 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

15 15 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

Page 7: APPENDIX TABLES.pdf

233

'Table A-3 Poisson Probabilities. Each number in this table represents the

probability of obtaining at least [P(r x) for x = 1, 2, . . . ] for selected

mean values of . This probability is indicated as the shaded area of the

histogram.

mu 1 2 3 4 5 6 7 8 9 10 11 12

0.1 .095 .005

0.2 .181 .018 .001

0.3 .259 .037 .004

0.4 .330 .062 .008

0.5 .393 .090 .014 .002

0.6 .451 .122 .023 .003

0.7 .503 .156 .034 .006

0.8 .551 .191 .047 .009 .001

0.9 .593 .228 .063 .013 .002

1.0 .632 .264 .080 .019 .004

1.1 .667 .301 .100 .026 .005

1.2 .699 .337 .121 .034 .008 .002

1.3 .727 .373 .143 .043 .011 .002

1.4 .753 .408 .167 .054 .014 .003

1.5 .777 .442 .191 .066 .019 .004

1.6 .798 .475 .217 .079 .024 .006 .001

1.7 .817 .507 .243 .093 .030 .008 .002

1.8 .835 .537 .269 .109 .036 .010 .003

1.9 .850 .566 .296 .125 .044 .013 .003

2.0 .865 .594 .323 .143 .053 .017 .005 .001

2.5 .918 .713 .456 .242 .109 .042 .014 .004 .001

3.0 .950 .801 .577 .353 .185 .084 .034 .012 .004 .001

3.5 .970 .864 .679 .463 .275 .142 .065 .027 .010 .003 .001

4.0 .982 .908 .762 .567 .371 .215 .111 .051 .021 .008 .003

4.5 .989 .939 .826 .658 .468 .297 .169 .087 .040 .017 .007 .002

5.0 .993 .960 .875 .735 .560 .384 .238 .133 .068 .032 .014 .005

5.5 .996 .973 .912 .798 .642 .471 .314 .191 .106 .054 .025 .011

6.0 .998 .983 .938 .849 .715 .554 .394 .256 .153 .084 .043 .020

Page 8: APPENDIX TABLES.pdf

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'Table A-4a. Normal Distribution. This table contains the cumulative probabilities

exceeding the z-values under the right-hand side of a normal

distribution curve. The z-values are shown in the first column up to

one digit after the decimal point, and in the top row for the second

digit after the decimal point.

x .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

.0 .500 .496 .492 .488 .484 .480 .476 .472 .468 .464

.1 .460 .456 .452 .448 .444 .440 .436 .433 .429 .425

.2 .421 .417 .413 .409 .405 .401 .397 .394 .390 .386

.3 .382 .378 .374 .371 .367 .363 .359 .356 .352 .348

.4 .345 .341 .337 .334 .330 .326 .323 .319 .316 .312

.5 .309 .305 .302 .298 .295 .291 .288 .284 .281 .278

.6 .274 .271 .268 .264 .261 .258 .255 .251 .248 .245

.7 .242 .239 .236 .233 .230 .227 .224 .221 .218 .215

.8 .212 .209 .206 .203 .200 .198 .195 .192 .189 .187

.9 .184 .181 .179 .176 .174 .171 .169 .166 .164 .161

1.0 .159 .156 .154 .152 .149 .147 .145 .142 .140 .138

1.1 .136 .133 .131 .129 .127 .125 .123 .121 .119 .117

1.2 .115 .113 .111 .109 .107 .106 .104 .102 .100 .099

1.3 .097 .095 .093 .092 .090 .089 .087 .085 .084 .082

1.4 .081 .079 .078 .076 .075 .074 .072 .071 .069 .068

1.5 .067 .066 .064 .063 .062 .061 .059 .058 .057 .056

1.6 .055 .054 .053 .052 .051 .049 .048 .047 .046 .046

1.7 .045 .044 .043 .042 .041 .040 .039 .038 .038 .037

1.8 .036 .035 .034 .034 .033 .032 .031 .031 .030 .029

1.9 .029 .028 .027 .027 .026 .026 .025 .024 .024 .023

2.0 .023 .022 .022 .021 .021 .020 .020 .019 .019 .018

2.1 .018 .017 .017 .017 .016 .016 .015 .015 .015 .014

2.2 .014 .014 .013 .013 .013 .012 .012 .012 .011 .011

2.3 .011 .010 .010 .010 .010 .009 .009 .009 .009 .008

2.4 .008 .008 .008 .008 .007 .007 .007 .007 .007 .006

2.5 .006 .006 .006 .006 .006 .005 .005 .005 .005 .005

2.6 .005 .005 .004 .004 .004 .004 .004 .004 .004 .004

2.7 .003 .003 .003 .003 .003 .003 .003 .003 .003 .003

2.8 .003 .002 .002 .002 .002 .002 .002 .002 .002 .002

2.9 .002 .002 .002 .002 .002 .002 .002 .001 .001 .001

3.0 .001 .001 .001 .001 .001 .001 .001 .001 .001 .001

3.1 .001 .001 .001 .001 .001 .001 .001 .001 .001 .001

3.2 .001 .001 .001 .001 .001 .001 .001 .001 .001 .001

3.3 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

Page 9: APPENDIX TABLES.pdf

235

'Table A-4b. AREA (Z) UNDER THE STANDARD NORMAL CURVE

.00 .01 .02 .03 .04 .05 .06 .07 .08 .09

.0 .500 .504 .508 .512 .516 .520 .524 .528 .532 .536

.1 .540 .544 .548 .552 .556 .560 .564 .567 .571 .575

.2 .579 .583 .587 .591 .595 .599 .603 .606 .610 .614

.3 .618 .622 .626 .629 .633 .637 .641 .644 .648 .652

.4 .655 .659 .663 .666 .670 .674 .677 .681 .684 .688

.5 .691 .695 .698 .702 .705 .709 .712 .716 .719 .722

.6 .726 .729 .732 .736 .739 .742 .745 .749 .752 .755

.7 .758 .761 .764 .767 .770 .773 .776 .779 .782 .785

.8 .788 .791 .794 .797 .800 .802 .805 .808 .811 .813

.9 .816 .819 .821 .824 .826 .829 .831 .834 .836 .839

1.0 .841 .844 .846 .848 .851 .853 .855 .858 .860 .862

1.1 .864 .867 .869 .871 .873 .875 .877 .879 .881 .883

1.2 .885 .887 .889 .891 .893 .894 .896 .898 .900 .901

1.3 .903 .905 .907 .908 .910 .911 .913 .915 .916 .918

1.4 .919 .921 .922 .924 .925 .926 .928 .929 .931 .932

1.5 .933 .934 .936 .937 .938 .939 .941 .942 .943 .944

1.6 .945 .946 .947 .948 .949 .951 .952 .953 .954 .954

1.7 .955 .956 .957 .958 .959 .960 .961 .962 .962 .963

1.8 .964 .965 .966 .966 .967 .968 .969 .969 .970 .971

1.9 .971 .972 .973 .973 .974 .974 .975 .976 .976 .977

2.0 .977 .978 .978 .979 .979 .980 .980 .981 .981 .982

2.1 .982 .983 .983 .983 .984 .984 .985 .985 .985 .986

2.2 .986 .986 .987 .987 .987 .988 .988 .988 .989 .989

2.3 .989 .990 .990 .990 .990 .991 .991 .991 .991 .992

2.4 .992 .992 .992 .992 .993 .993 .993 .993 .993 .994

2.5 .994 .994 .994 .994 .994 .995 .995 .995 .995 .995

2.6 .995 .995 .996 .996 .996 .996 .996 .996 .996 .996

2.7 .997 .997 .997 .997 .997 .997 .997 .997 .997 .997

2.8 .997 .998 .998 .998 .998 .998 .998 .998 .998 .998

2.9 .998 .998 .998 .998 .998 .998 .998 .999 .999 .999

3.0 .999 .999 .999 .999 .999 .999 .999 .999 .999 .999

3.1 .999 .999 .999 .999 .999 .999 .999 .999 .999 .999

3.2 .999 .999 .999 .999 .999 .999 .999 .999 .999 .999

3.3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Page 10: APPENDIX TABLES.pdf

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'Table A-5 Values of Chi-squares. This table is used to find values of

chi-square corresponding to selected probabilities. Each

number in this table is chi-square value for an indicated

degree of freedom (left column). Each number (i.e., .99,

.95, ...) in the top row of the table represents a probability of

obtaining a value as large of larger than the corresponding

chi-square value in the table.

df Probability of obtaining a value as large or larger

0.99 0.95 0.90 0.50 0.10 0.05 0.01 0.001

1 0.000 0.004 0.016 0.455 2.706 3.841 6.635 10.828

2 0.020 0.103 0.211 1.386 4.605 5.991 9.210 13.816

3 0.115 0.352 0.584 2.366 6.251 7.815 11.345 16.266

4 0.297 0.711 1.064 3.357 7.779 9.488 13.277 18.467

5 0.554 1.145 1.610 4.351 9.236 11.070 15.086 20.515

6 0.872 1.635 2.204 5.348 10.645 12.592 16.812 22.458

7 1.239 2.167 2.833 6.346 12.017 14.067 18.475 24.322

8 1.646 2.733 3.490 7.344 13.362 15.507 20.090 26.124

9 2.088 3.325 4.168 8.343 14.684 16.919 21.666 27.877

10 2.558 3.940 4.865 9.342 15.987 18.307 23.209 29.588

11 3.053 4.575 5.578 10.341 17.275 19.675 24.725 31.264

12 3.571 5.226 6.304 11.340 18.549 21.026 26.217 32.909

13 4.107 5.892 7.042 12.340 19.812 22.362 27.688 34.528

14 4.660 6.571 7.790 13.339 21.064 23.685 29.141 36.123

15 5.229 7.261 8.547 14.339 22.307 24.996 30.578 37.697

16 5.812 7.962 9.312 15.338 23.542 26.296 32.000 39.252

17 6.408 8.672 10.085 16.338 24.769 27.587 33.409 40.790

18 7.015 9.390 10.865 17.338 25.989 28.869 34.805 42.312

19 7.633 10.117 11.651 18.338 27.204 30.144 36.191 43.820

20 8.260 10.851 12.443 19.337 28.412 31.410 37.566 45.315

21 8.897 11.591 13.240 20.337 29.615 32.671 38.932 46.797

22 9.542 12.338 14.041 21.337 30.813 33.924 40.289 48.268

23 10.196 13.091 14.848 22.337 32.007 35.172 41.638 49.728

24 10.856 13.848 15.659 23.337 33.196 36.415 42.980 51.179

25 11.524 14.611 16.473 24.337 34.382 37.652 44.314 52.620

26 12.198 15.379 17.292 25.336 35.563 38.885 45.642 54.052

27 12.879 16.151 18.114 26.336 36.741 40.113 46.963 55.476

28 13.565 16.928 18.939 27.336 37.916 41.337 48.278 56.892

29 14.256 17.708 19.768 28.336 39.087 42.557 49.588 58.301

30 14.953 18.493 20.599 29.336 40.256 43.773 50.892 59.703

Page 11: APPENDIX TABLES.pdf

237

'Table A-6 Values of the Student t-distribution. The values in this table

are Student t-values which correspond to the indicated

cumulative probabilities (on the right-hand side under a t-

distribution curve) and to the indicated degrees of freedom.

df Probability of obtaining a larger value of t

0.25 0.20 0.15 0.10 0.05 0.025 0.01 0.005 0.001

1 1.000 1.376 1.963 3.078 6.314 12.706 31.821 63.657 636.62

2 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 31.599

3 0.765 0.978 1.250 1.638 2.353 3.182 4.541 5.841 12.924

4 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.604 8.610

5 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032 6.869

6 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.959

7 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 5.408

8 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355 5.041

9 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.781

10 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 4.587

11 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 4.437

12 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 4.318

13 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012 4.221

14 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 4.140

15 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 4.073

16 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.921 4.015

17 0.689 0.863 1.069 1.333 1.740 2.110 2.567 2.898 3.965

18 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878 3.922

19 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.883

20 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845 3.850

21 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 3.819

22 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.792

23 0.685 0.858 1.060 1.319 1.714 2.069 2.500 2.807 3.768

24 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.745

25 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 3.725

26 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.707

27 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 3.690

28 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 3.674

29 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756 3.659

30 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750 3.646

40 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.704 3.551

0.675 0.842 1.036 1.282 1.645 1.960 2.327 2.576 3.291

Page 12: APPENDIX TABLES.pdf

238

'Table A-7 Values of the F-Distribution - 10%, 5% and 1% level. This

table is used to find F-values at three probability levels (.10,

.05, .01) in the right tail of the F-distribution.

df for nume

degrees of freedom for denominator

1 1 1 2 2 2 3 3 3

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 39.86 161 4,052 8.53 18.51 98.50 5.54 10.13 34.12

2 49.50 199 4,999 9.00 19.00 99.00 5.46 9.55 30.82

3 53.59 216 5,403 9.16 19.16 99.17 5.39 9.28 29.46

4 55.83 225 5,625 9.24 19.25 99.25 5.34 9.12 28.71

5 57.24 230 5,764 9.29 19.30 99.30 5.31 9.01 28.24

6 58.20 234 5,859 9.33 19.33 99.33 5.28 8.94 27.91

7 58.91 237 5,928 9.35 19.35 99.36 5.27 8.89 27.67

8 59.44 239 5,981 9.37 19.37 99.37 5.25 8.85 27.49

9 59.86 241 6,022 9.38 19.38 99.39 5.24 8.81 27.35

10 60.19 242 6,056 9.39 19.40 99.40 5.23 8.79 27.23

12 60.71 244 6,106 9.41 19.41 99.42 5.22 8.74 27.05

14 61.07 245 6,143 9.42 19.42 99.43 5.20 8.71 26.92

16 61.35 246 6,170 9.43 19.43 99.44 5.20 8.69 26.83

18 61.57 247 6,192 9.44 19.44 99.44 5.19 8.67 26.75

.

df for nume

degrees of freedom for denominator

4 4 4 5 5 5 6 6 6

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 4.54 7.71 21.20 4.06 6.61 16.26 3.78 5.99 13.75

2 4.32 6.94 18.00 3.78 5.79 13.27 3.46 5.14 10.92

3 4.19 6.59 16.69 3.62 5.41 12.06 3.29 4.76 9.78

4 4.11 6.39 15.98 3.52 5.19 11.39 3.18 4.53 9.15

5 4.05 6.26 15.52 3.45 5.05 10.97 3.11 4.39 8.75

6 4.01 6.16 15.21 3.40 4.95 10.67 3.05 4.28 8.47

7 3.98 6.09 14.98 3.37 4.88 10.46 3.01 4.21 8.26

8 3.95 6.04 14.80 3.34 4.82 10.29 2.98 4.15 8.10

9 3.94 6.00 14.66 3.32 4.77 10.16 2.96 4.10 7.98

10 3.92 5.96 14.55 3.30 4.74 10.05 2.94 4.06 7.87

12 3.90 5.91 14.37 3.27 4.68 9.89 2.90 4.00 7.72

14 3.88 5.87 14.25 3.25 4.64 9.77 2.88 3.96 7.60

16 3.86 5.84 14.15 3.23 4.60 9.68 2.86 3.92 7.52

18 3.85 5.82 14.08 3.22 4.58 9.61 2.85 3.90 7.45

Page 13: APPENDIX TABLES.pdf

239

Table A-7 (continued)

df for nume

degrees of freedom for denominator

7 7 7 8 8 8 9 9 9

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 3.59 5.59 12.25 3.46 5.32 11.26 3.36 5.12 10.56

2 3.26 4.74 9.55 3.11 4.46 8.65 3.01 4.26 8.02

3 3.07 4.35 8.45 2.92 4.07 7.59 2.81 3.86 6.99

4 2.96 4.12 7.85 2.81 3.84 7.01 2.69 3.63 6.42

5 2.88 3.97 7.46 2.73 3.69 6.63 2.61 3.48 6.06

6 2.83 3.87 7.19 2.67 3.58 6.37 2.55 3.37 5.80

7 2.78 3.79 6.99 2.62 3.50 6.18 2.51 3.29 5.61

8 2.75 3.73 6.84 2.59 3.44 6.03 2.47 3.23 5.47

9 2.72 3.68 6.72 2.56 3.39 5.91 2.44 3.18 5.35

10 2.70 3.64 6.62 2.54 3.35 5.81 2.42 3.14 5.26

12 2.67 3.57 6.47 2.50 3.28 5.67 2.38 3.07 5.11

14 2.64 3.53 6.36 2.48 3.24 5.56 2.35 3.03 5.01

16 2.62 3.49 6.28 2.45 3.20 5.48 2.33 2.99 4.92

18 2.61 3.47 6.21 2.44 3.17 5.41 2.31 2.96 4.86

.

df for nume

degrees of freedom for denominator

10 10 10 11 11 11 12 12 12

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 3.29 4.96 10.04 3.23 4.84 9.65 3.18 4.75 9.33

2 2.92 4.10 7.56 2.86 3.98 7.21 2.81 3.89 6.93

3 2.73 3.71 6.55 2.66 3.59 6.22 2.61 3.49 5.95

4 2.61 3.48 5.99 2.54 3.36 5.67 2.48 3.26 5.41

5 2.52 3.33 5.64 2.45 3.20 5.32 2.39 3.11 5.06

6 2.46 3.22 5.39 2.39 3.09 5.07 2.33 3.00 4.82

7 2.41 3.14 5.20 2.34 3.01 4.89 2.28 2.91 4.64

8 2.38 3.07 5.06 2.30 2.95 4.74 2.24 2.85 4.50

9 2.35 3.02 4.94 2.27 2.90 4.63 2.21 2.80 4.39

10 2.32 2.98 4.85 2.25 2.85 4.54 2.19 2.75 4.30

12 2.28 2.91 4.71 2.21 2.79 4.40 2.15 2.69 4.16

14 2.26 2.86 4.60 2.18 2.74 4.29 2.12 2.64 4.05

16 2.23 2.83 4.52 2.16 2.70 4.21 2.09 2.60 3.97

18 2.22 2.80 4.46 2.14 2.67 4.15 2.08 2.57 3.91

Page 14: APPENDIX TABLES.pdf

240

Table A-7 (continued)

df for nume

degrees of freedom for denominator

13 13 13 14 14 14 15 15 15

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 3.14 4.67 9.07 3.10 4.60 8.86 3.07 4.54 8.68

2 2.76 3.81 6.70 2.73 3.74 6.51 2.70 3.68 6.36

3 2.56 3.41 5.74 2.52 3.34 5.56 2.49 3.29 5.42

4 2.43 3.18 5.21 2.39 3.11 5.04 2.36 3.06 4.89

5 2.35 3.03 4.86 2.31 2.96 4.69 2.27 2.90 4.56

6 2.28 2.92 4.62 2.24 2.85 4.46 2.21 2.79 4.32

7 2.23 2.83 4.44 2.19 2.76 4.28 2.16 2.71 4.14

8 2.20 2.77 4.30 2.15 2.70 4.14 2.12 2.64 4.00

9 2.16 2.71 4.19 2.12 2.65 4.03 2.09 2.59 3.89

10 2.14 2.67 4.10 2.10 2.60 3.94 2.06 2.54 3.80

12 2.10 2.60 3.96 2.05 2.53 3.80 2.02 2.48 3.67

14 2.07 2.55 3.86 2.02 2.48 3.70 1.99 2.42 3.56

16 2.04 2.51 3.78 2.00 2.44 3.62 1.96 2.38 3.49

18 2.02 2.48 3.72 1.98 2.41 3.56 1.94 2.35 3.42

.

df for nume

degrees of freedom for denominator

16 16 16 17 17 17 18 18 18

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 3.05 4.49 8.53 3.03 4.45 8.40 3.01 4.41 8.29

2 2.67 3.63 6.23 2.64 3.59 6.11 2.62 3.55 6.01

3 2.46 3.24 5.29 2.44 3.20 5.18 2.42 3.16 5.09

4 2.33 3.01 4.77 2.31 2.96 4.67 2.29 2.93 4.58

5 2.24 2.85 4.44 2.22 2.81 4.34 2.20 2.77 4.25

6 2.18 2.74 4.20 2.15 2.70 4.10 2.13 2.66 4.01

7 2.13 2.66 4.03 2.10 2.61 3.93 2.08 2.58 3.84

8 2.09 2.59 3.89 2.06 2.55 3.79 2.04 2.51 3.71

9 2.06 2.54 3.78 2.03 2.49 3.68 2.00 2.46 3.60

10 2.03 2.49 3.69 2.00 2.45 3.59 1.98 2.41 3.51

12 1.99 2.42 3.55 1.96 2.38 3.46 1.93 2.34 3.37

14 1.95 2.37 3.45 1.93 2.33 3.35 1.90 2.29 3.27

16 1.93 2.33 3.37 1.90 2.29 3.27 1.87 2.25 3.19

18 1.91 2.30 3.31 1.88 2.26 3.21 1.85 2.22 3.13

Page 15: APPENDIX TABLES.pdf

241

Table A-7 (continued)

df for nume

degrees of freedom for denominator

20 20 20 22 22 22 24 24 24

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 2.97 4.35 8.10 2.95 4.30 7.95 2.93 4.26 7.82

2 2.59 3.49 5.85 2.56 3.44 5.72 2.54 3.40 5.61

3 2.38 3.10 4.94 2.35 3.05 4.82 2.33 3.01 4.72

4 2.25 2.87 4.43 2.22 2.82 4.31 2.19 2.78 4.22

5 2.16 2.71 4.10 2.13 2.66 3.99 2.10 2.62 3.90

6 2.09 2.60 3.87 2.06 2.55 3.76 2.04 2.51 3.67

7 2.04 2.51 3.70 2.01 2.46 3.59 1.98 2.42 3.50

8 2.00 2.45 3.56 1.97 2.40 3.45 1.94 2.36 3.36

9 1.96 2.39 3.46 1.93 2.34 3.35 1.91 2.30 3.26

10 1.94 2.35 3.37 1.90 2.30 3.26 1.88 2.25 3.17

12 1.89 2.28 3.23 1.86 2.23 3.12 1.83 2.18 3.03

14 1.86 2.22 3.13 1.83 2.17 3.02 1.80 2.13 2.93

16 1.83 2.18 3.05 1.80 2.13 2.94 1.77 2.09 2.85

18 1.81 2.15 2.99 1.78 2.10 2.88 1.75 2.05 2.79

df for nume

degrees of freedom for denominator

26 26 26 28 28 28 30 30 30

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 2.91 4.23 7.72 2.89 4.20 7.64 2.88 4.17 7.56

2 2.52 3.37 5.53 2.50 3.34 5.45 2.49 3.32 5.39

3 2.31 2.98 4.64 2.29 2.95 4.57 2.28 2.92 4.51

4 2.17 2.74 4.14 2.16 2.71 4.07 2.14 2.69 4.02

5 2.08 2.59 3.82 2.06 2.56 3.75 2.05 2.53 3.70

6 2.01 2.47 3.59 2.00 2.45 3.53 1.98 2.42 3.47

7 1.96 2.39 3.42 1.94 2.36 3.36 1.93 2.33 3.30

8 1.92 2.32 3.29 1.90 2.29 3.23 1.88 2.27 3.17

9 1.88 2.27 3.18 1.87 2.24 3.12 1.85 2.21 3.07

10 1.86 2.22 3.09 1.84 2.19 3.03 1.82 2.16 2.98

12 1.81 2.15 2.96 1.79 2.12 2.90 1.77 2.09 2.84

14 1.77 2.09 2.86 1.75 2.06 2.79 1.74 2.04 2.74

16 1.75 2.05 2.78 1.73 2.02 2.72 1.71 1.99 2.66

18 1.72 2.02 2.72 1.70 1.99 2.65 1.69 1.96 2.60

Page 16: APPENDIX TABLES.pdf

242

Table A-7 (continued)

df for nume

degrees of freedom for denominator

35 35 35 40 40 40 45 45 45

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 2.85 4.12 7.42 2.84 4.08 7.31 2.82 4.06 7.23

2 2.46 3.27 5.27 2.44 3.23 5.18 2.42 3.20 5.11

3 2.25 2.87 4.40 2.23 2.84 4.31 2.21 2.81 4.25

4 2.11 2.64 3.91 2.09 2.61 3.83 2.07 2.58 3.77

5 2.02 2.49 3.59 2.00 2.45 3.51 1.98 2.42 3.45

6 1.95 2.37 3.37 1.93 2.34 3.29 1.91 2.31 3.23

7 1.90 2.29 3.20 1.87 2.25 3.12 1.85 2.22 3.07

8 1.85 2.22 3.07 1.83 2.18 2.99 1.81 2.15 2.94

9 1.82 2.16 2.96 1.79 2.12 2.89 1.77 2.10 2.83

10 1.79 2.11 2.88 1.76 2.08 2.80 1.74 2.05 2.74

12 1.74 2.04 2.74 1.71 2.00 2.66 1.70 1.97 2.61

14 1.70 1.99 2.64 1.68 1.95 2.56 1.66 1.92 2.51

16 1.67 1.94 2.56 1.65 1.90 2.48 1.63 1.87 2.43

18 1.65 1.91 2.50 1.62 1.87 2.42 1.60 1.84 2.36

df for nume

degrees of freedom for denominator

50 50 50 60 60 60

10% 5% 1% 10% 5% 1% 10% 5% 1%

1 2.81 4.03 7.17 2.79 4.00 7.08 2.71 3.84 6.64

2 2.41 3.18 5.06 2.39 3.15 4.98 2.30 3.00 4.61

3 2.20 2.79 4.20 2.18 2.76 4.13 2.08 2.61 3.78

4 2.06 2.56 3.72 2.04 2.53 3.65 1.95 2.37 3.32

5 1.97 2.40 3.41 1.95 2.37 3.34 1.85 2.21 3.02

6 1.90 2.29 3.19 1.87 2.25 3.12 1.77 2.10 2.80

7 1.84 2.20 3.02 1.82 2.17 2.95 1.72 2.01 2.64

8 1.80 2.13 2.89 1.77 2.10 2.82 1.67 1.94 2.51

9 1.76 2.07 2.78 1.74 2.04 2.72 1.63 1.88 2.41

10 1.73 2.03 2.70 1.71 1.99 2.63 1.60 1.83 2.32

12 1.68 1.95 2.56 1.66 1.92 2.50 1.55 1.75 2.19

14 1.64 1.89 2.46 1.62 1.86 2.39 1.51 1.69 2.08

16 1.61 1.85 2.38 1.59 1.82 2.31 1.47 1.64 2.00

18 1.59 1.81 2.32 1.56 1.78 2.25 1.44 1.60 1.94