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Statistical Tables
Table A.1 A Binomial Probability Table
Table A.2 A Poisson Probability Table
Table A.3 A Table of Areas under the Standard Normal Curve
Table A.4 A Table of Cumulative Areas under the Standard Normal Curve
Table A.5 A t Table: Values of taTable A.6 An F Table: Values of F0.10
Table A.7 An F Table: Values of F0.05
Table A.8 An F Table: Values of F0.025
Table A.9 An F Table: Values of F0.01
Table A.10 A Table of Percentage Points of the Studentized Range
Table A.11 A Table of Critical Values of r
Table A.12 A Table of Critical Values for the Durbin–Watson d Statistic (a 5 0.05)
Table A.13 A Table of Critical Values for the Durbin–Watson d Statistic (a 5 0.025)
Table A.14 A Table of Critical Values for the Durbin–Watson d Statistic (a 5 0.01)
Table A.15 A Wilcoxon Rank Sum Table: Values of TL and TU
Table A.16 A Wilcoxon Signed Ranks Table: Values of T0
Table A.17 A Table of Critical Values for Spearman’s Rank Correlation Coeffi cient
Table A.18 A Chi-Square Table: Values of x2a
APPENDIX A
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AP-2 Appendix A Statistical Tables
TABLE A.1 A Binomial Probability Table: Binomial Probabilities (n between 2 and 6)
n 5 2 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.9025 0.8100 0.7225 0.6400 0.5625 0.4900 0.4225 0.3600 0.3025 0.2500 21 0.0950 0.1800 0.2550 0.3200 0.3750 0.4200 0.4550 0.4800 0.4950 0.5000 12 0.0025 0.0100 0.0225 0.0400 0.0625 0.0900 0.1225 0.1600 0.2025 0.2500 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
n 5 3 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.8574 0.7290 0.6141 0.5120 0.4219 0.3430 0.2746 0.2160 0.1664 0.1250 31 0.1354 0.2430 0.3251 0.3840 0.4219 0.4410 0.4436 0.4320 0.4084 0.3750 22 0.0071 0.0270 0.0574 0.0960 0.1406 0.1890 0.2389 0.2880 0.3341 0.3750 13 0.0001 0.0010 0.0034 0.0080 0.0156 0.0270 0.0429 0.0640 0.0911 0.1250 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
n 5 4 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.8145 0.6561 0.5220 0.4096 0.3164 0.2401 0.1785 0.1296 0.0915 0.0625 41 0.1715 0.2916 0.3685 0.4096 0.4219 0.4116 0.3845 0.3456 0.2995 0.2500 32 0.0135 0.0486 0.0975 0.1536 0.2109 0.2646 0.3105 0.3456 0.3675 0.3750 23 0.0005 0.0036 0.0115 0.0256 0.0469 0.0756 0.1115 0.1536 0.2005 0.2500 14 0.0000 0.0001 0.0005 0.0016 0.0039 0.0081 0.0150 0.0256 0.0410 0.0625 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
n 5 5 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.7738 0.5905 0.4437 0.3277 0.2373 0.1681 0.1160 0.0778 0.0503 0.0313 51 0.2036 0.3281 0.3915 0.4096 0.3955 0.3602 0.3124 0.2592 0.2059 0.1563 42 0.0214 0.0729 0.1382 0.2048 0.2637 0.3087 0.3364 0.3456 0.3369 0.3125 33 0.0011 0.0081 0.0244 0.0512 0.0879 0.1323 0.1811 0.2304 0.2757 0.3125 24 0.0000 0.0005 0.0022 0.0064 0.0146 0.0284 0.0488 0.0768 0.1128 0.1563 15 0.0000 0.0000 0.0001 0.0003 0.0010 0.0024 0.0053 0.0102 0.0185 0.0313 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
n 5 6 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.7351 0.5314 0.3771 0.2621 0.1780 0.1176 0.0754 0.0467 0.0277 0.0156 61 0.2321 0.3543 0.3993 0.3932 0.3560 0.3025 0.2437 0.1866 0.1359 0.0938 52 0.0305 0.0984 0.1762 0.2458 0.2966 0.3241 0.3280 0.3110 0.2780 0.2344 43 0.0021 0.0146 0.0415 0.0819 0.1318 0.1852 0.2355 0.2765 0.3032 0.3125 34 0.0001 0.0012 0.0055 0.0154 0.0330 0.0595 0.0951 0.1382 0.1861 0.2344 25 0.0000 0.0001 0.0004 0.0015 0.0044 0.0102 0.0205 0.0369 0.0609 0.0938 16 0.0000 0.0000 0.0000 0.0001 0.0002 0.0007 0.0018 0.0041 0.0083 0.0156 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
(table continued)
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Appendix A Statistical Tables AP-3
TABLE A.1 (continued) Binomial Probabilities (n between 7 and 10)
n 5 7 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.6983 0.4783 0.3206 0.2097 0.1335 0.0824 0.0490 0.0280 0.0152 0.0078 7 1 0.2573 0.3720 0.3960 0.3670 0.3115 0.2471 0.1848 0.1306 0.0872 0.0547 6 2 0.0406 0.1240 0.2097 0.2753 0.3115 0.3177 0.2985 0.2613 0.2140 0.1641 5 3 0.0036 0.0230 0.0617 0.1147 0.1730 0.2269 0.2679 0.2903 0.2918 0.2734 4 4 0.0002 0.0026 0.0109 0.0287 0.0577 0.0972 0.1442 0.1935 0.2388 0.2734 3 5 0.0000 0.0002 0.0012 0.0043 0.0115 0.0250 0.0466 0.0774 0.1172 0.1641 2 6 0.0000 0.0000 0.0001 0.0004 0.0013 0.0036 0.0084 0.0172 0.0320 0.0547 1 7 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0006 0.0016 0.0037 0.0078 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
n 5 8 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.6634 0.4305 0.2725 0.1678 0.1001 0.0576 0.0319 0.0168 0.0084 0.0039 8 1 0.2793 0.3826 0.3847 0.3355 0.2670 0.1977 0.1373 0.0896 0.0548 0.0313 7 2 0.0515 0.1488 0.2376 0.2936 0.3115 0.2965 0.2587 0.2090 0.1569 0.1094 6 3 0.0054 0.0331 0.0839 0.1468 0.2076 0.2541 0.2786 0.2787 0.2568 0.2188 5 4 0.0004 0.0046 0.0185 0.0459 0.0865 0.1361 0.1875 0.2322 0.2627 0.2734 4 5 0.0000 0.0004 0.0026 0.0092 0.0231 0.0467 0.0808 0.1239 0.1719 0.2188 3 6 0.0000 0.0000 0.0002 0.0011 0.0038 0.0100 0.0217 0.0413 0.0703 0.1094 2 7 0.0000 0.0000 0.0000 0.0001 0.0004 0.0012 0.0033 0.0079 0.0164 0.0313 1 8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0007 0.0017 0.0039 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
n 5 9 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.6302 0.3874 0.2316 0.1342 0.0751 0.0404 0.0207 0.0101 0.0046 0.0020 9 1 0.2985 0.3874 0.3679 0.3020 0.2253 0.1556 0.1004 0.0605 0.0339 0.0176 8 2 0.0629 0.1722 0.2597 0.3020 0.3003 0.2668 0.2162 0.1612 0.1110 0.0703 7 3 0.0077 0.0446 0.1069 0.1762 0.2336 0.2668 0.2716 0.2508 0.2119 0.1641 6 4 0.0006 0.0074 0.0283 0.0661 0.1168 0.1715 0.2194 0.2508 0.2600 0.2461 5 5 0.0000 0.0008 0.0050 0.0165 0.0389 0.0735 0.1181 0.1672 0.2128 0.2461 4 6 0.0000 0.0001 0.0006 0.0028 0.0087 0.0210 0.0424 0.0743 0.1160 0.1641 3 7 0.0000 0.0000 0.0000 0.0003 0.0012 0.0039 0.0098 0.0212 0.0407 0.0703 2 8 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0013 0.0035 0.0083 0.0176 1 9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0008 0.0020 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
n 5 10 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.5987 0.3487 0.1969 0.1074 0.0563 0.0282 0.0135 0.0060 0.0025 0.0010 10 1 0.3151 0.3874 0.3474 0.2684 0.1877 0.1211 0.0725 0.0403 0.0207 0.0098 9 2 0.0746 0.1937 0.2759 0.3020 0.2816 0.2335 0.1757 0.1209 0.0763 0.0439 8 3 0.0105 0.0574 0.1298 0.2013 0.2503 0.2668 0.2522 0.2150 0.1665 0.1172 7 4 0.0010 0.0112 0.0401 0.0881 0.1460 0.2001 0.2377 0.2508 0.2384 0.2051 6 5 0.0001 0.0015 0.0085 0.0264 0.0584 0.1029 0.1536 0.2007 0.2340 0.2461 5 6 0.0000 0.0001 0.0012 0.0055 0.0162 0.0368 0.0689 0.1115 0.1596 0.2051 4 7 0.0000 0.0000 0.0001 0.0008 0.0031 0.0090 0.0212 0.0425 0.0746 0.1172 3 8 0.0000 0.0000 0.0000 0.0001 0.0004 0.0014 0.0043 0.0106 0.0229 0.0439 2 9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0016 0.0042 0.0098 110 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0010 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
(table continued)
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AP-4 Appendix A Statistical Tables
TABLE A.1 (continued) Binomial Probabilities (n equal to 12, 14, and 15)
n 5 12 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.5404 0.2824 0.1422 0.0687 0.0317 0.0138 0.0057 0.0022 0.0008 0.0002 12 1 0.3413 0.3766 0.3012 0.2062 0.1267 0.0712 0.0368 0.0174 0.0075 0.0029 11 2 0.0988 0.2301 0.2924 0.2835 0.2323 0.1678 0.1088 0.0639 0.0339 0.0161 10 3 0.0173 0.0852 0.1720 0.2362 0.2581 0.2397 0.1954 0.1419 0.0923 0.0537 9 4 0.0021 0.0213 0.0683 0.1329 0.1936 0.2311 0.2367 0.2128 0.1700 0.1208 8 5 0.0002 0.0038 0.0193 0.0532 0.1032 0.1585 0.2039 0.2270 0.2225 0.1934 7 6 0.0000 0.0005 0.0040 0.0155 0.0401 0.0792 0.1281 0.1766 0.2124 0.2256 6 7 0.0000 0.0000 0.0006 0.0033 0.0115 0.0291 0.0591 0.1009 0.1489 0.1934 5 8 0.0000 0.0000 0.0001 0.0005 0.0024 0.0078 0.0199 0.0420 0.0762 0.1208 4 9 0.0000 0.0000 0.0000 0.0001 0.0004 0.0015 0.0048 0.0125 0.0277 0.0537 310 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0008 0.0025 0.0068 0.0161 211 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0010 0.0029 112 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xcn 5 14 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.4877 0.2288 0.1028 0.0440 0.0178 0.0068 0.0024 0.0008 0.0002 0.0001 14 1 0.3593 0.3559 0.2539 0.1539 0.0832 0.0407 0.0181 0.0073 0.0027 0.0009 13 2 0.1229 0.2570 0.2912 0.2501 0.1802 0.1134 0.0634 0.0317 0.0141 0.0056 12 3 0.0259 0.1142 0.2056 0.2501 0.2402 0.1943 0.1366 0.0845 0.0462 0.0222 11 4 0.0037 0.0349 0.0998 0.1720 0.2202 0.2290 0.2022 0.1549 0.1040 0.0611 10 5 0.0004 0.0078 0.0352 0.0860 0.1468 0.1963 0.2178 0.2066 0.1701 0.1222 9 6 0.0000 0.0013 0.0093 0.0322 0.0734 0.1262 0.1759 0.2066 0.2088 0.1833 8 7 0.0000 0.0002 0.0019 0.0092 0.0280 0.0618 0.1082 0.1574 0.1952 0.2095 7 8 0.0000 0.0000 0.0003 0.0020 0.0082 0.0232 0.0510 0.0918 0.1398 0.1833 6 9 0.0000 0.0000 0.0000 0.0003 0.0018 0.0066 0.0183 0.0408 0.0762 0.1222 510 0.0000 0.0000 0.0000 0.0000 0.0003 0.0014 0.0049 0.0136 0.0312 0.0611 411 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0010 0.0033 0.0093 0.0222 312 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0019 0.0056 213 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0009 114 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xcn 5 15 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.4633 0.2059 0.0874 0.0352 0.0134 0.0047 0.0016 0.0005 0.0001 0.0000 15 1 0.3658 0.3432 0.2312 0.1319 0.0668 0.0305 0.0126 0.0047 0.0016 0.0005 14 2 0.1348 0.2669 0.2856 0.2309 0.1559 0.0916 0.0476 0.0219 0.0090 0.0032 13 3 0.0307 0.1285 0.2184 0.2501 0.2252 0.1700 0.1110 0.0634 0.0318 0.0139 12 4 0.0049 0.0428 0.1156 0.1876 0.2252 0.2186 0.1792 0.1268 0.0780 0.0417 11 5 0.0006 0.0105 0.0449 0.1032 0.1651 0.2061 0.2123 0.1859 0.1404 0.0916 10 6 0.0000 0.0019 0.0132 0.0430 0.0917 0.1472 0.1906 0.2066 0.1914 0.1527 9 7 0.0000 0.0003 0.0030 0.0138 0.0393 0.0811 0.1319 0.1771 0.2013 0.1964 8 8 0.0000 0.0000 0.0005 0.0035 0.0131 0.0348 0.0710 0.1181 0.1647 0.1964 7 9 0.0000 0.0000 0.0001 0.0007 0.0034 0.0116 0.0298 0.0612 0.1048 0.1527 610 0.0000 0.0000 0.0000 0.0001 0.0007 0.0030 0.0096 0.0245 0.0515 0.0916 511 0.0000 0.0000 0.0000 0.0000 0.0001 0.0006 0.0024 0.0074 0.0191 0.0417 412 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0016 0.0052 0.0139 313 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0010 0.0032 214 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 115 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
(table continued)
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Appendix A Statistical Tables AP-5
TABLE A.1 (continued) Binomial Probabilities (n equal to 16 and 18)
n 5 16 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.4401 0.1853 0.0743 0.0281 0.0100 0.0033 0.0010 0.0003 0.0001 0.0000 16 1 0.3706 0.3294 0.2097 0.1126 0.0535 0.0228 0.0087 0.0030 0.0009 0.0002 15 2 0.1463 0.2745 0.2775 0.2111 0.1336 0.0732 0.0353 0.0150 0.0056 0.0018 14 3 0.0359 0.1423 0.2285 0.2463 0.2079 0.1465 0.0888 0.0468 0.0215 0.0085 13 4 0.0061 0.0514 0.1311 0.2001 0.2252 0.2040 0.1553 0.1014 0.0572 0.0278 12 5 0.0008 0.0137 0.0555 0.1201 0.1802 0.2099 0.2008 0.1623 0.1123 0.0667 11 6 0.0001 0.0028 0.0180 0.0550 0.1101 0.1649 0.1982 0.1983 0.1684 0.1222 10 7 0.0000 0.0004 0.0045 0.0197 0.0524 0.1010 0.1524 0.1889 0.1969 0.1746 9 8 0.0000 0.0001 0.0009 0.0055 0.0197 0.0487 0.0923 0.1417 0.1812 0.1964 8 9 0.0000 0.0000 0.0001 0.0012 0.0058 0.0185 0.0442 0.0840 0.1318 0.1746 710 0.0000 0.0000 0.0000 0.0002 0.0014 0.0056 0.0167 0.0392 0.0755 0.1222 611 0.0000 0.0000 0.0000 0.0000 0.0002 0.0013 0.0049 0.0142 0.0337 0.0667 512 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0011 0.0040 0.0115 0.0278 413 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0008 0.0029 0.0085 314 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0018 215 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 1
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
n 5 18 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.3972 0.1501 0.0536 0.0180 0.0056 0.0016 0.0004 0.0001 0.0000 0.0000 18 1 0.3763 0.3002 0.1704 0.0811 0.0338 0.0126 0.0042 0.0012 0.0003 0.0001 17 2 0.1683 0.2835 0.2556 0.1723 0.0958 0.0458 0.0190 0.0069 0.0022 0.0006 16 3 0.0473 0.1680 0.2406 0.2297 0.1704 0.1046 0.0547 0.0246 0.0095 0.0031 15 4 0.0093 0.0700 0.1592 0.2153 0.2130 0.1681 0.1104 0.0614 0.0291 0.0117 14 5 0.0014 0.0218 0.0787 0.1507 0.1988 0.2017 0.1664 0.1146 0.0666 0.0327 13 6 0.0002 0.0052 0.0301 0.0816 0.1436 0.1873 0.1941 0.1655 0.1181 0.0708 12 7 0.0000 0.0010 0.0091 0.0350 0.0820 0.1376 0.1792 0.1892 0.1657 0.1214 11 8 0.0000 0.0002 0.0022 0.0120 0.0376 0.0811 0.1327 0.1734 0.1864 0.1669 10 9 0.0000 0.0000 0.0004 0.0033 0.0139 0.0386 0.0794 0.1284 0.1694 0.1855 910 0.0000 0.0000 0.0001 0.0008 0.0042 0.0149 0.0385 0.0771 0.1248 0.1669 811 0.0000 0.0000 0.0000 0.0001 0.0010 0.0046 0.0151 0.0374 0.0742 0.1214 712 0.0000 0.0000 0.0000 0.0000 0.0002 0.0012 0.0047 0.0145 0.0354 0.0708 613 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0012 0.0045 0.0134 0.0327 514 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0011 0.0039 0.0117 415 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0009 0.0031 316 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0006 217 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 1
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
(table continued)
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AP-6 Appendix A Statistical Tables
TABLE A.1 (concluded) Binomial Probabilities (n equal to 20)
TABLE A.2 A Poisson Probability Table Poisson Probabilities (m between 0.1 and 2.0)
n 5 20 p
xT 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0 0.3585 0.1216 0.0388 0.0115 0.0032 0.0008 0.0002 0.0000 0.0000 0.0000 20 1 0.3774 0.2702 0.1368 0.0576 0.0211 0.0068 0.0020 0.0005 0.0001 0.0000 19 2 0.1887 0.2852 0.2293 0.1369 0.0669 0.0278 0.0100 0.0031 0.0008 0.0002 18 3 0.0596 0.1901 0.2428 0.2054 0.1339 0.0716 0.0323 0.0123 0.0040 0.0011 17 4 0.0133 0.0898 0.1821 0.2182 0.1897 0.1304 0.0738 0.0350 0.0139 0.0046 16 5 0.0022 0.0319 0.1028 0.1746 0.2023 0.1789 0.1272 0.0746 0.0365 0.0148 15 6 0.0003 0.0089 0.0454 0.1091 0.1686 0.1916 0.1712 0.1244 0.0746 0.0370 14 7 0.0000 0.0020 0.0160 0.0545 0.1124 0.1643 0.1844 0.1659 0.1221 0.0739 13 8 0.0000 0.0004 0.0046 0.0222 0.0609 0.1144 0.1614 0.1797 0.1623 0.1201 12 9 0.0000 0.0001 0.0011 0.0074 0.0271 0.0654 0.1158 0.1597 0.1771 0.1602 1110 0.0000 0.0000 0.0002 0.0020 0.0099 0.0308 0.0686 0.1171 0.1593 0.1762 1011 0.0000 0.0000 0.0000 0.0005 0.0030 0.0120 0.0336 0.0710 0.1185 0.1602 912 0.0000 0.0000 0.0000 0.0001 0.0008 0.0039 0.0136 0.0355 0.0727 0.1201 813 0.0000 0.0000 0.0000 0.0000 0.0002 0.0010 0.0045 0.0146 0.0366 0.0739 714 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0012 0.0049 0.0150 0.0370 615 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0013 0.0049 0.0148 516 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0013 0.0046 417 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0011 318 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 2
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 xc
Source: Computed by D. K. Hildebrand. Found in D. K. Hildebrand and L. Ott, Statistical Thinking for Managers, 3rd ed. (Boston, MA: PWS-KENT Publishing Company, 1991).
M
x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0.4066 0.36791 0.0905 0.1637 0.2222 0.2681 0.3033 0.3293 0.3476 0.3595 0.3659 0.36792 0.0045 0.0164 0.0333 0.0536 0.0758 0.0988 0.1217 0.1438 0.1647 0.18393 0.0002 0.0011 0.0033 0.0072 0.0126 0.0198 0.0284 0.0383 0.0494 0.06134 0.0000 0.0001 0.0003 0.0007 0.0016 0.0030 0.0050 0.0077 0.0111 0.01535 0.0000 0.0000 0.0000 0.0001 0.0002 0.0004 0.0007 0.0012 0.0020 0.00316 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0003 0.0005
M
x 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
0 0.3329 0.3012 0.2725 0.2466 0.2231 0.2019 0.1827 0.1653 0.1496 0.13531 0.3662 0.3614 0.3543 0.3452 0.3347 0.3230 0.3106 0.2975 0.2842 0.27072 0.2014 0.2169 0.2303 0.2417 0.2510 0.2584 0.2640 0.2678 0.2700 0.27073 0.0738 0.0867 0.0998 0.1128 0.1255 0.1378 0.1496 0.1607 0.1710 0.18044 0.0203 0.0260 0.0324 0.0395 0.0471 0.0551 0.0636 0.0723 0.0812 0.09025 0.0045 0.0062 0.0084 0.0111 0.0141 0.0176 0.0216 0.0260 0.0309 0.03616 0.0008 0.0012 0.0018 0.0026 0.0035 0.0047 0.0061 0.0078 0.0098 0.01207 0.0001 0.0002 0.0003 0.0005 0.0008 0.0011 0.0015 0.0020 0.0027 0.00348 0.0000 0.0000 0.0001 0.0001 0.0001 0.0002 0.0003 0.0005 0.0006 0.0009
(table continued)
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Appendix A Statistical Tables AP-7
TABLE A.2 (continued) Poisson Probabilities (m between 2.1 and 5.0)
M
x 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0 0.1225 0.1108 0.1003 0.0907 0.0821 0.0743 0.0672 0.0608 0.0550 0.0498 1 0.2572 0.2438 0.2306 0.2177 0.2052 0.1931 0.1815 0.1703 0.1596 0.1494 2 0.2700 0.2681 0.2652 0.2613 0.2565 0.2510 0.2450 0.2384 0.2314 0.2240 3 0.1890 0.1966 0.2033 0.2090 0.2138 0.2176 0.2205 0.2225 0.2237 0.2240 4 0.0992 0.1082 0.1169 0.1254 0.1336 0.1414 0.1488 0.1557 0.1622 0.1680 5 0.0417 0.0476 0.0538 0.0602 0.0668 0.0735 0.0804 0.0872 0.0940 0.1008 6 0.0146 0.0174 0.0206 0.0241 0.0278 0.0319 0.0362 0.0407 0.0455 0.0504 7 0.0044 0.0055 0.0068 0.0083 0.0099 0.0118 0.0139 0.0163 0.0188 0.0216 8 0.0011 0.0015 0.0019 0.0025 0.0031 0.0038 0.0047 0.0057 0.0068 0.0081 9 0.0003 0.0004 0.0005 0.0007 0.0009 0.0011 0.0014 0.0018 0.0022 0.002710 0.0001 0.0001 0.0001 0.0002 0.0002 0.0003 0.0004 0.0005 0.0006 0.000811 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0002 0.0002
M
x 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0
0 0.0450 0.0408 0.0369 0.0334 0.0302 0.0273 0.0247 0.0224 0.0202 0.0183 1 0.1397 0.1304 0.1217 0.1135 0.1057 0.0984 0.0915 0.0850 0.0789 0.0733 2 0.2165 0.2087 0.2008 0.1929 0.1850 0.1771 0.1692 0.1615 0.1539 0.1465 3 0.2237 0.2226 0.2209 0.2186 0.2158 0.2125 0.2087 0.2046 0.2001 0.1954 4 0.1733 0.1781 0.1823 0.1858 0.1888 0.1912 0.1931 0.1944 0.1951 0.1954 5 0.1075 0.1140 0.1203 0.1264 0.1322 0.1377 0.1429 0.1477 0.1522 0.1563 6 0.0555 0.0608 0.0662 0.0716 0.0771 0.0826 0.0881 0.0936 0.0989 0.1042 7 0.0246 0.0278 0.0312 0.0348 0.0385 0.0425 0.0466 0.0508 0.0551 0.0595 8 0.0095 0.0111 0.0129 0.0148 0.0169 0.0191 0.0215 0.0241 0.0269 0.0298 9 0.0033 0.0040 0.0047 0.0056 0.0066 0.0076 0.0089 0.0102 0.0116 0.013210 0.0010 0.0013 0.0016 0.0019 0.0023 0.0028 0.0033 0.0039 0.0045 0.005311 0.0003 0.0004 0.0005 0.0006 0.0007 0.0009 0.0011 0.0013 0.0016 0.001912 0.0001 0.0001 0.0001 0.0002 0.0002 0.0003 0.0003 0.0004 0.0005 0.000613 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002
M
x 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0
0 0.0166 0.0150 0.0136 0.0123 0.0111 0.0101 0.0091 0.0082 0.0074 0.0067 1 0.0679 0.0630 0.0583 0.0540 0.0500 0.0462 0.0427 0.0395 0.0365 0.0337 2 0.1393 0.1323 0.1254 0.1188 0.1125 0.1063 0.1005 0.0948 0.0894 0.0842 3 0.1904 0.1852 0.1798 0.1743 0.1687 0.1631 0.1574 0.1517 0.1460 0.1404 4 0.1951 0.1944 0.1933 0.1917 0.1898 0.1875 0.1849 0.1820 0.1789 0.1755 5 0.1600 0.1633 0.1662 0.1687 0.1708 0.1725 0.1738 0.1747 0.1753 0.1755 6 0.1093 0.1143 0.1191 0.1237 0.1281 0.1323 0.1362 0.1398 0.1432 0.1462 7 0.0640 0.0686 0.0732 0.0778 0.0824 0.0869 0.0914 0.0959 0.1002 0.1044 8 0.0328 0.0360 0.0393 0.0428 0.0463 0.0500 0.0537 0.0575 0.0614 0.0653 9 0.0150 0.0168 0.0188 0.0209 0.0232 0.0255 0.0281 0.0307 0.0334 0.036310 0.0061 0.0071 0.0081 0.0092 0.0104 0.0118 0.0132 0.0147 0.0164 0.018111 0.0023 0.0027 0.0032 0.0037 0.0043 0.0049 0.0056 0.0064 0.0073 0.008212 0.0008 0.0009 0.0011 0.0013 0.0016 0.0019 0.0022 0.0026 0.0030 0.003413 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.0011 0.001314 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0003 0.0003 0.0004 0.000515 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002
(table continued)
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AP-8 Appendix A Statistical Tables
TABLE A.2 (concluded) Poisson Probabilities (m between 5.5 and 20.0)
M
x 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
0 0.0041 0.0025 0.0015 0.0009 0.0006 0.0003 0.0002 0.0001 0.0001 0.0000 1 0.0225 0.0149 0.0098 0.0064 0.0041 0.0027 0.0017 0.0011 0.0007 0.0005 2 0.0618 0.0446 0.0318 0.0223 0.0156 0.0107 0.0074 0.0050 0.0034 0.0023 3 0.1133 0.0892 0.0688 0.0521 0.0389 0.0286 0.0208 0.0150 0.0107 0.0076 4 0.1558 0.1339 0.1118 0.0912 0.0729 0.0573 0.0443 0.0337 0.0254 0.0189 5 0.1714 0.1606 0.1454 0.1277 0.1094 0.0916 0.0752 0.0607 0.0483 0.0378 6 0.1571 0.1606 0.1575 0.1490 0.1367 0.1221 0.1066 0.0911 0.0764 0.0631 7 0.1234 0.1377 0.1462 0.1490 0.1465 0.1396 0.1294 0.1171 0.1037 0.0901 8 0.0849 0.1033 0.1188 0.1304 0.1373 0.1396 0.1375 0.1318 0.1232 0.1126 9 0.0519 0.0688 0.0858 0.1014 0.1144 0.1241 0.1299 0.1318 0.1300 0.125110 0.0285 0.0413 0.0558 0.0710 0.0858 0.0993 0.1104 0.1186 0.1235 0.125111 0.0143 0.0225 0.0330 0.0452 0.0585 0.0722 0.0853 0.0970 0.1067 0.113712 0.0065 0.0113 0.0179 0.0263 0.0366 0.0481 0.0604 0.0728 0.0844 0.094813 0.0028 0.0052 0.0089 0.0142 0.0211 0.0296 0.0395 0.0504 0.0617 0.072914 0.0011 0.0022 0.0041 0.0071 0.0113 0.0169 0.0240 0.0324 0.0419 0.052115 0.0004 0.0009 0.0018 0.0033 0.0057 0.0090 0.0136 0.0194 0.0265 0.034716 0.0001 0.0003 0.0007 0.0014 0.0026 0.0045 0.0072 0.0109 0.0157 0.021717 0.0000 0.0001 0.0003 0.0006 0.0012 0.0021 0.0036 0.0058 0.0088 0.012818 0.0000 0.0000 0.0001 0.0002 0.0005 0.0009 0.0017 0.0029 0.0046 0.007119 0.0000 0.0000 0.0000 0.0001 0.0002 0.0004 0.0008 0.0014 0.0023 0.003720 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0003 0.0006 0.0011 0.001921 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0003 0.0005 0.000922 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0002 0.000423 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002
M
x 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0
0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.0010 0.0004 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3 0.0037 0.0018 0.0008 0.0004 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 4 0.0102 0.0053 0.0027 0.0013 0.0006 0.0003 0.0001 0.0001 0.0000 0.0000 5 0.0224 0.0127 0.0070 0.0037 0.0019 0.0010 0.0005 0.0002 0.0001 0.0001 6 0.0411 0.0255 0.0152 0.0087 0.0048 0.0026 0.0014 0.0007 0.0004 0.0002 7 0.0646 0.0437 0.0281 0.0174 0.0104 0.0060 0.0034 0.0019 0.0010 0.0005 8 0.0888 0.0655 0.0457 0.0304 0.0194 0.0120 0.0072 0.0042 0.0024 0.0013 9 0.1085 0.0874 0.0661 0.0473 0.0324 0.0213 0.0135 0.0083 0.0050 0.002910 0.1194 0.1048 0.0859 0.0663 0.0486 0.0341 0.0230 0.0150 0.0095 0.005811 0.1194 0.1144 0.1015 0.0844 0.0663 0.0496 0.0355 0.0245 0.0164 0.010612 0.1094 0.1144 0.1099 0.0984 0.0829 0.0661 0.0504 0.0368 0.0259 0.017613 0.0926 0.1056 0.1099 0.1060 0.0956 0.0814 0.0658 0.0509 0.0378 0.027114 0.0728 0.0905 0.1021 0.1060 0.1024 0.0930 0.0800 0.0655 0.0514 0.038715 0.0534 0.0724 0.0885 0.0989 0.1024 0.0992 0.0906 0.0786 0.0650 0.051616 0.0367 0.0543 0.0719 0.0866 0.0960 0.0992 0.0963 0.0884 0.0772 0.064617 0.0237 0.0383 0.0550 0.0713 0.0847 0.0934 0.0963 0.0936 0.0863 0.076018 0.0145 0.0255 0.0397 0.0554 0.0706 0.0830 0.0909 0.0936 0.0911 0.084419 0.0084 0.0161 0.0272 0.0409 0.0557 0.0699 0.0814 0.0887 0.0911 0.088820 0.0046 0.0097 0.0177 0.0286 0.0418 0.0559 0.0692 0.0798 0.0866 0.088821 0.0024 0.0055 0.0109 0.0191 0.0299 0.0426 0.0560 0.0684 0.0783 0.084622 0.0012 0.0030 0.0065 0.0121 0.0204 0.0310 0.0433 0.0560 0.0676 0.076923 0.0006 0.0016 0.0037 0.0074 0.0133 0.0216 0.0320 0.0438 0.0559 0.066924 0.0003 0.0008 0.0020 0.0043 0.0083 0.0144 0.0226 0.0328 0.0442 0.055725 0.0001 0.0004 0.0010 0.0024 0.0050 0.0092 0.0154 0.0237 0.0336 0.044626 0.0000 0.0002 0.0005 0.0013 0.0029 0.0057 0.0101 0.0164 0.0246 0.034327 0.0000 0.0001 0.0002 0.0007 0.0016 0.0034 0.0063 0.0109 0.0173 0.025428 0.0000 0.0000 0.0001 0.0003 0.0009 0.0019 0.0038 0.0070 0.0117 0.018129 0.0000 0.0000 0.0001 0.0002 0.0004 0.0011 0.0023 0.0044 0.0077 0.012530 0.0000 0.0000 0.0000 0.0001 0.0002 0.0006 0.0013 0.0026 0.0049 0.008331 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0007 0.0015 0.0030 0.005432 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0004 0.0009 0.0018 0.003433 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0005 0.0010 0.0020
Source: Computed by D. K. Hildebrand. Found in D. K. Hildebrand and L. Ott, Statistical Thinking for Managers, 3rd ed. (Boston, MA: PWS-KENT Publishing Company, 1991).
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Appendix A Statistical Tables AP-9
TABLE A.3 A Table of Areas under the Standard Normal Curve
z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.03590.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.07530.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.11410.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.15170.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.18790.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224
0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.25490.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.28520.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.31330.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.33891.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.38301.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.40151.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.41771.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.43191.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441
1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.45451.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.46331.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.47061.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.47672.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.48572.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.48902.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.49162.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.49362.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952
2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.49642.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.49742.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.49812.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.49863.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990
Source: A. Hald, Statistical Tables and Formulas (New York: Wiley, 1952), abridged from Table 1. Reproduced by permission of the publisher.
0 z
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AP-10 Appendix A Statistical Tables
TABLE A.4 A Table of Cumulative Areas under the Standard Normal Curve
z .00 .01 .02 .03 .04 .05 .06 .07 .08 .0923.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.000223.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.000323.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.000523.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.000723.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.001022.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.001422.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.001922.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.002622.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.003622.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.004822.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.006422.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.008422.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.011022.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.014322.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.018321.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.023321.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.029421.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.036721.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.045521.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.055921.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.068121.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.082321.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.098521.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.117021.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.137920.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.161120.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.186720.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.214820.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.245120.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.277620.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.312120.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.348320.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.385920.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.424720.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.68790.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.72240.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.75490.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.78520.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.83891.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.86211.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.88301.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.90151.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.91771.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.93191.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.94411.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.95451.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.96331.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.97061.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.97672.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.98172.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.98572.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.98902.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.99162.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.99362.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.99522.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.99642.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.99742.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.99812.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.99863.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.99903.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.99933.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.99953.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.99973.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
0z
0 z
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Appendix A Statistical Tables AP-11
TABLE A.5 A t Table: Values of tA for df 5 1 through 48
df t0.100 t0.05 t0.025 t0.01 t0.005 t0.001 t0.0005
1 3.078 6.314 12.706 31.821 63.657 318.309 636.6192 1.886 2.920 4.303 6.965 9.925 22.327 31.5993 1.638 2.353 3.182 4.541 5.841 10.215 12.9244 1.533 2.132 2.776 3.747 4.604 7.173 8.6105 1.476 2.015 2.571 3.365 4.032 5.893 6.8696 1.440 1.943 2.447 3.143 3.707 5.208 5.9597 1.415 1.895 2.365 2.998 3.499 4.785 5.4088 1.397 1.860 2.306 2.896 3.355 4.501 5.0419 1.383 1.833 2.262 2.821 3.250 4.297 4.781
10 1.372 1.812 2.228 2.764 3.169 4.144 4.58711 1.363 1.796 2.201 2.718 3.106 4.025 4.43712 1.356 1.782 2.179 2.681 3.055 3.930 4.31813 1.350 1.771 2.160 2.650 3.012 3.852 4.22114 1.345 1.761 2.145 2.624 2.977 3.787 4.14015 1.341 1.753 2.131 2.602 2.947 3.733 4.07316 1.337 1.746 2.120 2.583 2.921 3.686 4.01517 1.333 1.740 2.110 2.567 2.898 3.646 3.96518 1.330 1.734 2.101 2.552 2.878 3.610 3.92219 1.328 1.729 2.093 2.539 2.861 3.579 3.88320 1.325 1.725 2.086 2.528 2.845 3.552 3.85021 1.323 1.721 2.080 2.518 2.831 3.527 3.81922 1.321 1.717 2.074 2.508 2.819 3.505 3.79223 1.319 1.714 2.069 2.500 2.807 3.485 3.76824 1.318 1.711 2.064 2.492 2.797 3.467 3.74525 1.316 1.708 2.060 2.485 2.787 3.450 3.72526 1.315 1.706 2.056 2.479 2.779 3.435 3.70727 1.314 1.703 2.052 2.473 2.771 3.421 3.69028 1.313 1.701 2.048 2.467 2.763 3.408 3.67429 1.311 1.699 2.045 2.462 2.756 3.396 3.65930 1.310 1.697 2.042 2.457 2.750 3.385 3.64631 1.309 1.696 2.040 2.453 2.744 3.375 3.63332 1.309 1.694 2.037 2.449 2.738 3.365 3.62233 1.308 1.692 2.035 2.445 2.733 3.356 3.61134 1.307 1.691 2.032 2.441 2.728 3.348 3.60135 1.306 1.690 2.030 2.438 2.724 3.340 3.59136 1.306 1.688 2.028 2.434 2.719 3.333 3.58237 1.305 1.687 2.026 2.431 2.715 3.326 3.57438 1.304 1.686 2.024 2.429 2.712 3.319 3.56639 1.304 1.685 2.023 2.426 2.708 3.313 3.55840 1.303 1.684 2.021 2.423 2.704 3.307 3.55141 1.303 1.683 2.020 2.421 2.701 3.301 3.54442 1.302 1.682 2.018 2.418 2.698 3.296 3.53843 1.302 1.681 2.017 2.416 2.695 3.291 3.53244 1.301 1.680 2.015 2.414 2.692 3.286 3.52645 1.301 1.679 2.014 2.412 2.690 3.281 3.52046 1.300 1.679 2.013 2.410 2.687 3.277 3.51547 1.300 1.678 2.012 2.408 2.685 3.273 3.51048 1.299 1.677 2.011 2.407 2.682 3.269 3.505
(table continued)
0 ta
a
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AP-12 Appendix A Statistical Tables
TABLE A.5 (concluded) A t Table: Values of tA for df 5 49 through 100, 120, and `
df t0.100 t0.05 t0.025 t0.01 t0.005 t0.001 t0.0005
49 1.299 1.677 2.010 2.405 2.680 3.265 3.50050 1.299 1.676 2.009 2.403 2.678 3.261 3.49651 1.298 1.675 2.008 2.402 2.676 3.258 3.49252 1.298 1.675 2.007 2.400 2.674 3.255 3.48853 1.298 1.674 2.006 2.399 2.672 3.251 3.48454 1.297 1.674 2.005 2.397 2.670 3.248 3.48055 1.297 1.673 2.004 2.396 2.668 3.245 3.47656 1.297 1.673 2.003 2.395 2.667 3.242 3.47357 1.297 1.672 2.002 2.394 2.665 3.239 3.47058 1.296 1.672 2.002 2.392 2.663 3.237 3.46659 1.296 1.671 2.001 2.391 2.662 3.234 3.46360 1.296 1.671 2.000 2.390 2.660 3.232 3.46061 1.296 1.670 2.000 2.389 2.659 3.229 3.45762 1.295 1.670 1.999 2.388 2.657 3.227 3.45463 1.295 1.669 1.998 2.387 2.656 3.225 3.45264 1.295 1.669 1.998 2.386 2.655 3.223 3.44965 1.295 1.669 1.997 2.385 2.654 3.220 3.44766 1.295 1.668 1.997 2.384 2.652 3.218 3.44467 1.294 1.668 1.996 2.383 2.651 3.216 3.44268 1.294 1.668 1.995 2.382 2.650 3.214 3.43969 1.294 1.667 1.995 2.382 2.649 3.213 3.43770 1.294 1.667 1.994 2.381 2.648 3.211 3.43571 1.294 1.667 1.994 2.380 2.647 3.209 3.43372 1.293 1.666 1.993 2.379 2.646 3.207 3.43173 1.293 1.666 1.993 2.379 2.645 3.206 3.42974 1.293 1.666 1.993 2.378 2.644 3.204 3.42775 1.293 1.665 1.992 2.377 2.643 3.202 3.42576 1.293 1.665 1.992 2.376 2.642 3.201 3.42377 1.293 1.665 1.991 2.376 2.641 3.199 3.42178 1.292 1.665 1.991 2.375 2.640 3.198 3.42079 1.292 1.664 1.990 2.374 2.640 3.197 3.41880 1.292 1.664 1.990 2.374 2.639 3.195 3.41681 1.292 1.664 1.990 2.373 2.638 3.194 3.41582 1.292 1.664 1.989 2.373 2.637 3.193 3.41383 1.292 1.663 1.989 2.372 2.636 3.191 3.41284 1.292 1.663 1.989 2.372 2.636 3.190 3.41085 1.292 1.663 1.988 2.371 2.635 3.189 3.40986 1.291 1.663 1.988 2.370 2.634 3.188 3.40787 1.291 1.663 1.988 2.370 2.634 3.187 3.40688 1.291 1.662 1.987 2.369 2.633 3.185 3.40589 1.291 1.662 1.987 2.369 2.632 3.184 3.40390 1.291 1.662 1.987 2.368 2.632 3.183 3.40291 1.291 1.662 1.986 2.368 2.631 3.182 3.40192 1.291 1.662 1.986 2.368 2.630 3.181 3.39993 1.291 1.661 1.986 2.367 2.630 3.180 3.39894 1.291 1.661 1.986 2.367 2.629 3.179 3.39795 1.291 1.661 1.985 2.366 2.629 3.178 3.39696 1.290 1.661 1.985 2.366 2.628 3.177 3.39597 1.290 1.661 1.985 2.365 2.627 3.176 3.39498 1.290 1.661 1.984 2.365 2.627 3.175 3.39399 1.290 1.660 1.984 2.365 2.626 3.175 3.392
100 1.290 1.660 1.984 2.364 2.626 3.174 3.390120 1.289 1.658 1.980 2.358 2.617 3.160 3.373 ` 1.282 1.645 1.960 2.326 2.576 3.090 3.291
Source: Provided by J. B. Orris using Excel.
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Appendix A Statistical Tables AP-13
Nu
mer
ato
r D
egre
es o
f Fr
eed
om
(d
f 1)
1 2
3 4
5 6
7 8
9 10
12
15
20
24
30
40
60
12
0 `
1 39
.86
49.5
0 53
.59
55.8
3 57
.24
58.2
0 58
.91
59.4
4 59
.86
60.1
9 60
.71
61.2
2 61
.74
62.0
0 62
.26
62.5
3 62
.79
63.0
6 63
.33
2 8.
53
9.00
9.
16
9.24
9.
29
9.33
9.
35
9.37
9.
38
9.39
9.
41
9.42
9.
44
9.45
9.
46
9.47
9.
47
9.48
9
.49
3 5.
54
5.46
5.
39
5.34
5.
31
5.28
5.
27
5.25
5.
24
5.23
5.
22
5.20
5.
18
5.18
5.
17
5.16
5.
15
5.14
5
.13
4 4.
54
4.32
4.
19
4.11
4.
05
4.01
3.
98
3.95
3.
94
3.92
3.
90
3.87
3.
84
3.83
3.
82
3.80
3.
79
3.78
3
.76
5 4.
06
3.78
3.
62
3.52
3.
45
3.40
3.
37
3.34
3.
32
3.30
3.
27
3.24
3.
21
3.19
3.
17
3.16
3.
14
3.12
3
.10
6 3.
78
3.46
3.
29
3.18
3.
11
3.05
3.
01
2.98
2.
96
2.94
2.
90
2.87
2.
84
2.82
2.
80
2.78
2.
76
2.74
2
.72
7 3.
59
3.26
3.
07
2.96
2.
88
2.83
2.
78
2.75
2.
72
2.70
2.
67
2.63
2.
59
2.58
2.
56
2.54
2.
51
2.49
2
.47
8 3.
46
3.11
2.
92
2.81
2.
73
2.67
2.
62
2.59
2.
56
2.54
2.
50
2.46
2.
42
2.40
2.
38
2.36
2.
34
2.32
2
.29
9 3.
36
3.01
2.
81
2.69
2.
61
2.55
2.
51
2.47
2.
44
2.42
2.
38
2.34
2.
30
2.28
2.
25
2.23
2.
21
2.18
2
.16
1
0 3.
29
2.92
2.
73
2.61
2.
52
2.46
2.
41
2.38
2.
35
2.32
2.
28
2.24
2.
20
2.18
2.
16
2.13
2.
11
2.08
2
.06
1
1 3.
23
2.86
2.
66
2.54
2.
45
2.39
2.
34
2.30
2.
27
2.25
2.
21
2.17
2.
12
2.10
2.
08
2.05
2.
03
2.00
1
.97
1
2 3.
18
2.81
2.
61
2.48
2.
39
2.33
2.
28
2.24
2.
21
2.19
2.
15
2.10
2.
06
2.04
2.
01
1.99
1.
96
1.93
1
.90
1
3 3.
14
2.76
2.
56
2.43
2.
35
2.28
2.
23
2.20
2.
16
2.14
2.
10
2.05
2.
01
1.98
1.
96
1.93
1.
90
1.88
1
.85
1
4 3.
10
2.73
2.
52
2.39
2.
31
2.24
2.
19
2.15
2.
12
2.10
2.
05
2.01
1.
96
1.94
1.
91
1.89
1.
86
1.83
1
.80
1
5 3.
07
2.70
2.
49
2.36
2.
27
2.21
2.
16
2.12
2.
09
2.06
2.
02
1.97
1.
92
1.90
1.
87
1.85
1.
82
1.79
1
.76
1
6 3.
05
2.67
2.
46
2.33
2.
24
2.18
2.
13
2.09
2.
06
2.03
1.
99
1.94
1.
89
1.87
1.
84
1.81
1.
78
1.75
1
.72
1
7 3.
03
2.64
2.
44
2.31
2.
22
2.15
2.
10
2.06
2.
03
2.00
1.
96
1.91
1.
86
1.84
1.
81
1.78
1.
75
1.72
1
.69
1
8 3.
01
2.62
2.
42
2.29
2.
20
2.13
2.
08
2.04
2.
00
1.98
1.
93
1.89
1.
84
1.81
1.
78
1.75
1.
72
1.69
1
.66
1
9 2.
99
2.61
2.
40
2.27
2.
18
2.11
2.
06
2.02
1.
98
1.96
1.
91
1.86
1.
81
1.79
1.
76
1.73
1.
70
1.67
1
.63
2
0 2.
97
2.59
2.
38
2.25
2.
16
2.09
2.
04
2.00
1.
96
1.94
1.
89
1.84
1.
79
1.77
1.
74
1.71
1.
68
1.64
1
.61
2
1 2.
96
2.57
2.
36
2.23
2.
14
2.08
2.
02
1.98
1.
95
1.92
1.
87
1.83
1.
78
1.75
1.
72
1.69
1.
66
1.62
1
.59
2
2 2.
95
2.56
2.
35
2.22
2.
13
2.06
2.
01
1.97
1.
93
1.90
1.
86
1.81
1.
76
1.73
1.
70
1.67
1.
64
1.60
1
.57
2
3 2.
94
2.55
2.
34
2.21
2.
11
2.05
1.
99
1.95
1.
92
1.89
1.
84
1.80
1.
74
1.72
1.
69
1.66
1.
62
1.59
1
.55
2
4 2.
93
2.54
2.
33
2.19
2.
10
2.04
1.
98
1.94
1.
91
1.88
1.
83
1.78
1.
73
1.70
1.
67
1.64
1.
61
1.57
1
.53
2
5 2.
92
2.53
2.
32
2.18
2.
09
2.02
1.
97
1.93
1.
89
1.87
1.
82
1.77
1.
72
1.69
1.
66
1.63
1.
59
1.56
1
.52
2
6 2.
91
2.52
2.
31
2.17
2.
08
2.01
1.
96
1.92
1.
88
1.86
1.
81
1.76
1.
71
1.68
1.
65
1.61
1.
58
1.54
1
.50
2
7 2.
90
2.51
2.
30
2.17
2.
07
2.00
1.
95
1.91
1.
87
1.85
1.
80
1.75
1.
70
1.67
1.
64
1.60
1.
57
1.53
1
.49
2
8 2.
89
2.50
2.
29
2.16
2.
06
2.00
1.
94
1.90
1.
87
1.84
1.
79
1.74
1.
69
1.66
1.
63
1.59
1.
56
1.52
1
.48
2
9 2.
89
2.50
2.
28
2.15
2.
06
1.99
1.
93
1.89
1.
86
1.83
1.
78
1.73
1.
68
1.65
1.
62
1.58
1.
55
1.51
1
.47
3
0 2.
88
2.49
2.
28
2.14
2.
05
1.98
1.
93
1.88
1.
85
1.82
1.
77
1.72
1.
67
1.64
1.
61
1.57
1.
54
1.50
1
.46
4
0 2.
84
2.44
2.
23
2.09
2.
00
1.93
1.
87
1.83
1.
79
1.76
1.
71
1.66
1.
61
1.57
1.
54
1.51
1.
47
1.42
1
.38
6
0 2.
79
2.39
2.
18
2.04
1.
95
1.87
1.
82
1.77
1.
74
1.71
1.
66
1.60
1.
54
1.51
1.
48
1.44
1.
40
1.35
1
.29
12
0 2.
75
2.35
2.
13
1.99
1.
90
1.82
1.
77
1.72
1.
68
1.65
1.
60
1.55
1.
48
1.45
1.
41
1.37
1.
32
1.26
1
.19
`
2.71
2.
30
2.08
1.
94
1.85
1.
77
1.72
1.
67
1.63
1.
60
1.55
1.
49
1.42
1.
38
1.34
1.
30
1.24
1.
17
1.0
0
Sou
rce:
M.
Mer
rin
gto
n a
nd
C.
M.
Tho
mp
son
, “T
able
s o
f Pe
rcen
tag
e Po
ints
of
the
Inve
rted
Bet
a (F
)-D
istr
ibu
tio
n,”
Bio
met
rika
33
(194
3),
pp
. 73
–88.
Rep
rod
uce
d b
y p
erm
issi
on
of
the
Bio
met
rika
Tru
stee
s.
Denominator Degrees of Freedom (df2)
df 1
df 2
0F 0
.10
F0.
10
TAB
LE A
.6
An F
Tab
le: V
alue
s of
F0.
10
bow39604_appA_AP1-AP27.indd Page AP-13 21/11/13 1:35 PM f-w-512 bow39604_appA_AP1-AP27.indd Page AP-13 21/11/13 1:35 PM f-w-512 /203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles/203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles
AP-14 Appendix A Statistical Tables
TAB
LE A
.7
An F
Tab
le: V
alue
s of
F0.
05
Denominator Degrees of Freedom (df2)
df 1
df 2
Nu
mer
ato
r D
egre
es o
f Fr
eed
om
(d
f 1)
1 2
3 4
5 6
7 8
9 10
12
15
20
24
30
40
60
12
0 `
1 16
1.4
199.
5 21
5.7
224.
6 23
0.2
234.
0 23
6.8
238.
9 24
0.5
241.
9 24
3.9
245.
9 24
8.0
249.
1 25
0.1
251.
1 25
2.2
253.
3 25
4.3
2 18
.51
19.0
0 19
.16
19.2
5 19
.30
19.3
3 19
.35
19.3
7 19
.38
19.4
0 19
.41
19.4
3 19
.45
19.4
5 19
.46
19.4
7 19
.48
19.4
9 19
.50
3 10
.13
9.55
9.
28
9.12
9.
01
8.94
8.
89
8.85
8.
81
8.79
8.
74
8.70
8.
66
8.64
8.
62
8.59
8.
57
8.55
8.
53
4
7.71
6.
94
6.59
6.
39
6.26
6.
16
6.09
6.
04
6.00
5.
96
5.91
5.
86
5.80
5.
77
5.75
5.
72
5.69
5.
66
5.63
5 6.
61
5.79
5.
41
5.19
5.
05
4.95
4.
88
4.82
4.
77
4.74
4.
68
4.62
4.
56
4.53
4.
50
4.46
4.
43
4.40
4.
36
6
5.99
5.
14
4.76
4.
53
4.39
4.
28
4.21
4.
15
4.10
4.
06
4.00
3.
94
3.87
3.
84
3.81
3.
77
3.74
3.
70
3.67
7 5.
59
4.74
4.
35
4.12
3.
97
3.87
3.
79
3.73
3.
68
3.64
3.
57
3.51
3.
44
3.41
3.
38
3.34
3.
30
3.27
3.
23
8
5.32
4.
46
4.07
3.
84
3.69
3.
58
3.50
3.
44
3.39
3.
35
3.28
3.
22
3.15
3.
12
3.08
3.
04
3.01
2.
97
2.93
9 5.
12
4.26
3.
86
3.63
3.
48
3.37
3.
29
3.23
3.
18
3.14
3.
07
3.01
2.
94
2.90
2.
86
2.83
2.
79
2.75
2.
71
10
4.96
4.
10
3.71
3.
48
3.33
3.
22
3.14
3.
07
3.02
2.
98
2.91
2.
85
2.77
2.
74
2.70
2.
66
2.62
2.
58
2.54
1
1 4.
84
3.98
3.
59
3.36
3.
20
3.09
3.
01
2.95
2.
90
2.85
2.
79
2.72
2.
65
2.61
2.
57
2.53
2.
49
2.45
2.
40
12
4.75
3.
89
3.49
3.
26
3.11
3.
00
2.91
2.
85
2.80
2.
75
2.69
2.
62
2.54
2.
51
2.47
2.
43
2.38
2.
34
2.30
1
3 4.
67
3.81
3.
41
3.18
3.
03
2.92
2.
83
2.77
2.
71
2.67
2.
60
2.53
2.
46
2.42
2.
38
2.34
2.
30
2.25
2.
21
14
4.60
3.
74
3.34
3.
11
2.96
2.
85
2.76
2.
70
2.65
2.
60
2.53
2.
46
2.39
2.
35
2.31
2.
27
2.22
2.
18
2.13
1
5 4.
54
3.68
3.
29
3.06
2.
90
2.79
2.
71
2.64
2.
59
2.54
2.
48
2.40
2.
33
2.29
2.
25
2.20
2.
16
2.11
2.
07
16
4.49
3.
63
3.24
3.
01
2.85
2.
74
2.66
2.
59
2.54
2.
49
2.42
2.
35
2.28
2.
24
2.19
2.
15
2.11
2.
06
2.01
1
7 4.
45
3.59
3.
20
2.96
2.
81
2.70
2.
61
2.55
2.
49
2.45
2.
38
2.31
2.
23
2.19
2.
15
2.10
2.
06
2.01
1.
96
18
4.41
3.
55
3.16
2.
93
2.77
2.
66
2.58
2.
51
2.46
2.
41
2.34
2.
27
2.19
2.
15
2.11
2.
06
2.02
1.
97
1.92
1
9 4.
38
3.52
3.
13
2.90
2.
74
2.63
2.
54
2.48
2.
42
2.38
2.
31
2.23
2.
16
2.11
2.
07
2.03
1.
98
1.93
1.
88
20
4.35
3.
49
3.10
2.
87
2.71
2.
60
2.51
2.
45
2.39
2.
35
2.28
2.
20
2.12
2.
08
2.04
1.
99
1.95
1.
90
1.84
2
1 4.
32
3.47
3.
07
2.84
2.
68
2.57
2.
49
2.42
2.
37
2.32
2.
25
2.18
2.
10
2.05
2.
01
1.96
1.
92
1.87
1.
81
22
4.30
3.
44
3.05
2.
82
2.66
2.
55
2.46
2.
40
2.34
2.
30
2.23
2.
15
2.07
2.
03
1.98
1.
94
1.89
1.
84
1.78
2
3 4.
28
3.42
3.
03
2.80
2.
64
2.53
2.
44
2.37
2.
32
2.27
2.
20
2.13
2.
05
2.01
1.
96
1.91
1.
86
1.81
1.
76
24
4.26
3.
40
3.01
2.
78
2.62
2.
51
2.42
2.
36
2.30
2.
25
2.18
2.
11
2.03
1.
98
1.94
1.
89
1.84
1.
79
1.73
2
5 4.
24
3.39
2.
99
2.76
2.
60
2.49
2.
40
2.34
2.
28
2.24
2.
16
2.09
2.
01
1.96
1.
92
1.87
1.
82
1.77
1.
71
26
4.23
3.
37
2.98
2.
74
2.59
2.
47
2.39
2.
32
2.27
2.
22
2.15
2.
07
1.99
1.
95
1.90
1.
85
1.80
1.
75
1.69
2
7 4.
21
3.35
2.
96
2.73
2.
57
2.46
2.
37
2.31
2.
25
2.20
2.
13
2.06
1.
97
1.93
1.
88
1.84
1.
79
1.73
1.
67
28
4.20
3.
34
2.95
2.
71
2.56
2.
45
2.36
2.
29
2.24
2.
19
2.12
2.
04
1.96
1.
91
1.87
1.
82
1.77
1.
71
1.65
2
9 4.
18
3.33
2.
93
2.70
2.
55
2.43
2.
35
2.28
2.
22
2.18
2.
10
2.03
1.
94
1.90
1.
85
1.81
1.
75
1.70
1.
64
30
4.17
3.
32
2.92
2.
69
2.53
2.
42
2.33
2.
27
2.21
2.
16
2.09
2.
01
1.93
1.
89
1.84
1.
79
1.74
1.
68
1.62
4
0 4.
08
3.23
2.
84
2.61
2.
45
2.34
2.
25
2.18
2.
12
2.08
2.
00
1.92
1.
84
1.79
1.
74
1.69
1.
64
1.58
1.
51
60
4.00
3.
15
2.76
2.
53
2.37
2.
25
2.17
2.
10
2.04
1.
99
1.92
1.
84
1.75
1.
70
1.65
1.
59
1.53
1.
47
1.39
12
0 3.
92
3.07
2.
68
2.45
2.
29
2.17
2.
09
2.02
1.
96
1.91
1.
83
1.75
1.
66
1.61
1.
55
1.50
1.
43
1.35
1.
25
`
3.
84
3.00
2.
60
2.37
2.
21
2.10
2.
01
1.94
1.
88
1.83
1.
75
1.67
1.
57
1.52
1.
46
1.39
1.
32
1.22
1.
00
Sou
rce:
M.
Mer
rin
gto
n a
nd
C.
M.
Tho
mp
son
, “T
able
s o
f Pe
rcen
tag
e Po
ints
of
the
Inve
rted
Bet
a (F
)-D
istr
ibu
tio
n,”
Bio
met
rika
33
(194
3),
pp
. 73
–88.
Rep
rod
uce
d b
y p
erm
issi
on
of
the
Bio
met
rika
Tru
stee
s.
0F 0
.05
F0.
05
bow39604_appA_AP1-AP27.indd Page AP-14 21/11/13 1:35 PM f-w-512 bow39604_appA_AP1-AP27.indd Page AP-14 21/11/13 1:35 PM f-w-512 /203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles/203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles
Appendix A Statistical Tables AP-15
TAB
LE A
.8
An F
Tab
le: V
alue
s of
F0.
025
Nu
mer
ato
r D
egre
es o
f Fr
eed
om
(d
f 1)
1 2
3 4
5 6
7 8
9 10
12
15
20
24
30
40
60
12
0 `
1 64
7.8
799.
5 86
4.2
899.
6 92
1.8
937.
1 94
8.2
956.
7 96
3.3
968.
6 97
6.7
984.
9 99
3.1
997.
2 1,
001
1,00
6 1,
010
1,01
4 1,
018
2 38
.51
39.0
0 39
.17
39.2
5 39
.30
39.3
3 39
.36
39.3
7 39
.39
39.4
0 39
.41
39.4
3 39
.45
39.4
6 39
.46
39.4
7 39
.48
39.4
9 39
.50
3 17
.44
16.0
4 15
.44
15.1
0 14
.88
14.7
3 14
.62
14.5
4 14
.47
14.4
2 14
.34
14.2
5 14
.17
14.1
2 14
.08
14.0
4 13
.99
13.9
5 13
.90
4 12
.22
10.6
5 9.
98
9.60
9.
36
9.20
9.
07
8.98
8.
90
8.84
8.
75
8.66
8.
56
8.51
8.
46
8.41
8.
36
8.31
8.
26
5
10.0
1 8.
43
7.76
7.
39
7.15
6.
98
6.85
6.
76
6.68
6.
62
6.52
6.
43
6.33
6.
28
6.23
6.
18
6.12
6.
07
6.02
6 8.
81
7.26
6.
60
6.23
5.
99
5.82
5.
70
5.60
5.
52
5.46
5.
37
5.27
5.
17
5.12
5.
07
5.01
4.
96
4.90
4.
85
7
8.07
6.
54
5.89
5.
52
5.29
5.
12
4.99
4.
90
4.82
4.
76
4.67
4.
57
4.47
4.
42
4.36
4.
31
4.25
4.
20
4.14
8 7.
57
6.06
5.
42
5.05
4.
82
4.65
4.
53
4.43
4.
36
4.30
4.
20
4.10
4.
00
3.95
3.
89
3.84
3.
78
3.73
3.
67
9
7.21
5.
71
5.08
4.
72
4.48
4.
32
4.20
4.
10
4.03
3.
96
3.87
3.
77
3.67
3.
61
3.56
3.
51
3.45
3.
39
3.33
1
0 6.
94
5.46
4.
83
4.47
4.
24
4.07
3.
95
3.85
3.
78
3.72
3.
62
3.52
3.
42
3.37
3.
31
3.26
3.
20
3.14
3.
08
11
6.72
5.
26
4.63
4.
28
4.04
3.
88
3.76
3.
66
3.59
3.
53
3.43
3.
33
3.23
3.
17
3.12
3.
06
3.00
2.
94
2.88
1
2 6.
55
5.10
4.
47
4.12
3.
89
3.73
3.
61
3.51
3.
44
3.37
3.
28
3.18
3.
07
3.02
2.
96
2.91
2.
85
2.79
2.
72
13
6.41
4.
97
4.35
4.
00
3.77
3.
60
3.48
3.
39
3.31
3.
25
3.15
3.
05
2.95
2.
89
2.84
2.
78
2.72
2.
66
2.60
1
4 6.
30
4.86
4.
24
3.89
3.
66
3.50
3.
38
3.29
3.
21
3.15
3.
05
2.95
2.
84
2.79
2.
73
2.67
2.
61
2.55
2.
49
15
6.20
4.
77
4.15
3.
80
3.58
3.
41
3.29
3.
20
3.12
3.
06
2.96
2.
86
2.76
2.
70
2.64
2.
59
2.52
2.
46
2.40
1
6 6.
12
4.69
4.
08
3.73
3.
50
3.34
3.
22
3.12
3.
05
2.99
2.
89
2.79
2.
68
2.63
2.
57
2.51
2.
45
2.38
2.
32
17
6.04
4.
62
4.01
3.
66
3.44
3.
28
3.16
3.
06
2.98
2.
92
2.82
2.
72
2.62
2.
56
2.50
2.
44
2.38
2.
32
2.25
1
8 5.
98
4.56
3.
95
3.61
3.
38
3.22
3.
10
3.01
2.
93
2.87
2.
77
2.67
2.
56
2.50
2.
44
2.38
2.
32
2.26
2.
19
19
5.92
4.
51
3.90
3.
56
3.33
3.
17
3.05
2.
96
2.88
2.
82
2.72
2.
62
2.51
2.
45
2.39
2.
33
2.27
2.
20
2.13
2
0 5.
87
4.46
3.
86
3.51
3.
29
3.13
3.
01
2.91
2.
84
2.77
2.
68
2.57
2.
46
2.41
2.
35
2.29
2.
22
2.16
2.
09
21
5.83
4.
42
3.82
3.
48
3.25
3.
09
2.97
2.
87
2.80
2.
73
2.64
2.
53
2.42
2.
37
2.31
2.
25
2.18
2.
11
2.04
2
2 5.
79
4.38
3.
78
3.44
3.
22
3.05
2.
93
2.84
2.
76
2.70
2.
60
2.50
2.
39
2.33
2.
27
2.21
2.
14
2.08
2.
00
23
5.75
4.
35
3.75
3.
41
3.18
3.
02
2.90
2.
81
2.73
2.
67
2.57
2.
47
2.36
2.
30
2.24
2.
18
2.11
2.
04
1.97
2
4 5.
72
4.32
3.
72
3.38
3.
15
2.99
2.
87
2.78
2.
70
2.64
2.
54
2.44
2.
33
2.27
2.
21
2.15
2.
08
2.01
1.
94
25
5.69
4.
29
3.69
3.
35
3.13
2.
97
2.85
2.
75
2.68
2.
61
2.51
2.
41
2.30
2.
24
2.18
2.
12
2.05
1.
98
1.91
2
6 5.
66
4.27
3.
67
3.33
3.
10
2.94
2.
82
2.73
2.
65
2.59
2.
49
2.39
2.
28
2.22
2.
16
2.09
2.
03
1.95
1.
88
27
5.63
4.
24
3.65
3.
31
3.08
2.
92
2.80
2.
71
2.63
2.
57
2.47
2.
36
2.25
2.
19
2.13
2.
07
2.00
1.
93
1.85
2
8 5.
61
4.22
3.
63
3.29
3.
06
2.90
2.
78
2.69
2.
61
2.55
2.
45
2.34
2.
23
2.17
2.
11
2.05
1.
98
1.91
1.
83
29
5.59
4.
20
3.61
3.
27
3.04
2.
88
2.76
2.
67
2.59
2.
53
2.43
2.
32
2.21
2.
15
2.09
2.
03
1.96
1.
89
1.81
3
0 5.
57
4.18
3.
59
3.25
3.
03
2.87
2.
75
2.65
2.
57
2.51
2.
41
2.31
2.
20
2.14
2.
07
2.01
1.
94
1.87
1.
79
40
5.42
4.
05
3.46
3.
13
2.90
2.
74
2.62
2.
53
2.45
2.
39
2.29
2.
18
2.07
2.
01
1.94
1.
88
1.80
1.
72
1.64
6
0 5.
29
3.93
3.
34
3.01
2.
79
2.63
2.
51
2.41
2.
33
2.27
2.
17
2.06
1.
94
1.88
1.
82
1.74
1.
67
1.58
1.
48
120
5.15
3.
80
3.23
2.
89
2.67
2.
52
2.39
2.
30
2.22
2.
16
2.05
1.
94
1.82
1.
76
1.69
1.
61
1.53
1.
43
1.31
`
5.02
3.
69
3.12
2.
79
2.57
2.
41
2.29
2.
19
2.11
2.
05
1.94
1.
83
1.71
1.
64
1.57
1.
48
1.39
1.
27
1.00
Sou
rce:
M.
Mer
rin
gto
n a
nd
C.
M.
Tho
mp
son
, “T
able
s o
f Pe
rcen
tag
e Po
ints
of
the
Inve
rted
Bet
a (F
)-D
istr
ibu
tio
n,”
Bio
met
rika
33
(194
3),
pp
. 73
–88.
Rep
rod
uce
d b
y p
erm
issi
on
of
the
Bio
met
rika
Tru
stee
s.
Denominator Degrees of Freedom (df2)
df 1
df 2
0F 0
.025
F0.
025
bow39604_appA_AP1-AP27.indd Page AP-15 21/11/13 1:35 PM f-w-512 bow39604_appA_AP1-AP27.indd Page AP-15 21/11/13 1:35 PM f-w-512 /203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles/203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles
AP-16 Appendix A Statistical Tables
TAB
LE A
.9
An F
Tab
le: V
alue
s of
F0.
01
Nu
mer
ato
r D
egre
es o
f Fr
eed
om
(d
f 1)
1 2
3 4
5 6
7 8
9 10
12
15
20
24
30
40
60
12
0 `
1 4,
052
4,99
9.5
5,40
3 5,
625
5,76
4 5,
859
5,92
8 5,
982
6,02
2 6,
056
6,10
6 6,
157
6,20
9 6,
235
6,26
1 6,
287
6,31
3 6,
339
6,36
6
2
98.5
0 99
.00
99.1
7 99
.25
99.3
0 99
.33
99.3
6 99
.37
99.3
9 99
.40
99
.42
99.4
3 99
.45
99.4
6 99
.47
99.4
7 99
.48
99.4
9 99
.50
3 34
.12
30.8
2 29
.46
28.7
1 28
.24
27.9
1 27
.67
27.4
9 27
.35
27.2
3 27
.05
26.8
7 26
.69
26.6
0 26
.50
26.4
1 26
.32
26.2
2 26
.13
4 21
.20
18.0
0 16
.69
15.9
8 15
.52
15.2
1 14
.98
14.8
0
14.6
6 14
.55
14.3
7 14
.20
14.0
2 13
.93
13.8
4 13
.75
13.6
5 13
.56
13.4
6
5
16.2
6 13
.27
12.0
6 11
.39
10.9
7 10
.67
10.4
6 10
.29
10.1
6 10
.05
9.89
9.
72
9.55
9.
47
9.38
9.
29
9.20
9.
11
9.02
6 13
.75
10.9
2 9.
78
9.15
8.
75
8.47
8.
26
8.10
7.
98
7.87
7.
72
7.56
7.
40
7.31
7.
23
7.14
7.
06
6.97
6.
88
7
12.2
5 9.
55
8.45
7.
85
7.46
7.
19
6.99
6.
84
6.72
6.
62
6.47
6.
31
6.16
6.
07
5.99
5.
91
5.82
5.
74
5.65
8 11
.26
8.65
7.
59
7.01
6.
63
6.37
6.
18
6.03
5.
91
5.81
5.
67
5.52
5.
36
5.28
5.
20
5.12
5.
03
4.95
4.
86
9
10.5
6 8.
02
6.99
6.
42
6.06
5.
80
5.61
5.
47
5.35
5.
26
5.11
4.
96
4.81
4.
73
4.65
4.
57
4.48
4.
40
4.31
1
0 10
.04
7.56
6.
55
5.99
5.
64
5.39
5.
20
5.06
4.
94
4.85
4.
71
4.56
4.
41
4.33
4.
25
4.17
4.
08
4.00
3.
91
11
9.65
7.
21
6.22
5.
67
5.32
5.
07
4.89
4.
74
4.63
4.
54
4.40
4.
25
4.10
4.
02
3.94
3.
86
3.78
3.
69
3.60
1
2 9.
33
6.93
5.
95
5.41
5.
06
4.82
4.
64
4.50
4.
39
4.30
4.
16
4.01
3.
86
3.78
3.
70
3.62
3.
54
3.45
3.
36
13
9.07
6.
70
5.74
5.
21
4.86
4.
62
4.44
4.
30
4.19
4.
10
3.96
3.
82
3.66
3.
59
3.51
3.
43
3.34
3.
25
3.17
1
4 8.
86
6.51
5.
56
5.04
4.
69
4.46
4.
28
4.14
4.
03
3.94
3.
80
3.66
3.
51
3.43
3.
35
3.27
3.
18
3.09
3.
00
15
8.68
6.
36
5.42
4.
89
4.56
4.
32
4.14
4.
00
3.89
3.
80
3.67
3.
52
3.37
3.
29
3.21
3.
13
3.05
2.
96
2.87
1
6 8.
53
6.23
5.
29
4.77
4.
44
4.20
4.
03
3.89
3.
78
3.69
3.
55
3.41
3.
26
3.18
3.
10
3.02
2.
93
2.84
2.
75
17
8.40
6.
11
5.18
4.
67
4.34
4.
10
3.93
3.
79
3.68
3.
59
3.46
3.
31
3.16
3.
08
3.00
2.
92
2.83
2.
75
2.65
1
8 8.
29
6.01
5.
09
4.58
4.
25
4.01
3.
84
3.71
3.
60
3.51
3.
37
3.23
3.
08
3.00
2.
92
2.84
2.
75
2.66
2.
57
19
8.18
5.
93
5.01
4.
50
4.17
3.
94
3.77
3.
63
3.52
3.
43
3.30
3.
15
3.00
2.
92
2.84
2.
76
2.67
2.
58
2.49
2
0 8.
10
5.85
4.
94
4.43
4.
10
3.87
3.
70
3.56
3.
46
3.37
3.
23
3.09
2.
94
2.86
2.
78
2.69
2.
61
2.52
2.
42
21
8.02
5.
78
4.87
4.
37
4.04
3.
81
3.64
3.
51
3.40
3.
31
3.17
3.
03
2.88
2.
80
2.72
2.
64
2.55
2.
46
2.36
2
2 7.
95
5.72
4.
82
4.31
3.
99
3.76
3.
59
3.45
3.
35
3.26
3.
12
2.98
2.
83
2.75
2.
67
2.58
2.
50
2.40
2.
31
23
7.88
5.
66
4.76
4.
26
3.94
3.
71
3.54
3.
41
3.30
3.
21
3.07
2.
93
2.78
2.
70
2.62
2.
54
2.45
2.
35
2.26
2
4 7.
82
5.61
4.
72
4.22
3.
90
3.67
3.
50
3.36
3.
26
3.17
3.
03
2.89
2.
74
2.66
2.
58
2.49
2.
40
2.31
2.
21
25
7.77
5.
57
4.68
4.
18
3.85
3.
63
3.46
3.
32
3.22
3.
13
2.99
2.
85
2.70
2.
62
2.54
2.
45
2.36
2.
27
2.17
2
6 7.
72
5.53
4.
64
4.14
3.
82
3.59
3.
42
3.29
3.
18
3.09
2.
96
2.81
2.
66
2.58
2.
50
2.42
2.
33
2.23
2.
13
27
7.68
5.
49
4.60
4.
11
3.78
3.
56
3.39
3.
26
3.15
3.
06
2.93
2.
78
2.63
2.
55
2.47
2.
38
2.29
2.
20
2.10
2
8 7.
64
5.45
4.
57
4.07
3.
75
3.53
3.
36
3.23
3.
12
3.03
2.
90
2.75
2.
60
2.52
2.
44
2.35
2.
26
2.17
2.
06
29
7.60
5.
42
4.54
4.
04
3.73
3.
50
3.33
3.
20
3.09
3.
00
2.87
2.
73
2.57
2.
49
2.41
2.
33
2.23
2.
14
2.03
3
0 7.
56
5.39
4.
51
4.02
3.
70
3.47
3.
30
3.17
3.
07
2.98
2.
84
2.70
2.
55
2.47
2.
39
2.30
2.
21
2.11
2.
01
40
7.31
5.
18
4.31
3.
83
3.51
3.
29
3.12
2.
99
2.89
2.
80
2.66
2.
52
2.37
2.
29
2.20
2.
11
2.02
1.
92
1.80
6
0 7.
08
4.98
4.
13
3.65
3.
34
3.12
2.
95
2.82
2.
72
2.63
2.
50
2.35
2.
20
2.12
2.
03
1.94
1.
84
1.73
1.
60
120
6.85
4.
79
3.95
3.
48
3.17
2.
96
2.79
2.
66
2.56
2.
47
2.34
2.
19
2.03
1.
95
1.86
1.
76
1.66
1.
53
1.38
`
6.63
4.
61
3.78
3.
32
3.02
2.
80
2.64
2.
51
2.41
2.
32
2.18
2.
04
1.88
1.
79
1.70
1.
59
1.47
1.
32
1.00
Sou
rce:
M.
Mer
rin
gto
n a
nd
C.
M.
Tho
mp
son
, “T
able
s o
f Pe
rcen
tag
e Po
ints
of
the
Inve
rted
Bet
a (F
)-D
istr
ibu
tio
n,”
Bio
met
rika
33
(194
3),
pp
. 73
–88.
Rep
rod
uce
d b
y p
erm
issi
on
of
the
Bio
met
rika
Tru
stee
s.
Denominator Degrees of Freedom (df2)
df 1
df 2
0F 0
.01
F
0.01
bow39604_appA_AP1-AP27.indd Page AP-16 21/11/13 1:35 PM f-w-512 bow39604_appA_AP1-AP27.indd Page AP-16 21/11/13 1:35 PM f-w-512 /203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles/203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles
Appendix A Statistical Tables AP-17
TAB
LE A
.10
A
Tabl
e of
Per
cent
age
Poin
ts o
f the
Stu
dent
ized
Ran
ge
(Not
e: r
is th
e “fi
rst v
alue
” an
d v
is th
e “s
econ
d va
lue”
refe
rred
to in
Cha
pter
10.
)
Entr
y is
q0.
10
r
v
2 3
4 5
6 7
8 9
10
11
12
13
14
15
16
17
18
19
20
1
8.93
13
.4
16.4
18
.5
20.2
21
.5
22.6
23
.6
24.5
25
.2
25.9
26
.5
27.1
27
.6
28.1
28
.5
29.0
29
.3
29.7
2
4.13
5.
73
6.77
7.
54
8.14
8.
63
9.05
9.
41
9.72
10
.0
10.3
10
.5
10.7
10
.9
11.1
11
.2
11.4
11
.5
11.7
3
3.33
4.
47
5.20
5.
74
6.16
6.
51
6.81
7.
06
7.29
7.
49
7.67
7.
83
7.98
8.
12
8.25
8.
37
8.48
8.
58
8.68
4
3.01
3.
98
4.59
5.
03
5.39
5.
68
5.93
6.
14
6.33
6.
49
6.65
6.
78
6.91
7.
02
7.13
7.
23
7.33
7.
41
7.50
5
2.85
3.
72
4.26
4.
66
4.98
5.
24
5.46
5.
65
5.82
5.
97
6.10
6.
22
6.34
6.
44
6.54
6.
63
6.71
6.
79
6.86
6
2.75
3.
56
4.07
4.
44
4.73
4.
97
5.17
5.
34
5.50
5.
64
5.76
5.
87
5.98
6.
07
6.16
6.
25
6.32
6.
40
6.47
7
2.68
3.
45
3.93
4.
28
4.55
4.
78
4.97
5.
14
5.28
5.
41
5.53
5.
64
5.74
5.
83
5.91
5.
99
6.06
6.
13
6.19
8
2.63
3.
37
3.83
4.
17
4.43
4.
65
4.83
4.
99
5.13
5.
25
5.36
5.
46
5.56
5.
64
5.72
5.
80
5.87
5.
93
6.00
9
2.59
3.
32
3.76
4.
08
4.34
4.
54
4.72
4.
87
5.01
5.
13
5.23
5.
33
5.42
5.
51
5.58
5.
66
5.72
5.
79
5.85
10
2.56
3.
27
3.70
4.
02
4.26
4.
47
4.64
4.
78
4.91
5.
03
5.13
5.
23
5.32
5.
40
5.47
5.
54
5.61
5.
67
5.73
11
2.54
3.
23
3.66
3.
96
4.20
4.
40
4.57
4.
71
4.84
4.
95
5.05
5.
15
5.23
5.
31
5.38
5.
45
5.51
5.
57
5.63
12
2.52
3.
20
3.62
3.
92
4.16
4.
35
4.51
4.
65
4.78
4.
89
4.99
5.
08
5.16
5.
24
5.31
5.
37
5.44
5.
49
5.55
13
2.50
3.
18
3.59
3.
88
4.12
4.
30
4.46
4.
60
4.72
4.
83
4.93
5.
02
5.10
5.
18
5.25
5.
31
5.37
5.
43
5.48
14
2.49
3.
16
3.56
3.
85
4.08
4.
27
4.42
4.
56
4.68
4.
79
4.88
4.
97
5.05
5.
12
5.19
5.
26
5.32
5.
37
5.43
15
2.48
3.
14
3.54
3.
83
4.05
4.
23
4.39
4.
52
4.64
4.
75
4.84
4.
93
5.01
5.
08
5.15
5.
21
5.27
5.
32
5.38
16
2.47
3.
12
3.52
3.
80
4.03
4.
21
4.36
4.
49
4.61
4.
71
4.81
4.
89
4.97
5.
04
5.11
5.
17
5.23
5.
28
5.33
17
2.46
3.
11
3.50
3.
78
4.00
4.
18
4.33
4.
46
4.58
4.
68
4.77
4.
86
4.93
5.
01
5.07
5.
13
5.19
5.
24
5.30
18
2.45
3.
10
3.49
3.
77
3.98
4.
16
4.31
4.
44
4.55
4.
65
4.75
4.
83
4.90
4.
98
5.04
5.
10
5.16
5.
21
5.26
19
2.45
3.
09
3.47
3.
75
3.97
4.
14
4.29
4.
42
4.53
4.
63
4.72
4.
80
4.88
4.
95
5.01
5.
07
5.13
5.
18
5.23
20
2.44
3.
08
3.46
3.
74
3.95
4.
12
4.27
4.
40
4.51
4.
61
4.70
4.
78
4.85
4.
92
4.99
5.
05
5.10
5.
16
5.20
24
2.42
3.
05
3.42
3.
69
3.90
4.
07
4.21
4.
34
4.44
4.
54
4.63
4.
71
4.78
4.
85
4.91
4.
97
5.02
5.
07
5.12
30
2.40
3.
02
3.39
3.
65
3.85
4.
02
4.16
4.
28
4.38
4.
47
4.56
4.
64
4.71
4.
77
4.83
4.
89
4.94
4.
99
5.03
40
2.38
2.
99
3.35
3.
60
3.80
3.
96
4.10
4.
21
4.32
4.
41
4.49
4.
56
4.63
4.
69
4.75
4.
81
4.86
4.
90
4.95
60
2.36
2.
96
3.31
3.
56
3.75
3.
91
4.04
4.
16
4.25
4.
34
4.42
4.
49
4.56
4.
62
4.67
4.
73
4.78
4.
82
4.86
120
2.34
2.
93
3.28
3.
52
3.71
3.
86
3.99
4.
10
4.19
4.
28
4.35
4.
42
4.48
4.
54
4.60
4.
65
4.69
4.
74
4.78
`
2.33
2.
90
3.24
3.
48
3.66
3.
81
3.93
4.
04
4.13
4.
21
4.28
4.
35
4.41
4.
47
4.52
4.
57
4.61
4.
65
4.69
(tab
le c
on
tin
ued
)
bow39604_appA_AP1-AP27.indd Page AP-17 21/11/13 1:35 PM f-w-512 bow39604_appA_AP1-AP27.indd Page AP-17 21/11/13 1:35 PM f-w-512 /203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles/203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles
AP-18 Appendix A Statistical Tables
Entr
y is
q0.
05
r
v
2 3
4 5
6 7
8 9
10
11
12
13
14
15
16
17
18
19
20
1
18.0
27
.0
32.8
37
.1
40.4
43
.1
45.4
47
.4
49.1
50
.6
52.0
53
.2
54.3
55
.4
56.3
57
.2
58.0
58
.8
59.6
2
6.08
8.
33
9.80
10
.9
11.7
12
.4
13.0
13
.5
14.0
14
.4
14.7
15
.1
15.4
15
.7
15.9
16
.1
16.4
16
.6
16.8
3
4.50
5.
91
6.82
7.
50
8.04
8.
48
8.85
9.
18
9.46
9.
72
9.95
10
.2
10.3
10
.5
10.7
10
.8
11.0
11
.1
11.2
4
3.93
5.
04
5.76
6.
29
6.71
7.
05
7.35
7.
60
7.83
8.
03
8.21
8.
37
8.52
8.
66
8.79
8.
91
9.03
9.
13
9.23
5
3.64
4.
60
5.22
5.
67
6.03
6.
33
6.58
6.
80
6.99
7.
17
7.32
7.
47
7.60
7.
72
7.83
7.
93
8.03
8.
12
8.21
6
3.46
4.
34
4.90
5.
30
5.63
5.
90
6.12
6.
32
6.49
6.
65
6.79
6.
92
7.03
7.
14
7.24
7.
34
7.43
7.
51
7.59
7
3.34
4.
16
4.68
5.
06
5.36
5.
61
5.82
6.
00
6.16
6.
30
6.43
6.
55
6.66
6.
76
6.85
6.
94
7.02
7.
10
7.17
8
3.26
4.
04
4.53
4.
89
5.17
5.
40
5.60
5.
77
5.92
6.
05
6.18
6.
29
6.39
6.
48
6.57
6.
65
6.73
6.
80
6.87
9
3.20
3.
95
4.41
4.
76
5.02
5.
24
5.43
5.
59
5.74
5.
87
5.98
6.
09
6.19
6.
28
6.36
6.
44
6.51
6.
58
6.64
10
3.15
3.
88
4.33
4.
65
4.91
5.
12
5.30
5.
46
5.60
5.
72
5.83
5.
93
6.03
6.
11
6.19
6.
27
6.34
6.
40
6.47
11
3.11
3.
82
4.26
4.
57
4.82
5.
03
5.20
5.
35
5.49
5.
61
5.71
5.
81
5.90
5.
98
6.06
6.
13
6.20
6.
27
6.33
12
3.08
3.
77
4.20
4.
51
4.75
4.
95
5.12
5.
27
5.39
5.
51
5.61
5.
71
5.80
5.
88
5.95
6.
02
6.09
6.
15
6.21
13
3.06
3.
73
4.15
4.
45
4.69
4.
88
5.05
5.
19
5.32
5.
43
5.53
5.
63
5.71
5.
79
5.86
5.
93
5.99
6.
05
6.11
14
3.03
3.
70
4.11
4.
41
4.64
4.
83
4.99
5.
13
5.25
5.
36
5.46
5.
55
5.64
5.
71
5.79
5.
85
5.91
5.
97
6.03
15
3.01
3.
67
4.08
4.
37
4.59
4.
78
4.94
5.
08
5.20
5.
31
5.40
5.
49
5.57
5.
65
5.72
5.
78
5.85
5.
90
5.96
16
3.00
3.
65
4.05
4.
33
4.56
4.
74
4.90
5.
03
5.15
5.
26
5.35
5.
44
5.52
5.
59
5.66
5.
73
5.79
5.
84
5.90
17
2.98
3.
63
4.02
4.
30
4.52
4.
70
4.86
4.
99
5.11
5.
21
5.31
5.
39
5.47
5.
54
5.61
5.
67
5.73
5.
79
5.84
18
2.97
3.
61
4.00
4.
28
4.49
4.
67
4.82
4.
96
5.07
5.
17
5.27
5.
35
5.43
5.
50
5.57
5.
63
5.69
5.
74
5.79
19
2.96
3.
59
3.98
4.
25
4.47
4.
65
4.79
4.
92
5.04
5.
14
5.23
5.
31
5.39
5.
46
5.53
5.
59
5.65
5.
70
5.75
20
2.95
3.
58
3.96
4.
23
4.45
4.
62
4.77
4.
90
5.01
5.
11
5.20
5.
28
5.36
5.
43
5.49
5.
55
5.61
5.
66
5.71
24
2.92
3.
53
3.90
4.
17
4.37
4.
54
4.68
4.
81
4.92
5.
01
5.10
5.
18
5.25
5.
32
5.38
5.
44
5.49
5.
55
5.59
30
2.89
3.
49
3.85
4.
10
4.30
4.
46
4.60
4.
72
4.82
4.
92
5.00
5.
08
5.15
5.
21
5.27
5.
33
5.38
5.
43
5.47
40
2.86
3.
44
3.79
4.
04
4.23
4.
39
4.52
4.
63
4.73
4.
82
4.90
4.
98
5.04
5.
11
5.16
5.
22
5.27
5.
31
5.36
60
2.83
3.
40
3.74
3.
98
4.16
4.
31
4.44
4.
55
4.65
4.
73
4.81
4.
88
4.94
5.
00
5.06
5.
11
5.15
5.
20
5.24
120
2.80
3.
36
3.68
3.
92
4.10
4.
24
4.36
4.
47
4.56
4.
64
4.71
4.
78
4.84
4.
90
4.95
5.
00
5.04
5.
09
5.13
`
2.
77
3.31
3.
63
3.86
4.
03
4.17
4.
29
4.39
4.
47
4.55
4.
62
4.68
4.
74
4.80
4.
85
4.89
4.
93
4.97
5.
01
TAB
LE A
.10
(c
on
tin
ued
)
(tab
le c
on
tin
ued
)
bow39604_appA_AP1-AP27.indd Page AP-18 21/11/13 1:35 PM f-w-512 bow39604_appA_AP1-AP27.indd Page AP-18 21/11/13 1:35 PM f-w-512 /203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles/203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles
Appendix A Statistical Tables AP-19
TAB
LE A
.10
(c
on
clu
ded
)
Entr
y is
q0.
01
r
v
2 3
4 5
6 7
8 9
10
11
12
13
14
15
16
17
18
19
20
1
90.0
13
5 16
4 18
6 20
2 21
6 22
7 23
7 24
6 25
3 26
0 26
6 27
2 27
7 28
2 28
6 29
0 29
4 29
8
2 14
.0
19.0
22
.3
24.7
26
.6
28.2
29
.5
30.7
31
.7
32.6
33
.4
34.1
34
.8
35.4
36
.0
36.5
37
.0
37.5
37
.9
3 8.
26
10.6
12
.2
13.3
14
.2
15.0
15
.6
16.2
16
.7
17.1
17
.5
17.9
18
.2
18.5
18
.8
19.1
19
.3
19.5
19
.8
4 6.
51
8.12
9.
17
9.96
10
.6
11.1
11
.5
11.9
12
.3
12.6
12
.8
13.1
13
.3
13.5
13
.7
13.9
14
.1
14.2
14
.4
5 5.
70
6.97
7.
80
8.42
8.
91
9.32
9.
67
9.97
10
.2
10.5
10
.7
10.9
11
.1
11.2
11
.4
11.6
11
.7
11.8
11
.9
6 5.
24
6.33
7.
03
7.56
7.
97
8.32
8.
61
8.87
9.
10
9.30
9.
49
9.65
9.
81
9.95
10
.1
10.2
10
.3
10.4
10
.5
7 4.
95
5.92
6.
54
7.01
7.
37
7.68
7.
94
8.17
8.
37
8.55
8.
71
8.86
9.
00
9.12
9.
24
9.35
9.
46
9.55
9.
65
8 4.
74
5.63
6.
20
6.63
6.
96
7.24
7.
47
7.68
7.
87
8.03
8.
18
8.31
8.
44
8.55
8.
66
8.76
8.
85
8.94
9.
03
9 4.
60
5.43
5.
96
6.35
6.
66
6.91
7.
13
7.32
7.
49
7.65
7.
78
7.91
8.
03
8.13
8.
23
8.32
8.
41
8.49
8.
57 1
0 4.
48
5.27
5.
77
6.14
6.
43
6.67
6.
87
7.05
7.
21
7.36
7.
48
7.60
7.
71
7.81
7.
91
7.99
8.
07
8.15
8.
22 1
1 4.
39
5.14
5.
62
5.97
6.
25
6.48
6.
67
6.84
6.
99
7.13
7.
25
7.36
7.
46
7.56
7.
65
7.73
7.
81
7.88
7.
95 1
2 4.
32
5.04
5.
50
5.84
6.
10
6.32
6.
51
6.67
6.
81
6.94
7.
06
7.17
7.
26
7.36
7.
44
7.52
7.
59
7.66
7.
73 1
3 4.
26
4.96
5.
40
5.73
5.
98
6.19
6.
37
6.53
6.
67
6.79
6.
90
7.01
7.
10
7.19
7.
27
7.34
7.
42
7.48
7.
55 1
4 4.
21
4.89
5.
32
5.63
5.
88
6.08
6.
26
6.41
6.
54
6.66
6.
77
6.87
6.
96
7.05
7.
12
7.20
7.
27
7.33
7.
39 1
5 4.
17
4.83
5.
25
5.56
5.
80
5.99
6.
16
6.31
6.
44
6.55
6.
66
6.76
6.
84
6.93
7.
00
7.07
7.
14
7.20
7.
26 1
6 4.
13
4.78
5.
19
5.49
5.
72
5.92
6.
08
6.22
6.
35
6.46
6.
56
6.66
6.
74
6.82
6.
90
6.97
7.
03
7.09
7.
15 1
7 4.
10
4.74
5.
14
5.43
5.
66
5.85
6.
01
6.15
6.
27
6.38
6.
48
6.57
6.
66
6.73
6.
80
6.87
6.
94
7.00
7.
05 1
8 4.
07
4.70
5.
09
5.38
5.
60
5.79
5.
94
6.08
6.
20
6.31
6.
41
6.50
6.
58
6.65
6.
72
6.79
6.
85
6.91
6.
96 1
9 4.
05
4.67
5.
05
5.33
5.
55
5.73
5.
89
6.02
6.
14
6.25
6.
34
6.43
6.
51
6.58
6.
65
6.72
6.
78
6.84
6.
89 2
0 4.
02
4.64
5.
02
5.29
5.
51
5.69
5.
84
5.97
6.
09
6.19
6.
29
6.37
6.
45
6.52
6.
59
6.65
6.
71
6.76
6.
82 2
4 3.
96
4.54
4.
91
5.17
5.
37
5.54
5.
69
5.81
5.
92
6.02
6.
11
6.19
6.
26
6.33
6.
39
6.45
6.
51
6.56
6.
61 3
0 3.
89
4.45
4.
80
5.05
5.
24
5.40
5.
54
5.65
5.
76
5.85
5.
93
6.01
6.
08
6.14
6.
20
6.26
6.
31
6.36
6.
41 4
0 3.
82
4.37
4.
70
4.93
5.
11
5.27
5.
39
5.50
5.
60
5.69
5.
77
5.84
5.
90
5.96
6.
02
6.07
6.
12
6.17
6.
21 6
0 3.
76
4.28
4.
60
4.82
4.
99
5.13
5.
25
5.36
5.
45
5.53
5.
60
5.67
5.
73
5.79
5.
84
5.89
5.
93
5.98
6.
0212
0 3.
70
4.20
4.
50
4.71
4.
87
5.01
5.
12
5.21
5.
30
5.38
5.
44
5.51
5.
56
5.61
5.
66
5.71
5.
75
5.79
5.
83 `
3.
64
4.12
4.
40
4.60
4.
76
4.88
4.
99
5.08
5.
16
5.23
5.
29
5.35
5.
40
5.45
5.
49
5.54
5.
57
5.61
5.
65
Sou
rce:
Th
e A
nal
ysis
of
Var
ian
ce,
pp
. 41
4 –16
, b
y H
enry
Sch
effe
, ©
195
9 b
y Jo
hn
Wile
y &
So
ns,
In
c. R
epri
nte
d b
y p
erm
issi
on
of
Joh
n W
iley
& S
on
s, I
nc.
bow39604_appA_AP1-AP27.indd Page AP-19 21/11/13 1:35 PM f-w-512 bow39604_appA_AP1-AP27.indd Page AP-19 21/11/13 1:35 PM f-w-512 /203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles/203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles
AP-20 Appendix A Statistical Tables
Degrees of 5% 1%
Degrees of 5% 1% Freedom (df ) Freedom (df )
1 0.997 1.000 24 0.388 0.496 2 0.950 0.990 25 0.381 0.487 3 0.878 0.959 26 0.374 0.478 4 0.811 0.917 27 0.367 0.470 5 0.754 0.874 28 0.361 0.463 6 0.707 0.834 29 0.355 0.456 7 0.666 0.798 30 0.349 0.449 8 0.632 0.765 35 0.325 0.418 9 0.602 0.735 40 0.304 0.393 10 0.576 0.708 45 0.288 0.372 11 0.553 0.684 50 0.273 0.354 12 0.532 0.661 60 0.250 0.325 13 0.514 0.641 70 0.232 0.302 14 0.497 0.623 80 0.217 0.283 15 0.482 0.606 90 0.205 0.267 16 0.468 0.590 100 0.195 0.254 17 0.456 0.575 125 0.174 0.228 18 0.444 0.561 150 0.159 0.208 19 0.433 0.549 200 0.138 0.181 20 0.423 0.537 300 0.113 0.148 21 0.413 0.526 400 0.098 0.128 22 0.404 0.515 500 0.088 0.115 23 0.396 0.505 1000 0.062 0.081
Source: This table is adapted from Table VII of Fisher and Yates, Statistical Tables for Biological, Agricultural and Medical Research, published by Longman Group Ltd, London (previously published by Oliver and Boyd, Edinburgh), and by permission of Pearson Education Limited.
TABLE A.11 A Table of Critical Values of r (df 5 N 2 2 and N Is the Number of Pairs of Scores)
bow39604_appA_AP1-AP27.indd Page AP-20 21/11/13 1:35 PM f-w-512 bow39604_appA_AP1-AP27.indd Page AP-20 21/11/13 1:35 PM f-w-512 /203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles/203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles
Appendix A Statistical Tables AP-21
TAB
LE A
.13
A
Tabl
e of
Crit
ical
Val
ues
for t
he D
urbi
n–W
atso
n d
Stat
istic
(a 5
0.0
25)
k
5 1
k
5 2
k
5 3
k
5 4
k
5 5
n
dL,
0.02
5 d
U,0
.025
d
L,0.
025
dU
,0.0
25
dL,
0.02
5 d
U,0
.025
d
L,0.
025
dU
,0.0
25
dL,
0.02
5 d
U,0
.025
15
0.95
1.
23
0.83
1.
40
0.71
1.
61
0.59
1.
84
0.48
2.
09 1
6 0.
98
1.24
0.
86
1.40
0.
75
1.59
0.
64
1.80
0.
53
2.03
17
1.01
1.
25
0.90
1.
40
0.79
1.
58
0.68
1.
77
0.57
1.
98 1
8 1.
03
1.26
0.
93
1.40
0.
82
1.56
0.
72
1.74
0.
62
1.93
19
1.06
1.
28
0.96
1.
41
0.86
1.
55
0.76
1.
72
0.66
1.
90 2
0 1.
08
1.28
0.
99
1.41
0.
89
1.55
0.
79
1.70
0.
70
1.87
21
1.10
1.
30
1.01
1.
41
0.92
1.
54
0.83
1.
69
0.73
1.
84 2
2 1.
12
1.31
1.
04
1.42
0.
95
1.54
0.
86
1.68
0.
77
1.82
23
1.14
1.
32
1.06
1.
42
0.97
1.
54
0.89
1.
67
0.80
1.
80 2
4 1.
16
1.33
1.
08
1.43
1.
00
1.54
0.
91
1.66
0.
83
1.79
25
1.18
1.
34
1.10
1.
43
1.02
1.
54
0.94
1.
65
0.86
1.
77 2
6 1.
19
1.35
1.
12
1.44
1.
04
1.54
0.
96
1.65
0.
88
1.76
27
1.21
1.
36
1.13
1.
44
1.06
1.
54
0.99
1.
64
0.91
1.
75 2
8 1.
22
1.37
1.
15
1.45
1.
08
1.54
1.
01
1.64
0.
93
1.74
29
1.24
1.
38
1.17
1.
45
1.10
1.
54
1.03
1.
63
0.96
1.
73 3
0 1.
25
1.38
1.
18
1.46
1.
12
1.54
1.
05
1.63
0.
98
1.73
31
1.26
1.
39
1.20
1.
47
1.13
1.
55
1.07
1.
63
1.00
1.
72 3
2 1.
27
1.40
1.
21
1.47
1.
15
1.55
1.
08
1.63
1.
02
1.71
33
1.28
1.
41
1.22
1.
48
1.16
1.
55
1.10
1.
63
1.04
1.
71 3
4 1.
29
1.41
1.
24
1.48
1.
17
1.55
1.
12
1.63
1.
06
1.70
35
1.30
1.
42
1.25
1.
48
1.19
1.
55
1.13
1.
63
1.07
1.
70 3
6 1.
31
1.43
1.
26
1.49
1.
20
1.56
1.
15
1.63
1.
09
1.70
37
1.32
1.
43
1.27
1.
49
1.21
1.
56
1.16
1.
62
1.10
1.
70 3
8 1.
33
1.44
1.
28
1.50
1.
23
1.56
1.
17
1.62
1.
12
1.70
39
1.34
1.
44
1.29
1.
50
1.24
1.
56
1.19
1.
63
1.13
1.
69 4
0 1.
35
1.45
1.
30
1.51
1.
25
1.57
1.
20
1.63
1.
15
1.69
45
1.39
1.
48
1.34
1.
53
1.30
1.
58
1.25
1.
63
1.21
1.
69 5
0 1.
42
1.50
1.
38
1.54
1.
34
1.59
1.
30
1.64
1.
26
1.69
55
1.45
1.
52
1.41
1.
56
1.37
1.
60
1.33
1.
64
1.30
1.
69 6
0 1.
47
1.54
1.
44
1.57
1.
40
1.61
1.
37
1.65
1.
33
1.69
65
1.49
1.
55
1.46
1.
59
1.43
1.
62
1.40
1.
66
1.36
1.
69 7
0 1.
51
1.57
1.
48
1.60
1.
45
1.63
1.
42
1.66
1.
39
1.70
75
1.53
1.
58
1.50
1.
61
1.47
1.
64
1.45
1.
67
1.42
1.
70 8
0 1.
54
1.59
1.
52
1.62
1.
49
1.65
1.
47
1.67
1.
44
1.70
85
1.56
1.
60
1.53
1.
63
1.51
1.
65
1.49
1.
68
1.46
1.
71 9
0 1.
57
1.61
1.
55
1.64
1.
53
1.66
1.
50
1.69
1.
48
1.71
95
1.58
1.
62
1.56
1.
65
1.54
1.
67
1.52
1.
69
1.50
1.
7110
0 1.
59
1.63
1.
57
1.65
1.
55
1.67
1.
53
1.70
1.
51
1.72
Sou
rce:
J.
Du
rbin
an
d G
. S.
Wat
son
, “T
esti
ng
fo
r Se
rial
Co
rrel
atio
n i
n L
east
Sq
uar
es R
egre
ssio
n,
II,”
Bio
met
rika
30
(195
1),
pp
. 15
9–78
. R
epro
du
ced
by
per
mis
sio
n o
f th
e B
iom
etri
ka T
rust
ees.
k
5 1
k
5 2
k
5 3
k
5 4
k
5 5
n
dL,
0.05
d
U,0
.05
dL,
0.05
d
U,0
.05
dL,
0.05
d
U,0
.05
dL,
0.05
d
U,0
.05
dL,
0.05
d
U,0
.05
15
1.08
1.
36
0.95
1.
54
0.82
1.
75
0.69
1.
97
0.56
2.
21 1
6 1.
10
1.37
0.
98
1.54
0.
86
1.73
0.
74
1.93
0.
62
2.15
17
1.13
1.
38
1.02
1.
54
0.90
1.
71
0.78
1.
90
0.67
2.
10 1
8 1.
16
1.39
1.
05
1.53
0.
93
1.69
0.
82
1.87
0.
71
2.06
19
1.18
1.
40
1.08
1.
53
0.97
1.
68
0.86
1.
85
0.75
2.
02 2
0 1.
20
1.41
1.
10
1.54
1.
00
1.68
0.
90
1.83
0.
79
1.99
21
1.22
1.
42
1.13
1.
54
1.03
1.
67
0.93
1.
81
0.83
1.
96 2
2 1.
24
1.43
1.
15
1.54
1.
05
1.66
0.
96
1.80
0.
86
1.94
23
1.26
1.
44
1.17
1.
54
1.08
1.
66
0.99
1.
79
0.90
1.
92 2
4 1.
27
1.45
1.
19
1.55
1.
10
1.66
1.
01
1.78
0.
93
1.90
25
1.29
1.
45
1.21
1.
55
1.12
1.
66
1.04
1.
77
0.95
1.
89 2
6 1.
30
1.46
1.
22
1.55
1.
14
1.65
1.
06
1.76
0.
98
1.88
27
1.32
1.
47
1.24
1.
56
1.16
1.
65
1.08
1.
76
1.01
1.
86 2
8 1.
33
1.48
1.
26
1.56
1.
18
1.65
1.
10
1.75
1.
03
1.85
29
1.34
1.
48
1.27
1.
56
1.20
1.
65
1.12
1.
74
1.05
1.
84 3
0 1.
35
1.49
1.
28
1.57
1.
21
1.65
1.
14
1.74
1.
07
1.83
31
1.36
1.
50
1.30
1.
57
1.23
1.
65
1.16
1.
74
1.09
1.
83 3
2 1.
37
1.50
1.
31
1.57
1.
24
1.65
1.
18
1.73
1.
11
1.82
33
1.38
1.
51
1.32
1.
58
1.26
1.
65
1.19
1.
73
1.13
1.
81 3
4 1.
39
1.51
1.
33
1.58
1.
27
1.65
1.
21
1.73
1.
15
1.81
35
1.40
1.
52
1.34
1.
58
1.28
1.
65
1.22
1.
73
1.16
1.
80 3
6 1.
41
1.52
1.
35
1.59
1.
29
1.65
1.
24
1.73
1.
18
1.80
37
1.42
1.
53
1.36
1.
59
1.31
1.
66
1.25
1.
72
1.19
1.
80 3
8 1.
43
1.54
1.
37
1.59
1.
32
1.66
1.
26
1.72
1.
21
1.79
39
1.43
1.
54
1.38
1.
60
1.33
1.
66
1.27
1.
72
1.22
1.
79 4
0 1.
44
1.54
1.
39
1.60
1.
34
1.66
1.
29
1.72
1.
23
1.79
45
1.48
1.
57
1.43
1.
62
1.38
1.
67
1.34
1.
72
1.29
1.
78 5
0 1.
50
1.59
1.
46
1.63
1.
42
1.67
1.
38
1.72
1.
34
1.77
55
1.53
1.
60
1.49
1.
64
1.45
1.
68
1.41
1.
72
1.38
1.
77 6
0 1.
55
1.62
1.
51
1.65
1.
48
1.69
1.
44
1.73
1.
41
1.77
65
1.57
1.
63
1.54
1.
66
1.50
1.
70
1.47
1.
73
1.44
1.
77 7
0 1.
58
1.64
1.
55
1.67
1.
52
1.70
1.
49
1.74
1.
46
1.77
75
1.60
1.
65
1.57
1.
68
1.54
1.
71
1.51
1.
74
1.49
1.
77 8
0 1.
61
1.66
1.
59
1.69
1.
56
1.72
1.
53
1.74
1.
51
1.77
85
1.62
1.
67
1.60
1.
70
1.57
1.
72
1.55
1.
75
1.52
1.
77 9
0 1.
63
1.68
1.
61
1.70
1.
59
1.73
1.
57
1.75
1.
54
1.78
95
1.64
1.
69
1.62
1.
71
1.60
1.
73
1.58
1.
75
1.56
1.
7810
0 1.
65
1.69
1.
63
1.72
1.
61
1.74
1.
59
1.76
1.
57
1.78
Sou
rce:
J.
Du
rbin
an
d G
. S.
Wat
son
, “T
esti
ng
fo
r Se
rial
Co
rrel
atio
n i
n L
east
Sq
uar
es R
egre
ssio
n,
II,”
Bio
met
rika
30
(195
1),
pp
. 15
9–78
. R
epro
du
ced
by
per
mis
sio
n o
f th
e B
iom
etri
ka T
rust
ees.
TAB
LE A
.12
A
Tabl
e of
Crit
ical
Val
ues
for t
he D
urbi
n–W
atso
n d
Stat
istic
(a 5
0.0
5)
bow39604_appA_AP1-AP27.indd Page AP-21 21/11/13 1:35 PM f-w-512 bow39604_appA_AP1-AP27.indd Page AP-21 21/11/13 1:35 PM f-w-512 /203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles/203/MHR00232/bow39604_disk1of1/0071339604/bow39604_pagefiles
AP-22 Appendix A Statistical Tables
k 5 1 k 5 2 k 5 3 k 5 4 k 5 5
n dL,0.01 dU,0.01 dL,0.01 dU,0.01 dL,0.01 dU,0.01 dL,0.01 dU,0.01 dL,0.01 dU,0.01
15 0.81 1.07 0.70 1.25 0.59 1.46 0.49 1.70 0.39 1.96 16 0.84 1.09 0.74 1.25 0.63 1.44 0.53 1.66 0.44 1.90 17 0.87 1.10 0.77 1.25 0.67 1.43 0.57 1.63 0.48 1.85 18 0.90 1.12 0.80 1.26 0.71 1.42 0.61 1.60 0.52 1.80 19 0.93 1.13 0.83 1.26 0.74 1.41 0.65 1.58 0.56 1.77 20 0.95 1.15 0.86 1.27 0.77 1.41 0.68 1.57 0.60 1.74 21 0.97 1.16 0.89 1.27 0.80 1.41 0.72 1.55 0.63 1.71 22 1.00 1.17 0.91 1.28 0.83 1.40 0.75 1.54 0.66 1.69 23 1.02 1.19 0.94 1.29 0.86 1.40 0.77 1.53 0.70 1.67 24 1.04 1.20 0.96 1.30 0.88 1.41 0.80 1.53 0.72 1.66 25 1.05 1.21 0.98 1.30 0.90 1.41 0.83 1.52 0.75 1.65 26 1.07 1.22 1.00 1.31 0.93 1.41 0.85 1.52 0.78 1.64 27 1.09 1.23 1.02 1.32 0.95 1.41 0.88 1.51 0.81 1.63 28 1.10 1.24 1.04 1.32 0.97 1.41 0.90 1.51 0.83 1.62 29 1.12 1.25 1.05 1.33 0.99 1.42 0.92 1.51 0.85 1.61 30 1.13 1.26 1.07 1.34 1.01 1.42 0.94 1.51 0.88 1.61 31 1.15 1.27 1.08 1.34 1.02 1.42 0.96 1.51 0.90 1.60 32 1.16 1.28 1.10 1.35 1.04 1.43 0.98 1.51 0.92 1.60 33 1.17 1.29 1.11 1.36 1.05 1.43 1.00 1.51 0.94 1.59 34 1.18 1.30 1.13 1.36 1.07 1.43 1.01 1.51 0.95 1.59 35 1.19 1.31 1.14 1.37 1.08 1.44 1.03 1.51 0.97 1.59 36 1.21 1.32 1.15 1.38 1.10 1.44 1.04 1.51 0.99 1.59 37 1.22 1.32 1.16 1.38 1.11 1.45 1.06 1.51 1.00 1.59 38 1.23 1.33 1.18 1.39 1.12 1.45 1.07 1.52 1.02 1.58 39 1.24 1.34 1.19 1.39 1.14 1.45 1.09 1.52 1.03 1.58 40 1.25 1.34 1.20 1.40 1.15 1.46 1.10 1.52 1.05 1.58 45 1.29 1.38 1.24 1.42 1.20 1.48 1.16 1.53 1.11 1.58 50 1.32 1.40 1.28 1.45 1.24 1.49 1.20 1.54 1.16 1.59 55 1.36 1.43 1.32 1.47 1.28 1.51 1.25 1.55 1.21 1.59 60 1.38 1.45 1.35 1.48 1.32 1.52 1.28 1.56 1.25 1.60 65 1.41 1.47 1.38 1.50 1.35 1.53 1.31 1.57 1.28 1.61 70 1.43 1.49 1.40 1.52 1.37 1.55 1.34 1.58 1.31 1.61 75 1.45 1.50 1.42 1.53 1.39 1.56 1.37 1.59 1.34 1.62 80 1.47 1.52 1.44 1.54 1.42 1.57 1.39 1.60 1.36 1.62 85 1.48 1.53 1.46 1.55 1.43 1.58 1.41 1.60 1.39 1.63 90 1.50 1.54 1.47 1.56 1.45 1.59 1.43 1.61 1.41 1.64 95 1.51 1.55 1.49 1.57 1.47 1.60 1.45 1.62 1.42 1.64100 1.52 1.56 1.50 1.58 1.48 1.60 1.46 1.63 1.44 1.65
Source: J. Durbin and G. S. Watson, “Testing for Serial Correlation in Least Squares Regression, II,” Biometrika 30 (1951), pp. 159–78. Reproduced by permission of the Biometrika Trustees.
TABLE A.14 A Table of Critical Values for the Durbin–Watson d Statistic (a 5 0.01)
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Appendix A Statistical Tables AP-23
3 4 5 6 7 8 9 10
TL TU TL TU TL TU TL TU TL TU TL TU TL TU TL TU
3 5 16 6 18 6 21 7 23 7 26 8 28 8 31 9 33 4 6 18 11 25 12 28 12 32 13 35 14 38 15 41 16 44 5 6 21 12 28 18 37 19 41 20 45 21 49 22 53 24 56 6 7 23 12 32 19 41 26 52 28 56 29 61 31 65 32 70 7 7 26 13 35 20 45 28 56 37 68 39 73 41 78 43 83 8 8 28 14 38 21 49 29 61 39 73 49 87 51 93 54 98 9 8 31 15 41 22 53 31 65 41 78 51 93 63 108 66 11410 9 33 16 44 24 56 32 70 43 83 54 98 66 114 79 131
n1
n2
3 4 5 6 7 8 9 10
TL TU TL TU TL TU TL TU TL TU TL TU TL TU TL TU
3 6 15 7 17 7 20 8 22 9 24 9 27 10 29 11 31 4 7 17 12 24 13 27 14 30 15 33 16 36 17 39 18 42 5 7 20 13 27 19 36 20 40 22 43 24 46 25 50 26 54 6 8 22 14 30 20 40 28 50 30 54 32 58 33 63 35 67 7 9 24 15 33 22 43 30 54 39 66 41 71 43 76 46 80 8 9 27 16 36 24 46 32 58 41 71 52 84 54 90 57 95 9 10 29 17 39 25 50 33 63 43 76 54 90 66 105 69 11110 11 31 18 42 26 54 35 67 46 80 57 95 69 111 83 127
Source: F. Wilcoxon and R. A. Wilcox, “Some Rapid Approximate Statistical Procedures” (New York: American Cyanamid Company, 1964), pp. 20–23. Reproduced with the permission of American Cyanamid Company.
n1
n2
(b) A 5 0.05 one-sided; A 5 0.10 two-sided
(a) A 5 0.025 one-sided; A 5 0.05 two-sided
TABLE A.15 A Wilcoxon Rank Sum Table: Values of TL and TU
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AP-24 Appendix A Statistical Tables
TABLE A.16 A Wilcoxon Signed Ranks Table: Values of T0
One-Sided Two-Sided n 5 5 n 5 6 n 5 7 n 5 8 n 5 9 n 5 10
a 5 0.05 a 5 0.10 1 2 4 6 8 11a 5 0.025 a 5 0.05 1 2 4 6 8a 5 0.01 a 5 0.02 0 2 3 5a 5 0.005 a 5 0.01 0 2 3
n 5 11 n 5 12 n 5 13 n 5 14 n 5 15 n 5 16
a 5 0.05 a 5 0.10 14 17 21 26 30 36a 5 0.025 a 5 0.05 11 14 17 21 25 30a 5 0.01 a 5 0.02 7 10 13 16 20 24a 5 0.005 a 5 0.01 5 7 10 13 16 19
n 5 17 n 5 18 n 5 19 n 5 20 n 5 21 n 5 22
a 5 0.05 a 5 0.10 41 47 54 60 68 75a 5 0.025 a 5 0.05 35 40 46 52 59 66a 5 0.01 a 5 0.02 28 33 38 43 49 56a 5 0.005 a 5 0.01 23 28 32 37 43 49
n 5 23 n 5 24 n 5 25 n 5 26 n 5 27 n 5 28
a 5 0.05 a 5 0.10 83 92 101 110 120 130a 5 0.025 a 5 0.05 73 81 90 98 107 117a 5 0.01 a 5 0.02 62 69 77 85 93 102a 5 0.005 a 5 0.01 55 61 68 76 84 92
n 5 29 n 5 30 n 5 31 n 5 32 n 5 33 n 5 34
a 5 0.05 a 5 0.10 141 152 163 175 188 201a 5 0.025 a 5 0.05 127 137 148 159 171 183a 5 0.01 a 5 0.02 111 120 130 141 151 162a 5 0.005 a 5 0.01 100 109 118 128 138 149
n 5 35 n 5 36 n 5 37 n 5 38 n 5 39
a 5 0.05 a 5 0.10 214 228 242 256 271a 5 0.025 a 5 0.05 195 208 222 235 250a 5 0.01 a 5 0.02 174 186 198 211 224a 5 0.005 a 5 0.01 160 171 183 195 208
n 5 40 n 5 41 n 5 42 n 5 43 n 5 44 n 5 45
a 5 0.05 a 5 0.10 287 303 319 336 353 371a 5 0.025 a 5 0.05 264 279 295 311 327 344a 5 0.01 a 5 0.02 238 252 267 281 297 313a 5 0.005 a 5 0.01 221 234 248 262 277 292
n 5 46 n 5 47 n 5 48 n 5 49 n 5 50
a 5 0.05 a 5 0.10 389 408 427 446 466a 5 0.025 a 5 0.05 361 379 397 415 434a 5 0.01 a 5 0.02 329 345 362 380 398a 5 0.005 a 5 0.01 307 323 339 356 373
Source: F. Wilcoxon and R. A. Wilcox, “Some Rapid Approximate Statistical Procedures” (New York: American Cyanamid Company, 1964), p. 28. Reproduced with the permission of American Cyanamid Company.
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Appendix A Statistical Tables AP-25
TABLE A.17 A Table of Critical Values for Spearman’s Rank Correlation Coeffi cient
n A 5 0.05 A 5 0.025 A 5 0.01 A 5 0.005 n A 5 0.05 A 5 0.025 A 5 0.01 A 5 0.005
5 0.900 — — — 18 0.399 0.476 0.564 0.625 6 0.829 0.886 0.943 — 19 0.388 0.462 0.549 0.608 7 0.714 0.786 0.893 — 20 0.377 0.450 0.534 0.591 8 0.643 0.738 0.833 0.881 21 0.368 0.438 0.521 0.576 9 0.600 0.683 0.783 0.833 22 0.359 0.428 0.508 0.56210 0.564 0.648 0.745 0.794 23 0.351 0.418 0.496 0.54911 0.523 0.623 0.736 0.818 24 0.343 0.409 0.485 0.53712 0.497 0.591 0.703 0.780 25 0.336 0.400 0.475 0.52613 0.475 0.566 0.673 0.745 26 0.329 0.392 0.465 0.51514 0.457 0.545 0.646 0.716 27 0.323 0.385 0.456 0.50515 0.441 0.525 0.623 0.689 28 0.317 0.377 0.448 0.49616 0.425 0.507 0.601 0.666 29 0.311 0.370 0.440 0.48717 0.412 0.490 0.582 0.645 30 0.305 0.364 0.432 0.478
Source: E. G. Olds, “Distribution of Sums of Squares of Rank Differences for Small Samples,” Annals of Mathematical Statistics, 1938, 9. Reproduced with the permission of the editor, Annals of Mathematical Statistics.
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AP-26 Appendix A Statistical Tables
TABLE A.18 A Chi-Square Table: Values of χ2a
df X20.995 X2
0.99 X20.975 X2
0.95 X20.90
1 0.0000393 0.0001571 0.0009821 0.0039321 0.0157908 2 0.0100251 0.0201007 0.0506356 0.102587 0.210720 3 0.0717212 0.114832 0.215795 0.341846 0.584375 4 0.206990 0.297110 0.484419 0.710721 0.063623 5 0.411740 0.554300 0.831211 1.145476 1.61031 6 0.675727 0.872085 1.237347 1.63539 2.20413 7 0.989265 1.239043 1.68987 2.16735 2.83311 8 1.344419 1.646482 2.17973 2.73264 3.48954 9 1.734926 2.087912 2.70039 3.32511 4.16816 10 2.15585 2.55821 3.24697 3.94030 4.86518 11 2.60321 3.05347 3.81575 4.57481 5.57779 12 3.07382 3.57056 4.40379 5.22603 6.30380 13 3.56503 4.10691 5.00874 5.89186 7.04150 14 4.07468 4.66043 5.62872 6.57063 7.78953 15 4.60094 5.22935 6.26214 7.26094 8.54675 16 5.14224 5.81221 6.90766 7.96164 9.31223 17 5.69724 6.40776 7.56418 8.67176 10.0852 18 6.26481 7.01491 8.23075 9.39046 10.8649 19 6.84398 7.63273 8.90655 10.1170 11.6509 20 7.43386 8.26040 9.59083 10.8508 12.4426 21 8.03366 8.89720 10.28293 11.5913 13.2396 22 8.64272 9.54249 10.9823 12.3380 14.0415 23 9.26042 10.19567 11.6885 13.0905 14.8479 24 9.88623 10.8564 12.4011 13.8484 15.6587 25 10.5197 11.5240 13.1197 14.6114 16.4734 26 11.1603 12.1981 13.8439 15.3791 17.2919 27 11.8076 12.8786 14.5733 16.1513 18.1138 28 12.4613 13.5648 15.3079 16.9279 18.9392 29 13.1211 14.2565 16.0471 17.7083 19.7677 30 13.7867 14.9535 16.7908 18.4926 20.5992 40 20.7065 22.1643 24.4331 26.5093 29.0505 50 27.9907 29.7067 32.3574 34.7642 37.6886 60 35.5346 37.4848 40.4817 43.1879 46.4589 70 43.2752 45.4418 48.7576 51.7393 55.3290 80 51.1720 53.5400 57.1532 60.3915 64.2778 90 59.1963 61.7541 65.6466 69.1260 73.2912 100 67.3276 70.0648 74.2219 77.9295 82.3581
0 x2a
a
(table continued)
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Appendix A Statistical Tables AP-27
TABLE A.18 (concluded) A Chi-Square Table: Values of χ2a
Source: C. M. Thompson, “Tables of the Percentage Points of the x2 Distribution,” Biometrika 32 (1941), pp. 188–89. Reproduced by permission of the Biometrika Trustees.
df X20.10 X2
0.05 X20.025 X2
0.01 X20.005
1 2.70554 3.84146 5.02389 6.63490 7.87944 2 4.60517 5.99147 7.37776 9.21034 10.5966 3 6.25139 7.81473 9.34840 11.3449 12.8381 4 7.77944 9.48773 11.1433 13.2767 14.8602 5 9.23635 11.0705 12.8325 15.0863 16.7496 6 10.6446 12.5916 14.4494 16.8119 18.5476 7 12.0170 14.0671 16.0128 18.4753 20.2777 8 13.3616 15.5073 17.5346 20.0902 21.9550 9 14.6837 16.9190 19.0228 21.6660 23.5893 10 15.9871 18.3070 20.4831 23.2093 25.1882 11 17.2750 19.6751 21.9200 24.7250 26.7569 12 18.5494 21.0261 23.3367 26.2170 28.2995 13 19.8119 22.3621 24.7356 27.6883 29.8194 14 21.0642 23.6848 26.1190 29.1413 31.3193 15 22.3072 24.9958 27.4884 30.5779 32.8013 16 23.5418 26.2962 28.8454 31.9999 34.2672 17 24.7690 27.5871 30.1910 33.4087 35.7185 18 25.9894 28.8693 31.5264 34.8053 37.1564 19 27.2036 30.1435 32.8523 36.1908 38.5822 20 28.4120 31.4104 34.1696 37.5662 39.9968 21 29.6151 32.6705 35.4789 38.9321 41.4010 22 30.8133 33.9244 36.7807 40.2894 42.7956 23 32.0069 35.1725 38.0757 41.6384 44.1813 24 33.1963 36.4151 39.3641 42.9798 45.5585 25 34.3816 37.6525 40.6465 44.3141 46.9278 26 35.5631 38.8852 41.9232 45.6417 48.2899 27 36.7412 40.1133 43.1944 46.9630 49.6449 28 37.9159 41.3372 44.4607 48.2782 50.9933 29 39.0875 42.5569 45.7222 49.5879 52.3356 30 40.2560 43.7729 46.9792 50.8922 53.6720 40 51.8050 55.7585 59.3417 63.6907 66.7659 50 63.1671 67.5048 71.4202 76.1539 79.4900 60 74.3970 79.0819 83.2976 88.3794 91.9517 70 85.5271 90.5312 95.0231 100.425 104.215 80 96.5782 101.879 106.629 112.329 116.321 90 107.565 113.145 118.136 124.116 128.299 100 118.498 124.342 129.561 135.807 140.169
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