Tables
This report creates the tables.
knitr::opts_knit$set(root.dir='../') #Don't combine this call with any other chunk -especially one that uses file paths.
library(knitr)
opts_chunk$set(
results = 'asis',
message = TRUE,
comment = NA,
tidy = FALSE
)
echoChunks <- FALSE
options(width=120) #So the output is 50% wider than the default.
read_chunk("./tables/tables.R")
Table A.1: Standard normal distribution
0.00 |
.0000 |
.5000 |
0.38 |
.1480 |
.3520 |
0.76 |
.2764 |
.2236 |
1.14 |
.3729 |
.1271 |
1.52 |
.4357 |
.0643 |
1.90 |
.4713 |
.0287 |
2.28 |
.4887 |
.0113 |
2.66 |
.4961 |
.0039 |
3.04 |
.4988 |
.0012 |
0.01 |
.0040 |
.4960 |
0.39 |
.1517 |
.3483 |
0.77 |
.2794 |
.2206 |
1.15 |
.3749 |
.1251 |
1.53 |
.4370 |
.0630 |
1.91 |
.4719 |
.0281 |
2.29 |
.4890 |
.0110 |
2.67 |
.4962 |
.0038 |
3.05 |
.4989 |
.0011 |
0.02 |
.0080 |
.4920 |
0.40 |
.1554 |
.3446 |
0.78 |
.2823 |
.2177 |
1.16 |
.3770 |
.1230 |
1.54 |
.4382 |
.0618 |
1.92 |
.4726 |
.0274 |
2.30 |
.4893 |
.0107 |
2.68 |
.4963 |
.0037 |
3.06 |
.4989 |
.0011 |
0.03 |
.0120 |
.4880 |
0.41 |
.1591 |
.3409 |
0.79 |
.2852 |
.2148 |
1.17 |
.3790 |
.1210 |
1.55 |
.4394 |
.0606 |
1.93 |
.4732 |
.0268 |
2.31 |
.4896 |
.0104 |
2.69 |
.4964 |
.0036 |
3.07 |
.4989 |
.0011 |
0.04 |
.0160 |
.4840 |
0.42 |
.1628 |
.3372 |
0.80 |
.2881 |
.2119 |
1.18 |
.3810 |
.1190 |
1.56 |
.4406 |
.0594 |
1.94 |
.4738 |
.0262 |
2.32 |
.4898 |
.0102 |
2.70 |
.4965 |
.0035 |
3.08 |
.4990 |
.0010 |
0.05 |
.0199 |
.4801 |
0.43 |
.1664 |
.3336 |
0.81 |
.2910 |
.2090 |
1.19 |
.3830 |
.1170 |
1.57 |
.4418 |
.0582 |
1.95 |
.4744 |
.0256 |
2.33 |
.4901 |
.0099 |
2.71 |
.4966 |
.0034 |
3.09 |
.4990 |
.0010 |
0.06 |
.0239 |
.4761 |
0.44 |
.1700 |
.3300 |
0.82 |
.2939 |
.2061 |
1.20 |
.3849 |
.1151 |
1.58 |
.4429 |
.0571 |
1.96 |
.4750 |
.0250 |
2.34 |
.4904 |
.0096 |
2.72 |
.4967 |
.0033 |
3.10 |
.4990 |
.0010 |
0.07 |
.0279 |
.4721 |
0.45 |
.1736 |
.3264 |
0.83 |
.2967 |
.2033 |
1.21 |
.3869 |
.1131 |
1.59 |
.4441 |
.0559 |
1.97 |
.4756 |
.0244 |
2.35 |
.4906 |
.0094 |
2.73 |
.4968 |
.0032 |
3.11 |
.4991 |
.0009 |
0.08 |
.0319 |
.4681 |
0.46 |
.1772 |
.3228 |
0.84 |
.2995 |
.2005 |
1.22 |
.3888 |
.1112 |
1.60 |
.4452 |
.0548 |
1.98 |
.4761 |
.0239 |
2.36 |
.4909 |
.0091 |
2.74 |
.4969 |
.0031 |
3.12 |
.4991 |
.0009 |
0.09 |
.0359 |
.4641 |
0.47 |
.1808 |
.3192 |
0.85 |
.3023 |
.1977 |
1.23 |
.3907 |
.1093 |
1.61 |
.4463 |
.0537 |
1.99 |
.4767 |
.0233 |
2.37 |
.4911 |
.0089 |
2.75 |
.4970 |
.0030 |
3.13 |
.4991 |
.0009 |
0.10 |
.0398 |
.4602 |
0.48 |
.1844 |
.3156 |
0.86 |
.3051 |
.1949 |
1.24 |
.3925 |
.1075 |
1.62 |
.4474 |
.0526 |
2.00 |
.4772 |
.0228 |
2.38 |
.4913 |
.0087 |
2.76 |
.4971 |
.0029 |
3.14 |
.4992 |
.0008 |
0.11 |
.0438 |
.4562 |
0.49 |
.1879 |
.3121 |
0.87 |
.3078 |
.1922 |
1.25 |
.3944 |
.1056 |
1.63 |
.4484 |
.0516 |
2.01 |
.4778 |
.0222 |
2.39 |
.4916 |
.0084 |
2.77 |
.4972 |
.0028 |
3.15 |
.4992 |
.0008 |
0.12 |
.0478 |
.4522 |
0.50 |
.1915 |
.3085 |
0.88 |
.3106 |
.1894 |
1.26 |
.3962 |
.1038 |
1.64 |
.4495 |
.0505 |
2.02 |
.4783 |
.0217 |
2.40 |
.4918 |
.0082 |
2.78 |
.4973 |
.0027 |
3.16 |
.4992 |
.0008 |
0.13 |
.0517 |
.4483 |
0.51 |
.1950 |
.3050 |
0.89 |
.3133 |
.1867 |
1.27 |
.3980 |
.1020 |
1.65 |
.4505 |
.0495 |
2.03 |
.4788 |
.0212 |
2.41 |
.4920 |
.0080 |
2.79 |
.4974 |
.0026 |
3.17 |
.4992 |
.0008 |
0.14 |
.0557 |
.4443 |
0.52 |
.1985 |
.3015 |
0.90 |
.3159 |
.1841 |
1.28 |
.3997 |
.1003 |
1.66 |
.4515 |
.0485 |
2.04 |
.4793 |
.0207 |
2.42 |
.4922 |
.0078 |
2.80 |
.4974 |
.0026 |
3.18 |
.4993 |
.0007 |
0.15 |
.0596 |
.4404 |
0.53 |
.2019 |
.2981 |
0.91 |
.3186 |
.1814 |
1.29 |
.4015 |
.0985 |
1.67 |
.4525 |
.0475 |
2.05 |
.4798 |
.0202 |
2.43 |
.4925 |
.0075 |
2.81 |
.4975 |
.0025 |
3.19 |
.4993 |
.0007 |
0.16 |
.0636 |
.4364 |
0.54 |
.2054 |
.2946 |
0.92 |
.3212 |
.1788 |
1.30 |
.4032 |
.0968 |
1.68 |
.4535 |
.0465 |
2.06 |
.4803 |
.0197 |
2.44 |
.4927 |
.0073 |
2.82 |
.4976 |
.0024 |
3.20 |
.4993 |
.0007 |
0.17 |
.0675 |
.4325 |
0.55 |
.2088 |
.2912 |
0.93 |
.3238 |
.1762 |
1.31 |
.4049 |
.0951 |
1.69 |
.4545 |
.0455 |
2.07 |
.4808 |
.0192 |
2.45 |
.4929 |
.0071 |
2.83 |
.4977 |
.0023 |
3.21 |
.4993 |
.0007 |
0.18 |
.0714 |
.4286 |
0.56 |
.2123 |
.2877 |
0.94 |
.3264 |
.1736 |
1.32 |
.4066 |
.0934 |
1.70 |
.4554 |
.0446 |
2.08 |
.4812 |
.0188 |
2.46 |
.4931 |
.0069 |
2.84 |
.4977 |
.0023 |
3.22 |
.4994 |
.0006 |
0.19 |
.0753 |
.4247 |
0.57 |
.2157 |
.2843 |
0.95 |
.3289 |
.1711 |
1.33 |
.4082 |
.0918 |
1.71 |
.4564 |
.0436 |
2.09 |
.4817 |
.0183 |
2.47 |
.4932 |
.0068 |
2.85 |
.4978 |
.0022 |
3.23 |
.4994 |
.0006 |
0.20 |
.0793 |
.4207 |
0.58 |
.2190 |
.2810 |
0.96 |
.3315 |
.1685 |
1.34 |
.4099 |
.0901 |
1.72 |
.4573 |
.0427 |
2.10 |
.4821 |
.0179 |
2.48 |
.4934 |
.0066 |
2.86 |
.4979 |
.0021 |
3.24 |
.4994 |
.0006 |
0.21 |
.0832 |
.4168 |
0.59 |
.2224 |
.2776 |
0.97 |
.3340 |
.1660 |
1.35 |
.4115 |
.0885 |
1.73 |
.4582 |
.0418 |
2.11 |
.4826 |
.0174 |
2.49 |
.4936 |
.0064 |
2.87 |
.4979 |
.0021 |
3.25 |
.4994 |
.0006 |
0.22 |
.0871 |
.4129 |
0.60 |
.2257 |
.2743 |
0.98 |
.3365 |
.1635 |
1.36 |
.4131 |
.0869 |
1.74 |
.4591 |
.0409 |
2.12 |
.4830 |
.0170 |
2.50 |
.4938 |
.0062 |
2.88 |
.4980 |
.0020 |
3.30 |
.49952 |
.00048 |
0.23 |
.0910 |
.4090 |
0.61 |
.2291 |
.2709 |
0.99 |
.3389 |
.1611 |
1.37 |
.4147 |
.0853 |
1.75 |
.4599 |
.0401 |
2.13 |
.4834 |
.0166 |
2.51 |
.4940 |
.0060 |
2.89 |
.4981 |
.0019 |
3.35 |
.49960 |
.00040 |
0.24 |
.0948 |
.4052 |
0.62 |
.2324 |
.2676 |
1.00 |
.3413 |
.1587 |
1.38 |
.4162 |
.0838 |
1.76 |
.4608 |
.0392 |
2.14 |
.4838 |
.0162 |
2.52 |
.4941 |
.0059 |
2.90 |
.4981 |
.0019 |
3.40 |
.49966 |
.00034 |
0.25 |
.0987 |
.4013 |
0.63 |
.2357 |
.2643 |
1.01 |
.3438 |
.1562 |
1.39 |
.4177 |
.0823 |
1.77 |
.4616 |
.0384 |
2.15 |
.4842 |
.0158 |
2.53 |
.4943 |
.0057 |
2.91 |
.4982 |
.0018 |
3.45 |
.49972 |
.00028 |
0.26 |
.1026 |
.3974 |
0.64 |
.2389 |
.2611 |
1.02 |
.3461 |
.1539 |
1.40 |
.4192 |
.0808 |
1.78 |
.4625 |
.0375 |
2.16 |
.4846 |
.0154 |
2.54 |
.4945 |
.0055 |
2.92 |
.4982 |
.0018 |
3.50 |
.49977 |
.00023 |
0.27 |
.1064 |
.3936 |
0.65 |
.2422 |
.2578 |
1.03 |
.3485 |
.1515 |
1.41 |
.4207 |
.0793 |
1.79 |
.4633 |
.0367 |
2.17 |
.4850 |
.0150 |
2.55 |
.4946 |
.0054 |
2.93 |
.4983 |
.0017 |
3.60 |
.49984 |
.00016 |
0.28 |
.1103 |
.3897 |
0.66 |
.2454 |
.2546 |
1.04 |
.3508 |
.1492 |
1.42 |
.4222 |
.0778 |
1.80 |
.4641 |
.0359 |
2.18 |
.4854 |
.0146 |
2.56 |
.4948 |
.0052 |
2.94 |
.4984 |
.0016 |
3.70 |
.49989 |
.00011 |
0.29 |
.1141 |
.3859 |
0.67 |
.2486 |
.2514 |
1.05 |
.3531 |
.1469 |
1.43 |
.4236 |
.0764 |
1.81 |
.4649 |
.0351 |
2.19 |
.4857 |
.0143 |
2.57 |
.4949 |
.0051 |
2.95 |
.4984 |
.0016 |
3.80 |
.49993 |
.00007 |
0.30 |
.1179 |
.3821 |
0.68 |
.2517 |
.2483 |
1.06 |
.3554 |
.1446 |
1.44 |
.4251 |
.0749 |
1.82 |
.4656 |
.0344 |
2.20 |
.4861 |
.0139 |
2.58 |
.4951 |
.0049 |
2.96 |
.4985 |
.0015 |
3.90 |
.49995 |
.00005 |
0.31 |
.1217 |
.3783 |
0.69 |
.2549 |
.2451 |
1.07 |
.3577 |
.1423 |
1.45 |
.4265 |
.0735 |
1.83 |
.4664 |
.0336 |
2.21 |
.4864 |
.0136 |
2.59 |
.4952 |
.0048 |
2.97 |
.4985 |
.0015 |
4.00 |
.49997 |
.00003 |
0.32 |
.1255 |
.3745 |
0.70 |
.2580 |
.2420 |
1.08 |
.3599 |
.1401 |
1.46 |
.4279 |
.0721 |
1.84 |
.4671 |
.0329 |
2.22 |
.4868 |
.0132 |
2.60 |
.4953 |
.0047 |
2.98 |
.4986 |
.0014 |
|
|
|
0.33 |
.1293 |
.3707 |
0.71 |
.2611 |
.2389 |
1.09 |
.3621 |
.1379 |
1.47 |
.4292 |
.0708 |
1.85 |
.4678 |
.0322 |
2.23 |
.4871 |
.0129 |
2.61 |
.4955 |
.0045 |
2.99 |
.4986 |
.0014 |
|
|
|
0.34 |
.1331 |
.3669 |
0.72 |
.2642 |
.2358 |
1.10 |
.3643 |
.1357 |
1.48 |
.4306 |
.0694 |
1.86 |
.4686 |
.0314 |
2.24 |
.4875 |
.0125 |
2.62 |
.4956 |
.0044 |
3.00 |
.4987 |
.0013 |
|
|
|
0.35 |
.1368 |
.3632 |
0.73 |
.2673 |
.2327 |
1.11 |
.3665 |
.1335 |
1.49 |
.4319 |
.0681 |
1.87 |
.4693 |
.0307 |
2.25 |
.4878 |
.0122 |
2.63 |
.4957 |
.0043 |
3.01 |
.4987 |
.0013 |
|
|
|
0.36 |
.1406 |
.3594 |
0.74 |
.2704 |
.2296 |
1.12 |
.3686 |
.1314 |
1.50 |
.4332 |
.0668 |
1.88 |
.4699 |
.0301 |
2.26 |
.4881 |
.0119 |
2.64 |
.4959 |
.0041 |
3.02 |
.4987 |
.0013 |
|
|
|
0.37 |
.1443 |
.3557 |
0.75 |
.2734 |
.2266 |
1.13 |
.3708 |
.1292 |
1.51 |
.4345 |
.0655 |
1.89 |
.4706 |
.0294 |
2.27 |
.4884 |
.0116 |
2.65 |
.4960 |
.0040 |
3.03 |
.4988 |
.0012 |
|
|
|
Table B.1: Critical values for t distributions
1 |
3.078 |
6.314 |
12.706 |
31.821 |
63.657 |
636.619 |
2 |
1.886 |
2.920 |
4.303 |
6.965 |
9.925 |
31.599 |
3 |
1.638 |
2.353 |
3.182 |
4.541 |
5.841 |
12.924 |
4 |
1.533 |
2.132 |
2.776 |
3.747 |
4.604 |
8.610 |
5 |
1.476 |
2.015 |
2.571 |
3.365 |
4.032 |
6.869 |
6 |
1.440 |
1.943 |
2.447 |
3.143 |
3.707 |
5.959 |
7 |
1.415 |
1.895 |
2.365 |
2.998 |
3.499 |
5.408 |
8 |
1.397 |
1.860 |
2.306 |
2.896 |
3.355 |
5.041 |
9 |
1.383 |
1.833 |
2.262 |
2.821 |
3.250 |
4.781 |
10 |
1.372 |
1.812 |
2.228 |
2.764 |
3.169 |
4.587 |
11 |
1.363 |
1.796 |
2.201 |
2.718 |
3.106 |
4.437 |
12 |
1.356 |
1.782 |
2.179 |
2.681 |
3.055 |
4.318 |
13 |
1.350 |
1.771 |
2.160 |
2.650 |
3.012 |
4.221 |
14 |
1.345 |
1.761 |
2.145 |
2.624 |
2.977 |
4.140 |
15 |
1.341 |
1.753 |
2.131 |
2.602 |
2.947 |
4.073 |
16 |
1.337 |
1.746 |
2.120 |
2.583 |
2.921 |
4.015 |
17 |
1.333 |
1.740 |
2.110 |
2.567 |
2.898 |
3.965 |
18 |
1.330 |
1.734 |
2.101 |
2.552 |
2.878 |
3.922 |
19 |
1.328 |
1.729 |
2.093 |
2.539 |
2.861 |
3.883 |
20 |
1.325 |
1.725 |
2.086 |
2.528 |
2.845 |
3.850 |
21 |
1.323 |
1.721 |
2.080 |
2.518 |
2.831 |
3.819 |
22 |
1.321 |
1.717 |
2.074 |
2.508 |
2.819 |
3.792 |
23 |
1.319 |
1.714 |
2.069 |
2.500 |
2.807 |
3.768 |
24 |
1.318 |
1.711 |
2.064 |
2.492 |
2.797 |
3.745 |
25 |
1.316 |
1.708 |
2.060 |
2.485 |
2.787 |
3.725 |
26 |
1.315 |
1.706 |
2.056 |
2.479 |
2.779 |
3.707 |
27 |
1.314 |
1.703 |
2.052 |
2.473 |
2.771 |
3.690 |
28 |
1.313 |
1.701 |
2.048 |
2.467 |
2.763 |
3.674 |
29 |
1.311 |
1.699 |
2.045 |
2.462 |
2.756 |
3.659 |
30 |
1.310 |
1.697 |
2.042 |
2.457 |
2.750 |
3.646 |
35 |
1.306 |
1.690 |
2.030 |
2.438 |
2.724 |
3.591 |
40 |
1.303 |
1.684 |
2.021 |
2.423 |
2.704 |
3.551 |
45 |
1.301 |
1.679 |
2.014 |
2.412 |
2.690 |
3.520 |
50 |
1.299 |
1.676 |
2.009 |
2.403 |
2.678 |
3.496 |
55 |
1.297 |
1.673 |
2.004 |
2.396 |
2.668 |
3.476 |
60 |
1.296 |
1.671 |
2.000 |
2.390 |
2.660 |
3.460 |
70 |
1.294 |
1.667 |
1.994 |
2.381 |
2.648 |
3.435 |
80 |
1.292 |
1.664 |
1.990 |
2.374 |
2.639 |
3.416 |
90 |
1.291 |
1.662 |
1.987 |
2.368 |
2.632 |
3.402 |
120 |
1.289 |
1.658 |
1.980 |
2.358 |
2.617 |
3.373 |
100000 |
1.282 |
1.645 |
1.960 |
2.326 |
2.576 |
3.291 |
Table C.1: Critical values for F distributions
1 |
0.05 |
161 |
199 |
216 |
225 |
230 |
234 |
237 |
239 |
241 |
242 |
243 |
244 |
245 |
246 |
248 |
1 |
0.01 |
4052 |
4999 |
5403 |
5625 |
5764 |
5859 |
5928 |
5981 |
6022 |
6056 |
6083 |
6106 |
6143 |
6170 |
6209 |
2 |
0.05 |
18.51 |
19.00 |
19.16 |
19.25 |
19.30 |
19.33 |
19.35 |
19.37 |
19.38 |
19.40 |
19.40 |
19.41 |
19.42 |
19.43 |
19.45 |
2 |
0.01 |
98.50 |
99.00 |
99.17 |
99.25 |
99.30 |
99.33 |
99.36 |
99.37 |
99.39 |
99.40 |
99.41 |
99.42 |
99.43 |
99.44 |
99.45 |
3 |
0.05 |
10.13 |
9.55 |
9.28 |
9.12 |
9.01 |
8.94 |
8.89 |
8.85 |
8.81 |
8.79 |
8.76 |
8.74 |
8.71 |
8.69 |
8.66 |
3 |
0.01 |
34.12 |
30.82 |
29.46 |
28.71 |
28.24 |
27.91 |
27.67 |
27.49 |
27.35 |
27.23 |
27.13 |
27.05 |
26.92 |
26.83 |
26.69 |
4 |
0.05 |
7.71 |
6.94 |
6.59 |
6.39 |
6.26 |
6.16 |
6.09 |
6.04 |
6.00 |
5.96 |
5.94 |
5.91 |
5.87 |
5.84 |
5.80 |
4 |
0.01 |
21.20 |
18.00 |
16.69 |
15.98 |
15.52 |
15.21 |
14.98 |
14.80 |
14.66 |
14.55 |
14.45 |
14.37 |
14.25 |
14.15 |
14.02 |
5 |
0.05 |
6.61 |
5.79 |
5.41 |
5.19 |
5.05 |
4.95 |
4.88 |
4.82 |
4.77 |
4.74 |
4.70 |
4.68 |
4.64 |
4.60 |
4.56 |
5 |
0.01 |
16.26 |
13.27 |
12.06 |
11.39 |
10.97 |
10.67 |
10.46 |
10.29 |
10.16 |
10.05 |
9.96 |
9.89 |
9.77 |
9.68 |
9.55 |
6 |
0.05 |
5.99 |
5.14 |
4.76 |
4.53 |
4.39 |
4.28 |
4.21 |
4.15 |
4.10 |
4.06 |
4.03 |
4.00 |
3.96 |
3.92 |
3.87 |
6 |
0.01 |
13.75 |
10.92 |
9.78 |
9.15 |
8.75 |
8.47 |
8.26 |
8.10 |
7.98 |
7.87 |
7.79 |
7.72 |
7.60 |
7.52 |
7.40 |
7 |
0.05 |
5.59 |
4.74 |
4.35 |
4.12 |
3.97 |
3.87 |
3.79 |
3.73 |
3.68 |
3.64 |
3.60 |
3.57 |
3.53 |
3.49 |
3.44 |
7 |
0.01 |
12.25 |
9.55 |
8.45 |
7.85 |
7.46 |
7.19 |
6.99 |
6.84 |
6.72 |
6.62 |
6.54 |
6.47 |
6.36 |
6.28 |
6.16 |
8 |
0.05 |
5.32 |
4.46 |
4.07 |
3.84 |
3.69 |
3.58 |
3.50 |
3.44 |
3.39 |
3.35 |
3.31 |
3.28 |
3.24 |
3.20 |
3.15 |
8 |
0.01 |
11.26 |
8.65 |
7.59 |
7.01 |
6.63 |
6.37 |
6.18 |
6.03 |
5.91 |
5.81 |
5.73 |
5.67 |
5.56 |
5.48 |
5.36 |
9 |
0.05 |
5.12 |
4.26 |
3.86 |
3.63 |
3.48 |
3.37 |
3.29 |
3.23 |
3.18 |
3.14 |
3.10 |
3.07 |
3.03 |
2.99 |
2.94 |
9 |
0.01 |
10.56 |
8.02 |
6.99 |
6.42 |
6.06 |
5.80 |
5.61 |
5.47 |
5.35 |
5.26 |
5.18 |
5.11 |
5.01 |
4.92 |
4.81 |
10 |
0.05 |
4.96 |
4.10 |
3.71 |
3.48 |
3.33 |
3.22 |
3.14 |
3.07 |
3.02 |
2.98 |
2.94 |
2.91 |
2.86 |
2.83 |
2.77 |
10 |
0.01 |
10.04 |
7.56 |
6.55 |
5.99 |
5.64 |
5.39 |
5.20 |
5.06 |
4.94 |
4.85 |
4.77 |
4.71 |
4.60 |
4.52 |
4.41 |
11 |
0.05 |
4.84 |
3.98 |
3.59 |
3.36 |
3.20 |
3.09 |
3.01 |
2.95 |
2.90 |
2.85 |
2.82 |
2.79 |
2.74 |
2.70 |
2.65 |
11 |
0.01 |
9.65 |
7.21 |
6.22 |
5.67 |
5.32 |
5.07 |
4.89 |
4.74 |
4.63 |
4.54 |
4.46 |
4.40 |
4.29 |
4.21 |
4.10 |
12 |
0.05 |
4.75 |
3.89 |
3.49 |
3.26 |
3.11 |
3.00 |
2.91 |
2.85 |
2.80 |
2.75 |
2.72 |
2.69 |
2.64 |
2.60 |
2.54 |
12 |
0.01 |
9.33 |
6.93 |
5.95 |
5.41 |
5.06 |
4.82 |
4.64 |
4.50 |
4.39 |
4.30 |
4.22 |
4.16 |
4.05 |
3.97 |
3.86 |
13 |
0.05 |
4.67 |
3.81 |
3.41 |
3.18 |
3.03 |
2.92 |
2.83 |
2.77 |
2.71 |
2.67 |
2.63 |
2.60 |
2.55 |
2.51 |
2.46 |
13 |
0.01 |
9.07 |
6.70 |
5.74 |
5.21 |
4.86 |
4.62 |
4.44 |
4.30 |
4.19 |
4.10 |
4.02 |
3.96 |
3.86 |
3.78 |
3.66 |
14 |
0.05 |
4.60 |
3.74 |
3.34 |
3.11 |
2.96 |
2.85 |
2.76 |
2.70 |
2.65 |
2.60 |
2.57 |
2.53 |
2.48 |
2.44 |
2.39 |
14 |
0.01 |
8.86 |
6.51 |
5.56 |
5.04 |
4.69 |
4.46 |
4.28 |
4.14 |
4.03 |
3.94 |
3.86 |
3.80 |
3.70 |
3.62 |
3.51 |
15 |
0.05 |
4.54 |
3.68 |
3.29 |
3.06 |
2.90 |
2.79 |
2.71 |
2.64 |
2.59 |
2.54 |
2.51 |
2.48 |
2.42 |
2.38 |
2.33 |
15 |
0.01 |
8.68 |
6.36 |
5.42 |
4.89 |
4.56 |
4.32 |
4.14 |
4.00 |
3.89 |
3.80 |
3.73 |
3.67 |
3.56 |
3.49 |
3.37 |
16 |
0.05 |
4.49 |
3.63 |
3.24 |
3.01 |
2.85 |
2.74 |
2.66 |
2.59 |
2.54 |
2.49 |
2.46 |
2.42 |
2.37 |
2.33 |
2.28 |
16 |
0.01 |
8.53 |
6.23 |
5.29 |
4.77 |
4.44 |
4.20 |
4.03 |
3.89 |
3.78 |
3.69 |
3.62 |
3.55 |
3.45 |
3.37 |
3.26 |
17 |
0.05 |
4.45 |
3.59 |
3.20 |
2.96 |
2.81 |
2.70 |
2.61 |
2.55 |
2.49 |
2.45 |
2.41 |
2.38 |
2.33 |
2.29 |
2.23 |
17 |
0.01 |
8.40 |
6.11 |
5.18 |
4.67 |
4.34 |
4.10 |
3.93 |
3.79 |
3.68 |
3.59 |
3.52 |
3.46 |
3.35 |
3.27 |
3.16 |
18 |
0.05 |
4.41 |
3.55 |
3.16 |
2.93 |
2.77 |
2.66 |
2.58 |
2.51 |
2.46 |
2.41 |
2.37 |
2.34 |
2.29 |
2.25 |
2.19 |
18 |
0.01 |
8.29 |
6.01 |
5.09 |
4.58 |
4.25 |
4.01 |
3.84 |
3.71 |
3.60 |
3.51 |
3.43 |
3.37 |
3.27 |
3.19 |
3.08 |
19 |
0.05 |
4.38 |
3.52 |
3.13 |
2.90 |
2.74 |
2.63 |
2.54 |
2.48 |
2.42 |
2.38 |
2.34 |
2.31 |
2.26 |
2.21 |
2.16 |
19 |
0.01 |
8.18 |
5.93 |
5.01 |
4.50 |
4.17 |
3.94 |
3.77 |
3.63 |
3.52 |
3.43 |
3.36 |
3.30 |
3.19 |
3.12 |
3.00 |
20 |
0.05 |
4.35 |
3.49 |
3.10 |
2.87 |
2.71 |
2.60 |
2.51 |
2.45 |
2.39 |
2.35 |
2.31 |
2.28 |
2.22 |
2.18 |
2.12 |
20 |
0.01 |
8.10 |
5.85 |
4.94 |
4.43 |
4.10 |
3.87 |
3.70 |
3.56 |
3.46 |
3.37 |
3.29 |
3.23 |
3.13 |
3.05 |
2.94 |
21 |
0.05 |
4.32 |
3.47 |
3.07 |
2.84 |
2.68 |
2.57 |
2.49 |
2.42 |
2.37 |
2.32 |
2.28 |
2.25 |
2.20 |
2.16 |
2.10 |
21 |
0.01 |
8.02 |
5.78 |
4.87 |
4.37 |
4.04 |
3.81 |
3.64 |
3.51 |
3.40 |
3.31 |
3.24 |
3.17 |
3.07 |
2.99 |
2.88 |
22 |
0.05 |
4.30 |
3.44 |
3.05 |
2.82 |
2.66 |
2.55 |
2.46 |
2.40 |
2.34 |
2.30 |
2.26 |
2.23 |
2.17 |
2.13 |
2.07 |
22 |
0.01 |
7.95 |
5.72 |
4.82 |
4.31 |
3.99 |
3.76 |
3.59 |
3.45 |
3.35 |
3.26 |
3.18 |
3.12 |
3.02 |
2.94 |
2.83 |
23 |
0.05 |
4.28 |
3.42 |
3.03 |
2.80 |
2.64 |
2.53 |
2.44 |
2.37 |
2.32 |
2.27 |
2.24 |
2.20 |
2.15 |
2.11 |
2.05 |
23 |
0.01 |
7.88 |
5.66 |
4.76 |
4.26 |
3.94 |
3.71 |
3.54 |
3.41 |
3.30 |
3.21 |
3.14 |
3.07 |
2.97 |
2.89 |
2.78 |
24 |
0.05 |
4.26 |
3.40 |
3.01 |
2.78 |
2.62 |
2.51 |
2.42 |
2.36 |
2.30 |
2.25 |
2.22 |
2.18 |
2.13 |
2.09 |
2.03 |
24 |
0.01 |
7.82 |
5.61 |
4.72 |
4.22 |
3.90 |
3.67 |
3.50 |
3.36 |
3.26 |
3.17 |
3.09 |
3.03 |
2.93 |
2.85 |
2.74 |
25 |
0.05 |
4.24 |
3.39 |
2.99 |
2.76 |
2.60 |
2.49 |
2.40 |
2.34 |
2.28 |
2.24 |
2.20 |
2.16 |
2.11 |
2.07 |
2.01 |
25 |
0.01 |
7.77 |
5.57 |
4.68 |
4.18 |
3.85 |
3.63 |
3.46 |
3.32 |
3.22 |
3.13 |
3.06 |
2.99 |
2.89 |
2.81 |
2.70 |
26 |
0.05 |
4.23 |
3.37 |
2.98 |
2.74 |
2.59 |
2.47 |
2.39 |
2.32 |
2.27 |
2.22 |
2.18 |
2.15 |
2.09 |
2.05 |
1.99 |
26 |
0.01 |
7.72 |
5.53 |
4.64 |
4.14 |
3.82 |
3.59 |
3.42 |
3.29 |
3.18 |
3.09 |
3.02 |
2.96 |
2.86 |
2.78 |
2.66 |
27 |
0.05 |
4.21 |
3.35 |
2.96 |
2.73 |
2.57 |
2.46 |
2.37 |
2.31 |
2.25 |
2.20 |
2.17 |
2.13 |
2.08 |
2.04 |
1.97 |
27 |
0.01 |
7.68 |
5.49 |
4.60 |
4.11 |
3.78 |
3.56 |
3.39 |
3.26 |
3.15 |
3.06 |
2.99 |
2.93 |
2.82 |
2.75 |
2.63 |
28 |
0.05 |
4.20 |
3.34 |
2.95 |
2.71 |
2.56 |
2.45 |
2.36 |
2.29 |
2.24 |
2.19 |
2.15 |
2.12 |
2.06 |
2.02 |
1.96 |
28 |
0.01 |
7.64 |
5.45 |
4.57 |
4.07 |
3.75 |
3.53 |
3.36 |
3.23 |
3.12 |
3.03 |
2.96 |
2.90 |
2.79 |
2.72 |
2.60 |
29 |
0.05 |
4.18 |
3.33 |
2.93 |
2.70 |
2.55 |
2.43 |
2.35 |
2.28 |
2.22 |
2.18 |
2.14 |
2.10 |
2.05 |
2.01 |
1.94 |
29 |
0.01 |
7.60 |
5.42 |
4.54 |
4.04 |
3.73 |
3.50 |
3.33 |
3.20 |
3.09 |
3.00 |
2.93 |
2.87 |
2.77 |
2.69 |
2.57 |
30 |
0.05 |
4.17 |
3.32 |
2.92 |
2.69 |
2.53 |
2.42 |
2.33 |
2.27 |
2.21 |
2.16 |
2.13 |
2.09 |
2.04 |
1.99 |
1.93 |
30 |
0.01 |
7.56 |
5.39 |
4.51 |
4.02 |
3.70 |
3.47 |
3.30 |
3.17 |
3.07 |
2.98 |
2.91 |
2.84 |
2.74 |
2.66 |
2.55 |
32 |
0.05 |
4.15 |
3.29 |
2.90 |
2.67 |
2.51 |
2.40 |
2.31 |
2.24 |
2.19 |
2.14 |
2.10 |
2.07 |
2.01 |
1.97 |
1.91 |
32 |
0.01 |
7.50 |
5.34 |
4.46 |
3.97 |
3.65 |
3.43 |
3.26 |
3.13 |
3.02 |
2.93 |
2.86 |
2.80 |
2.70 |
2.62 |
2.50 |
34 |
0.05 |
4.13 |
3.28 |
2.88 |
2.65 |
2.49 |
2.38 |
2.29 |
2.23 |
2.17 |
2.12 |
2.08 |
2.05 |
1.99 |
1.95 |
1.89 |
34 |
0.01 |
7.44 |
5.29 |
4.42 |
3.93 |
3.61 |
3.39 |
3.22 |
3.09 |
2.98 |
2.89 |
2.82 |
2.76 |
2.66 |
2.58 |
2.46 |
36 |
0.05 |
4.11 |
3.26 |
2.87 |
2.63 |
2.48 |
2.36 |
2.28 |
2.21 |
2.15 |
2.11 |
2.07 |
2.03 |
1.98 |
1.93 |
1.87 |
36 |
0.01 |
7.40 |
5.25 |
4.38 |
3.89 |
3.57 |
3.35 |
3.18 |
3.05 |
2.95 |
2.86 |
2.79 |
2.72 |
2.62 |
2.54 |
2.43 |
38 |
0.05 |
4.10 |
3.24 |
2.85 |
2.62 |
2.46 |
2.35 |
2.26 |
2.19 |
2.14 |
2.09 |
2.05 |
2.02 |
1.96 |
1.92 |
1.85 |
38 |
0.01 |
7.35 |
5.21 |
4.34 |
3.86 |
3.54 |
3.32 |
3.15 |
3.02 |
2.92 |
2.83 |
2.75 |
2.69 |
2.59 |
2.51 |
2.40 |
40 |
0.05 |
4.08 |
3.23 |
2.84 |
2.61 |
2.45 |
2.34 |
2.25 |
2.18 |
2.12 |
2.08 |
2.04 |
2.00 |
1.95 |
1.90 |
1.84 |
40 |
0.01 |
7.31 |
5.18 |
4.31 |
3.83 |
3.51 |
3.29 |
3.12 |
2.99 |
2.89 |
2.80 |
2.73 |
2.66 |
2.56 |
2.48 |
2.37 |
42 |
0.05 |
4.07 |
3.22 |
2.83 |
2.59 |
2.44 |
2.32 |
2.24 |
2.17 |
2.11 |
2.06 |
2.03 |
1.99 |
1.94 |
1.89 |
1.83 |
42 |
0.01 |
7.28 |
5.15 |
4.29 |
3.80 |
3.49 |
3.27 |
3.10 |
2.97 |
2.86 |
2.78 |
2.70 |
2.64 |
2.54 |
2.46 |
2.34 |
44 |
0.05 |
4.06 |
3.21 |
2.82 |
2.58 |
2.43 |
2.31 |
2.23 |
2.16 |
2.10 |
2.05 |
2.01 |
1.98 |
1.92 |
1.88 |
1.81 |
44 |
0.01 |
7.25 |
5.12 |
4.26 |
3.78 |
3.47 |
3.24 |
3.08 |
2.95 |
2.84 |
2.75 |
2.68 |
2.62 |
2.52 |
2.44 |
2.32 |
46 |
0.05 |
4.05 |
3.20 |
2.81 |
2.57 |
2.42 |
2.30 |
2.22 |
2.15 |
2.09 |
2.04 |
2.00 |
1.97 |
1.91 |
1.87 |
1.80 |
46 |
0.01 |
7.22 |
5.10 |
4.24 |
3.76 |
3.44 |
3.22 |
3.06 |
2.93 |
2.82 |
2.73 |
2.66 |
2.60 |
2.50 |
2.42 |
2.30 |
48 |
0.05 |
4.04 |
3.19 |
2.80 |
2.57 |
2.41 |
2.29 |
2.21 |
2.14 |
2.08 |
2.03 |
1.99 |
1.96 |
1.90 |
1.86 |
1.79 |
48 |
0.01 |
7.19 |
5.08 |
4.22 |
3.74 |
3.43 |
3.20 |
3.04 |
2.91 |
2.80 |
2.71 |
2.64 |
2.58 |
2.48 |
2.40 |
2.28 |
50 |
0.05 |
4.03 |
3.18 |
2.79 |
2.56 |
2.40 |
2.29 |
2.20 |
2.13 |
2.07 |
2.03 |
1.99 |
1.95 |
1.89 |
1.85 |
1.78 |
50 |
0.01 |
7.17 |
5.06 |
4.20 |
3.72 |
3.41 |
3.19 |
3.02 |
2.89 |
2.78 |
2.70 |
2.63 |
2.56 |
2.46 |
2.38 |
2.27 |
55 |
0.05 |
4.02 |
3.16 |
2.77 |
2.54 |
2.38 |
2.27 |
2.18 |
2.11 |
2.06 |
2.01 |
1.97 |
1.93 |
1.88 |
1.83 |
1.76 |
55 |
0.01 |
7.12 |
5.01 |
4.16 |
3.68 |
3.37 |
3.15 |
2.98 |
2.85 |
2.75 |
2.66 |
2.59 |
2.53 |
2.42 |
2.34 |
2.23 |
60 |
0.05 |
4.00 |
3.15 |
2.76 |
2.53 |
2.37 |
2.25 |
2.17 |
2.10 |
2.04 |
1.99 |
1.95 |
1.92 |
1.86 |
1.82 |
1.75 |
60 |
0.01 |
7.08 |
4.98 |
4.13 |
3.65 |
3.34 |
3.12 |
2.95 |
2.82 |
2.72 |
2.63 |
2.56 |
2.50 |
2.39 |
2.31 |
2.20 |
70 |
0.05 |
3.98 |
3.13 |
2.74 |
2.50 |
2.35 |
2.23 |
2.14 |
2.07 |
2.02 |
1.97 |
1.93 |
1.89 |
1.84 |
1.79 |
1.72 |
70 |
0.01 |
7.01 |
4.92 |
4.07 |
3.60 |
3.29 |
3.07 |
2.91 |
2.78 |
2.67 |
2.59 |
2.51 |
2.45 |
2.35 |
2.27 |
2.15 |
80 |
0.05 |
3.96 |
3.11 |
2.72 |
2.49 |
2.33 |
2.21 |
2.13 |
2.06 |
2.00 |
1.95 |
1.91 |
1.88 |
1.82 |
1.77 |
1.70 |
80 |
0.01 |
6.96 |
4.88 |
4.04 |
3.56 |
3.26 |
3.04 |
2.87 |
2.74 |
2.64 |
2.55 |
2.48 |
2.42 |
2.31 |
2.23 |
2.12 |
100 |
0.05 |
3.94 |
3.09 |
2.70 |
2.46 |
2.31 |
2.19 |
2.10 |
2.03 |
1.97 |
1.93 |
1.89 |
1.85 |
1.79 |
1.75 |
1.68 |
100 |
0.01 |
6.90 |
4.82 |
3.98 |
3.51 |
3.21 |
2.99 |
2.82 |
2.69 |
2.59 |
2.50 |
2.43 |
2.37 |
2.27 |
2.19 |
2.07 |
125 |
0.05 |
3.92 |
3.07 |
2.68 |
2.44 |
2.29 |
2.17 |
2.08 |
2.01 |
1.96 |
1.91 |
1.87 |
1.83 |
1.77 |
1.73 |
1.66 |
125 |
0.01 |
6.84 |
4.78 |
3.94 |
3.47 |
3.17 |
2.95 |
2.79 |
2.66 |
2.55 |
2.47 |
2.39 |
2.33 |
2.23 |
2.15 |
2.03 |
150 |
0.05 |
3.90 |
3.06 |
2.66 |
2.43 |
2.27 |
2.16 |
2.07 |
2.00 |
1.94 |
1.89 |
1.85 |
1.82 |
1.76 |
1.71 |
1.64 |
150 |
0.01 |
6.81 |
4.75 |
3.91 |
3.45 |
3.14 |
2.92 |
2.76 |
2.63 |
2.53 |
2.44 |
2.37 |
2.31 |
2.20 |
2.12 |
2.00 |
200 |
0.05 |
3.89 |
3.04 |
2.65 |
2.42 |
2.26 |
2.14 |
2.06 |
1.98 |
1.93 |
1.88 |
1.84 |
1.80 |
1.74 |
1.69 |
1.62 |
200 |
0.01 |
6.76 |
4.71 |
3.88 |
3.41 |
3.11 |
2.89 |
2.73 |
2.60 |
2.50 |
2.41 |
2.34 |
2.27 |
2.17 |
2.09 |
1.97 |
400 |
0.05 |
3.86 |
3.02 |
2.63 |
2.39 |
2.24 |
2.12 |
2.03 |
1.96 |
1.90 |
1.85 |
1.81 |
1.78 |
1.72 |
1.67 |
1.60 |
400 |
0.01 |
6.70 |
4.66 |
3.83 |
3.37 |
3.06 |
2.85 |
2.68 |
2.56 |
2.45 |
2.37 |
2.29 |
2.23 |
2.13 |
2.05 |
1.92 |
1000 |
0.05 |
3.85 |
3.00 |
2.61 |
2.38 |
2.22 |
2.11 |
2.02 |
1.95 |
1.89 |
1.84 |
1.80 |
1.76 |
1.70 |
1.65 |
1.58 |
1000 |
0.01 |
6.66 |
4.63 |
3.80 |
3.34 |
3.04 |
2.82 |
2.66 |
2.53 |
2.43 |
2.34 |
2.27 |
2.20 |
2.10 |
2.02 |
1.90 |
10000000 |
0.05 |
3.84 |
3.00 |
2.60 |
2.37 |
2.21 |
2.10 |
2.01 |
1.94 |
1.88 |
1.83 |
1.79 |
1.75 |
1.69 |
1.64 |
1.57 |
10000000 |
0.01 |
6.63 |
4.61 |
3.78 |
3.32 |
3.02 |
2.80 |
2.64 |
2.51 |
2.41 |
2.32 |
2.25 |
2.18 |
2.08 |
2.00 |
1.88 |
Table D.1: Critical values for χ^2 distributions
1 |
2.71 |
3.84 |
6.63 |
10.83 |
2 |
4.61 |
5.99 |
9.21 |
13.82 |
3 |
6.25 |
7.81 |
11.34 |
16.27 |
4 |
7.78 |
9.49 |
13.28 |
18.47 |
5 |
9.24 |
11.07 |
15.09 |
20.52 |
6 |
10.64 |
12.59 |
16.81 |
22.46 |
7 |
12.02 |
14.07 |
18.48 |
24.32 |
8 |
13.36 |
15.51 |
20.09 |
26.12 |
9 |
14.68 |
16.92 |
21.67 |
27.88 |
10 |
15.99 |
18.31 |
23.21 |
29.59 |
11 |
17.28 |
19.68 |
24.72 |
31.26 |
12 |
18.55 |
21.03 |
26.22 |
32.91 |
13 |
19.81 |
22.36 |
27.69 |
34.53 |
14 |
21.06 |
23.68 |
29.14 |
36.12 |
15 |
22.31 |
25.00 |
30.58 |
37.70 |
16 |
23.54 |
26.30 |
32.00 |
39.25 |
17 |
24.77 |
27.59 |
33.41 |
40.79 |
18 |
25.99 |
28.87 |
34.81 |
42.31 |
19 |
27.20 |
30.14 |
36.19 |
43.82 |
20 |
28.41 |
31.41 |
37.57 |
45.31 |
21 |
29.62 |
32.67 |
38.93 |
46.80 |
22 |
30.81 |
33.92 |
40.29 |
48.27 |
23 |
32.01 |
35.17 |
41.64 |
49.73 |
24 |
33.20 |
36.42 |
42.98 |
51.18 |
25 |
34.38 |
37.65 |
44.31 |
52.62 |
26 |
35.56 |
38.89 |
45.64 |
54.05 |
27 |
36.74 |
40.11 |
46.96 |
55.48 |
28 |
37.92 |
41.34 |
48.28 |
56.89 |
29 |
39.09 |
42.56 |
49.59 |
58.30 |
30 |
40.26 |
43.77 |
50.89 |
59.70 |
40 |
51.81 |
55.76 |
63.69 |
73.40 |
50 |
63.17 |
67.50 |
76.15 |
86.66 |
60 |
74.40 |
79.08 |
88.38 |
99.61 |
70 |
85.53 |
90.53 |
100.43 |
112.32 |
Session Info
For the sake of documentation and reproducibility, the current report was build on a system using the following software.
Report created by wibeasley at 2016-01-17, 01:37 -0600
R version 3.2.3 (2015-12-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 14.04.3 LTS
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8 LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] grid stats graphics grDevices utils datasets methods base
other attached packages:
[1] rgl_0.95.1441 mnormt_1.5-3 MASS_7.3-45 ggthemes_3.0.1 gridExtra_2.0.0 epade_0.3.8
[7] plotrix_3.6-1 reshape2_1.4.1 scales_0.3.0 plyr_1.8.3 RColorBrewer_1.1-2 dichromat_2.0-0
[13] extrafont_0.17 wesanderson_0.3.2 ggplot2_2.0.0 knitr_1.12
loaded via a namespace (and not attached):
[1] Rcpp_0.12.3 Rttf2pt1_1.3.3 magrittr_1.5 munsell_0.4.2 colorspace_1.2-6 highr_0.5.1
[7] stringr_1.0.0.9000 tools_3.2.3 gtable_0.1.2 extrafontdb_1.0 htmltools_0.3 assertthat_0.1
[13] yaml_2.1.13 digest_0.6.9 formatR_1.2.1 rsconnect_0.4.1.4 evaluate_0.8 rmarkdown_0.9.2
[19] labeling_0.3 stringi_1.0-1