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

Z Inside Outside Z Inside Outside Z Inside Outside Z Inside Outside Z Inside Outside Z Inside Outside Z Inside Outside Z Inside Outside Z Inside Outside
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

df Alpha10 Alpha05 Alpha025 Alpha01 Alpha005 Alpha0005
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

DenominatorDF Alpha 1 2 3 4 5 6 7 8 9 10 11 12 14 16 20
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

df Alpha10 Alpha05 Alpha01 Alpha001
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     

License

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 Unported License.