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Table 1: Cumulative distribution function of the standard normal distribution

.00 .01 .02 .03 .04 .05   .06 .07 .08 .09 .10   .11 .12 .13 .14 .15   .16 .17 .18 .19 .20     1.21 1.22 1.23 1.24 1.25   1.26 1.27 1.28 1.29 1.30   1.31 1.32 1.33 1.34 1.35   1.36 1.37 1.38 1.39 1.40   1.41 1.42 1.43 1.44 1.45 .5000 .5040 .5080 .5120 .5160 .5199   .5239 .5279 .5319 .5359 .5398   .5438 .5478 .5517 .5557 .5596   .5636 .5675 .5714 .5753 .5793     .8869 .8888 .8907 .8925 .8944   .8962 .8980 .8997 .9015 .9032   .9049 .9066 .9082 .9099 .9115   .9131 .9147 .9162 .9177 .9192   .9207 .9222 .9236 .9251 .9265   .21 .22 .23 .24 .25   .26 .27 .28 .29 .30   .31 .32 .33 .34 .35   .36 .37 .38 .39 .40     1.46 1.47 1.48 1.49 1.50   1.51 1.52 1.53 1.54 1.55   1.56 1.57 1.58 1.59 1.60   1.61 1.62 1.63 1.64 1.65   1.66 1.67 1.68 1.69 1.70   .5832 .5871 .5910 .5948 .5987   .6026 .6064 .6103 .6141 .6179   .6217 .6255 .6293 .6331 .6368   .6406 .6443 .6480 .6517 .6554     .9279 .9292 .9306 .9319 .9332   .9345 .9357 .9370 .9382 .9394   .9406 .9418 .9429 .9441 .9452   .9463 .9474 .9484 .9495 .9505   .9515 .9525 .9535 .9545 .9554   .41 .42 .43 .44 .45   .46 .47 .48 .49 .50   .51 .52 .53 .54 .55   .56 .57 .58 .59 .60     1.71 1.72 1.73 1.74 1.75   1.76 1.77 1.78 1.79 1.80   1.81 1.82 1.83 1.84 1.85   1.86 1.87 1.88 1.89 1.90   1.91 1.92 1.93 1.94 1.95   .6591 .6628 .6664 .6700 .6736   .6772 .6803 .6844 .6879 .6915   .6950 .6985 .7019 .7054 .7088   .7123 .7157 .7190 .7224 .7257     .9564 .9573 .9582 .9591 .9599   .9608 .9616 .9615 .9633 .9641   .9649 .9656 .9664 .9671 .9678   .9686 .9693 .9699 .9706 .9713   .9719 .9726 .9732 .9738 .9744   .61 .62 .63 .64 .65   .66 .67 .68 .69 .70   .71 .72 .73 .74 .75   .76 .77 .78 .79 .80     1.96 1.97 1.98 1.99 2.00   2.01 2.02 2.03 2.04 2.05   2.06 2.07 2.08 2.09 2.10   2.11 2.12 2.13 2.14 2.15   2.16 2.17 2.18 2.19 2.20   .7291 .7324 .7357 .7389 .7422   .7454 .7486 .7517 .7549 .7580   .7611 .7642 .7673 .7704 .7734   .7764 .7794 .7823 .7852 .7881     .9750 .9756 .9761 .9767 .9772   .9778 .9783 .9788 .9793 .9798   .9803 .9808 .9812 .9817 .9821   .9826 .9830 .9834 .9838 .9842   .9846 .9850 .9854 .9857 .9861   .81 .82 .83 .84 .85   .86 .87 .88 .89 .90   .91 .92 .93 .94 .95   .96 .97 .98 .99 1.00     2.21 2.22 2.23 2.24 2.25   2.26 2.27 2.28 2.29 2.30   2.31 2.32 2.33 2.34 2.35   2.36 2.37 2.38 2.39 2.40   2.41 2.42 2.43 2.44 2.45   .7910 .7939 .7967 .7995 .8023   .8051 .8078 .8106 .8133 .8159   .8186 .8212 .8238 .8264 .8289   .8315 .8340 .8365 .8389 .8413     .9864 .9868 .9871 .9875 .9878   .9881 .9884 .9887 .9890 .9893   .9896 .9898 .9901 .9904 .9906   .9909 .9911 .9913 .9916 .9918   .9920 .9922 .9925 .9927 .9929   1.01 1.02 1.03 1.04 1.05   1.06 1.07 1.08 1.09 1.10   1.11 1.12 1.13 1.14 1.15   1.16 1.17 1.18 1.19 1.20     2.46 2.47 2.48 2.49 2.50   2.51 2.52 2.53 2.54 2.55   2.56 2.57 2.58 2.59 2.60   2.61 2.62 2.63 2.64 2.65   2.66 2.67 2.68 2.69 2.70   .8438 .8461 .8485 .8508 .8531   .8554 .8577 .8599 .8621 .8643   .8665 .8686 .8708 .8729 .8749   .8770 .8790 .8810 .8830 .8849     .9931 .9932 .9934 .9936 .9938   .9940 .9941 .9943 .9945 .9946   .9948 .9949 .9951 .9952 .9953   .9955 .9956 .9957 .9959 .9960   .9961 .9962 .9963 .9964 .9965

Table 1: Cumulative distribution function of the standard normal distribution (continue)

  2.71 2.72 2.73 2.74 2.75   2.76 2.77 2.78 2.79 2.80   2.81 2.82 2.83 2.84 2.85   2.86 2.87 2.88 2.89 2.90   .9966 .9967 .9968 .9969 .9970   .9971 .9972 .9973 .9974 .9974   .9975 .9976 .9977 .9977 .9978   .9979 .9979 .9980 .9981 .9981   2.91 2.92 2.93 2.94 2.95   2.96 2.97 2.98 2.99 3.00   3.01 3.02 3.03 3.04 3.05   3.06 3.07 3.08 3.09 3.10   .9982 .9982 .9983 .9984 .9984   .9985 .9985 .9986 .9986 .9986   .9987 .9987 .9988 .9988 .9989   .9989 .9989 .9990 .9990 .9990   3.11 3.12 3.13 3.14 3.15   3.16 3.17 3.18 3.19 3.20   3.21 3.22 3.23 3.24 3.25   3.26 3.27 3.28 3.29 3.30   .9991 .9991 .9991 .9992 .9992   .9992 .9992 .9993 .9993 .9993   .9993 .9994 .9994 .9994 .9994   .9994 .9995 .9995 .9995 .9995   3.31 3.32 3.33 3.34 3.35   3.36 3.37 3.38 3.39 3.40   3.41 3.42 3.43 3.44 3.45   3.46 3.47 3.48 3.49 3.50   .9995 .9996 .9996 .9996 .9996   .9996 .9996 .9996 .9997 .9997   .9997 .9997 .9997 .9997 .9997   .9997 .9997 .9997 .9998 .9998   3.51 3.52 3.53 3.54 3.55   3.56 3.57 3.58 3.59 3.60   3.61 3.62 3.63 3.64 3.65   3.66 3.67 3.68 3.69 3.70   .9998 .9998 .9998 .9998 .9998   .9998 .9998 .9998 .9998 .9998   .9998 .9999 .9999.9999.9999   .9999.9999.9999.9999.9999   3.71 3.72 3.73 3.74 3.75   3.76 3.77 3.78 3.79 3.80   3.81 3.82 3.83 3.84 3.85   3.86 3.87 3.88 3.89 3.90   .9999 .9999 .9999 .9999 .9999   .9999 .9999 .9999 .9999 .9999   .9999 .9999 .9999 .9999 .9999   .9999 .9999 .9999 1.0000 1.0000   3.91 3.92 3.93 3.94 3.95   3.96 3.97 3.98 3.99     1.0000 1.0000 1.0000 1.0000 1.0000   1.0000 1.0000 1.0000 1.0000  

Table 2: Cut-off point of Student’s t distribution

       
  0.100 0.050 0.025 0.010 0.005
            3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372   1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325   1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310   1.303 1.296   1.282   6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812   1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725   1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697   1.684 1.671   1.645   12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228   2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086   2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042   2.021 2.000   1.960   31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764   2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528   2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457   2.423 2.390   2.326   63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169   3.160 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845   2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750   2.704 2.660   2.576

Table 3: Chi- square distribution

                 
  .995 .990 .975 .950 .900 .100 .050 .025 .010 .005
    0.04393 0.0100 0.072 0.207 0.412 0.676 0.989 1.34 1.73 2.16 2.60 3.07 3.57 4.07 4.60 5.14 5.70 6.26 6.84 7.43 8.03 8.64 9.26 9.89 10.52 11.16 11.81 12.46 13.12 13.79 20.71 27.99 35.53 43.28 51.17 59.20 67.33   0.03157 0.0201 0.115 0.297 0.554 0.872 1.24 1.65 2.09 2.56 3.05 3.57 4.11 4.66 5.23 5.81 6.41 7.01 7.63 8.26 8.90 9.54 10.20 10.86 11.52 12.20 12.88 13.56 14.26 14.95 22.16 29.71 37.48 45.44 53.54 61.75 70.06   0.03982 0.0506 0.216 0.484 0.831 1.24 1.69 2.18 2.70 3.25 3.82 4.40 5.01 5.63 6.26 6.91 7.56 8.23 8.91 9.59 10.28 10.98 11.69 12.40 13.12 13.84 14.57 15.31 16.05 16.79 24.43 32.36 40.48 48.76 57.15 65.65 74.22     0.02393 0.103 0.352 0.711 1.145 1.64 2.17 2.73 3.33 3.94 4.57 5.23 5.89 6.57 7.26 7.96 8.67 9.39 10.12 10.85 11.59 12.34 13.09 13.85 14.61 15.38 16.15 16.93 17.71 18.49 26.51 34.76 43.19 51.74 60.39 69.16 77.93     0.0158 0.211 0.584 1.064 1.61 2.20 2.83 3.49 4.17 4.87 5.58 6.30 7.04 7.79 8.55 9.31 10.09 10.86 11.65 12.44 13.24 14.04 14.85 15.66 16.47 17.29 18.11 18.94 19.77 20.60 29.05 37.69 46.46 55.33 64.28 73.29 82.36   2.71 4.61 6.25 7.78 9.24 10.64 12.02 13.36 14.68 15.99 17.28 18.55 19.81 21.06 22.31 23.54 24.77 25.99 27.20 28.41 29.62 30.81 32.01 33.20 34.38 35.56 36.74 37.92 39.09 40.26 51.81 63.17 74.40 85.53 96.58 107.6 118.5     3.84 5.99 7.81 9.49 11.07 12.59 14.07 15.51 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 37.65 38.89 40.11 41.34 42.56 43.77 55.76 67.50 79.08 90.53 101.9 113.1 124.3   5.02 7.38 9.35 11.14 12.83 14.45 16.01 17.53 19.02 20.48 21.92 23.34 24.74 26.12 27.49 28.85 30.19 31.53 32.85 34.17 35.48 36.78 38.08 39.36 40.65 41.92 43.19 44.46 45.72 46.98 59.34 71.42 83.30 95.02 106.6 118.1 129.6   6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 21.67 23.21 24.73 26.22 27.69 29.14 30.58 32.00 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 44.31 45.64 46.96 48.28 49.59 50.89 63.69 76.15 88.38 100.4 112.3 124.1 135.8   7.88 10.60 12.84 14.86 16.75 18.55 20.28 21.96 23.59 25.19 26.76 28.30 29.82 31.32 32.80 34.27 35.72 37.16 38.58 40.00 41.40 42.80 44.18 45.56 46.93 48.29 49.64 50.99 52.34 53.67 66.77 79.49 91.95 104.2 116.3 128.3 140.2  

 

 

Table 4: Cutoff point of the distribution of the Wicoxon test statistic

n        
  0.005 0.01 0.025 0.05 0.10
           

Table 5: Cutoff point of the distribution of the Spearman’s rank correlation coefficient

n      
  0.05 0.025 0.01 0.005
          .900 .829 .714 .643 .600 .564   .523 .497 .475 .457 .441   .425 .412 .399 .388 .377   .368 .359 .351 .343 .336   .329 .323 .317 .311 .305 - .886 .786 .738 .683 .648   .623 .591 .566 .545 .525   .507 .490 .476 .462 .450   .438 .428 .418 .409 .400   .392 .385 .377 .370 .364   - .943 .893 .833 .783 .745   .736 .703 .673 .646 .623   .601 .582 .564 .549 .534   .521 .508 .496 .485 .475   .465 .456 .448 .440 .432   - - - .881 .833 .794   .818 .780 .745 .716 .689   .666 .645 .625 .608 .591   .576 .562 .549 .537 .526   .515 .505 .496 .487 .478  

 

 

Table 2: Cutoff points for the F distribution

                                     
  161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.9 245.9 248.0 249.1 250.1 251.1 252.2 253.3 254.3
  18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.41 19.43 19.45 19.45 19.46 19.47 19.48 19.49 19.50
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
                                     
  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
  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
  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
  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
  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
  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
  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
  4.08 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
  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
  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

 

 

                                     
                                       
  98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39 99.40 99.42 99.43 99.45 99.46 99.47 99.47 99.48 99.48 99.50
  34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 27.05 26.87 26.69 26.60 26.50 26.41 26.32 26.22 26.13
  21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.37 14.20 14.02 13.93 13.84 13.75 13.65 13.56 13.46
  16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.89 9.72 9.55 9.47 9.38 9.29 9.20 9.11 9.02
  13.75 10.92 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
  12.25 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
  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
  10.56 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
  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
  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
  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
                                     
  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
  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
  8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.67 3.52 3.38 3.29 3.21 3.13 3.05 2.96 2.87
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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
  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

 

Table 7. Cumulative distribution function of the runs test statistic

                                       
  .100 .029 .008 .002 .001 .000 .000 .000 .300 .114 .040 .013 .004 .001 .000 .000 .700 .371 .167 .067 .025 .009 .003 .001 .900 .629 .357 .175 .078 .032 .012 .004 1.00 .886 .643 .392 .209 .100 .044 .019   .971 .833 .608 .383 .214 .109 .051   1.00 .960 .825 .617 .405 .238 .128     .992 .933 .791 .595 .399 .242     1.00 .987 .922 .786 .601 .414   .998 .975 .900 .762 .586   1.00 .996 .968 .891 .758     .999 .991 .956 .872     1.00 .999 .988 .949   1.00 .997 .981   1.00 1.00 .996     1.00 .999     1.00 1.00   1.00   1.00

N R


References

1.Paul Newbold, William L. Carlson, Betty M. Thorne, “Statistics for business and economics”, Pearson education, Inc., upper saddle river, New jersey, 2003.

2.David R. Anderson, Dennis J. Sweeney, Thomas A.Williams, “ Introduction to statistics” West Publishing company, St. Paul, Minnesota., 1981.

3. H. T. Hayslett, MS,: Statistics”, British library cataloguing in publication data, 1981.

4. Paul Newbold, “Statistics for business and economics” Prentice – Hall Inc., 1995.

5. James T.McClave, P.George Benson; Therry Sincich, “ Statistics for business and economics”, Prentice-Hall, Inc., 1998.

6. David F.Groebner, Patric W. Shannon, Phillip C.Fry, Kent D.Smith, Business statistics, Pearson education, Inc., upper saddle river, New jersey, 2005.

 

 



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