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Tablas Estadsticas

130

Estadstica para Ciencias Qumicas

TABLA 48 : Percentiles de la distribucin Normal tipificada TABLA 49 : Percentiles de la distribucin t de Student TABLA 50 : Percentiles de la distribucin F de Fisher TABLA 51 : Percentiles de la prueba de rango mltiple de Duncan TABLA 52 : Percentiles de la distribucin ChiCuadrado TABLA 53 : Arcoseno de la raz cuadrada de datos expresados en porcentaje TABLA 54 : Coeficientes de Correlacin

Tablas Estadsticas

131

TABLA 48 Percentiles de la distribucin Normal tipificad aZ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 0.00 0.5 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 0.01 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7612 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 0.9207 0.9345 0.9463 0.9564 0.9649 0.9719 0.9778 0.9826 0.9864 0.9896 0.9920 0.9940 0.9955 0.9966 0.9975 0.9982 0.9987 0.9991 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 0.02 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.8461 0.8686 0.8888 0.9066 0.9222 0.9357 0.9474 0.9573 0.9656 0.9726 0.9783 0.9830 0.9868 0.9898 0.9922 0.9941 0.9956 0.9967 0.9976 0.9982 0.9987 0.9991 0.9994 0.9995 0.9997 0.9998 0.9999 0.9999 0.9999 0.03 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9484 0.9582 0.9664 0.9732 0.9788 0.9834 0.9871 0.9901 0.9925 0.9943 0.9957 0.9968 0.9977 0.9983 0.9988 0.9991 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 0.04 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 0.7704 0.7995 0.8264 0.8508 0.8729 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9875 0.9904 0.9927 0.9945 0.9959 0.9969 0.9977 0.9984 0.9988 0.9992 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 0.05 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.8023 0.8289 0.8531 0.8749 0.8944 0.9115 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 0.9798 0.9842 0.9878 0.9906 0.9929 0.9946 0.9960 0.9970 0.9978 0.9984 0.9989 0.9992 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 0.06 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.8051 0.8315 0.8554 0.8770 0.8962 0.9131 0.9279 0.9406 0.9515 0.9608 0.9686 0.9750 0.9803 0.9846 0.9881 0.9909 0.9931 0.9948 0.9961 0.9971 0.9979 0.9985 0.9989 0.9992 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 0.07 0.5279 0.5675 0.6064 0.6443 0.6808 0.7157 0.7486 0.7794 0.8078 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.9616 0.9693 0.9756 0.9808 0.9850 0.9884 0.9911 0.9932 0.9949 0.9962 0.9972 0.9979 0.9985 0.9989 0.9992 0.9995 0.9996 0.9997 0.9998 0.9999 0.9999 1 0.08 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.7518 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 0.9162 0.9306 0.9429 0.9535 0.9625 0.9699 0.9761 0.9812 0.9854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.9990 0.9993 0.9995 0.9996 0.9998 0.9998 0.9999 0.9999 1 0.09 0.5359 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1

132

Estadstica para Ciencias Qumicas

TABLA 49 Percentiles de la distribucin t de StudentPrueba de 2 Colas Prueba de1 Cola G.L. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 g 0.5 0.25 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.677 0.674 0.4 0.2 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.851 0.848 0.845 0.842 0.3 0.15 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1.058 1.058 1.057 1.056 1.055 1.055 1.050 1.046 1.041 1.936 0.2 0.10 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.371 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 1.289 1.282 0.1 0.05 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 1.658 1.645 0.05 0.025 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 1.980 1.960 0.02 0.01 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 2.358 2.326 0.01 0.005 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 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 2.617 2.576 0.001 0.0005 636.619 31.598 12.941 8.610 6.869 5.959 5.405 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.833 3.850 3.819 3.792 3.767 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.373 3.291

Tablas Estadsticas

133

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR G.L. DEL NUMERADOR 1 2 3 4 5 6 7 8 9 E 0.100 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.86 0.050 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 0.025 647.79 799.48 864.15 899.60 921.83 937.11 948.20 956.64 963.28 0.010 4052.18 4999.34 5403.53 5624.26 5763.96 5858.95 5928.33 5980.95 6022.40 0.005 16212.46 19997.36 21614.13 22500.75 23055.82 23439.53 23715.20 23923.81 24091.45 0.001 405311.58 499725.34 540256.50 562667.85 576496.12 586032.87 593185.42 597953.80 602245.33 0.100 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 0.050 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 0.025 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 0.010 98.50 99.00 99.16 99.25 99.30 99.33 99.36 99.38 99.39 0.005 198.50 199.01 199.16 199.24 199.30 199.33 199.36 199.38 199.39 0.001 998.38 998.84 999.31 999.31 999.31 999.31 999.31 999.31 999.31 0.100 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 0.050 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 0.025 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 0.010 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.34 0.005 55.55 49.80 47.47 46.20 45.39 44.84 44.43 44.13 43.88 0.001 167.06 148.49 141.10 137.08 134.58 132.83 131.61 130.62 129.86 0.100 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 0.050 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 0.025 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 0.010 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 0.005 31.33 26.28 24.26 23.15 22.46 21.98 21.62 21.35 21.14 0.001 74.13 61.25 56.17 53.43 51.72 50.52 49.65 49.00 48.47 0.100 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32 0.050 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 0.025 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 0.010 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 0.005 22.78 18.31 16.53 15.56 14.94 14.51 14.20 13.96 13.77 0.001 47.18 37.12 33.20 31.08 29.75 28.83 28.17 27.65 27.24 0.100 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 0.050 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 0.025 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 0.010 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 0.005 18.63 14.54 12.92 12.03 11.46 11.07 10.79 10.57 10.39 0.001 35.51 27.00 23.71 21.92 20.80 20.03 19.46 19.03 18.69 0.100 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 0.050 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 0.025 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 0.010 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 0.005 16.24 12.40 10.88 10.05 9.52 9.16 8.89 8.68 8.51 0.001 29.25 21.69 18.77 17.20 16.21 15.52 15.02 14.63 14.33

1

2

3

4

5

6

7

134

Estadstica para Ciencias Qumicas

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR 1 3.46 5.32 7.57 11.26 14.69 25.41 3.36 5.12 7.21 10.56 13.61 22.86 3.29 4.96 6.94 10.04 12.83 21.04 3.23 4.84 6.72 9.65 12.23 19.69 3.18 4.75 6.55 9.33 11.75 18.64 3.14 4.67 6.41 9.07 11.37 17.82 3.10 4.60 6.30 8.86 11.06 17.14 2 3.11 4.46 6.06 8.65 11.04 18.49 3.01 4.26 5.71 8.02 10.11 16.39 2.92 4.10 5.46 7.56 9.43 14.90 2.86 3.98 5.26 7.21 8.91 13.81 2.81 3.89 5.10 6.93 8.51 12.97 2.76 3.81 4.97 6.70 8.19 12.31 2.73 3.74 4.86 6.51 7.92 11.78 3 2.92 4.07 5.42 7.59 9.60 15.83 2.81 3.86 5.08 6.99 8.72 13.90 2.73 3.71 4.83 6.55 8.08 12.55 2.66 3.59 4.63 6.22 7.60 11.56 2.61 3.49 4.47 5.95 7.23 10.80 2.56 3.41 4.35 5.74 6.93 10.21 2.52 3.34 4.24 5.56 6.68 9.73 G.L. DEL NUMERADOR 4 5 6 2.81 2.73 2.67 3.84 3.69 3.58 5.05 4.82 4.65 7.01 6.63 6.37 8.81 8.30 7.95 14.39 13.48 12.86 2.69 2.61 2.55 3.63 3.48 3.37 4.72 4.48 4.32 6.42 6.06 5.80 7.96 7.47 7.13 12.56 11.71 11.13 2.61 2.52 2.46 3.48 3.33 3.22 4.47 4.24 4.07 5.99 5.64 5.39 7.34 6.87 6.54 11.28 10.48 9.93 2.54 2.45 2.39 3.36 3.20 3.09 4.28 4.04 3.88 5.67 5.32 5.07 6.88 6.42 6.10 10.35 9.58 9.05 2.48 2.39 2.33 3.26 3.11 3.00 4.12 3.89 3.73 5.41 5.06 4.82 6.52 6.07 5.76 9.63 8.89 8.38 2.43 2.35 2.28 3.18 3.03 2.92 4.00 3.77 3.60 5.21 4.86 4.62 6.23 5.79 5.48 9.07 8.35 7.86 2.39 2.31 2.24 3.11 2.96 2.85 3.89 3.66 3.50 5.04 4.69 4.46 6.00 5.56 5.26 8.62 7.92 7.44 7 2.62 3.50 4.53 6.18 7.69 12.40 2.51 3.29 4.20 5.61 6.88 10.70 2.41 3.14 3.95 5.20 6.30 9.52 2.34 3.01 3.76 4.89 5.86 8.65 2.28 2.91 3.61 4.64 5.52 8.00 2.23 2.83 3.48 4.44 5.25 7.49 2.19 2.76 3.38 4.28 5.03 7.08 8 2.59 3.44 4.43 6.03 7.50 12.05 2.47 3.23 4.10 5.47 6.69 10.37 2.38 3.07 3.85 5.06 6.12 9.20 2.30 2.95 3.66 4.74 5.68 8.35 2.24 2.85 3.51 4.50 5.35 7.71 2.20 2.77 3.39 4.30 5.08 7.21 2.15 2.70 3.29 4.14 4.86 6.80 9 2.56 3.39 4.36 5.91 7.34 11.77 2.44 3.18 4.03 5.35 6.54 10.11 2.35 3.02 3.78 4.94 5.97 8.96 2.27 2.90 3.59 4.63 5.54 8.12 2.21 2.80 3.44 4.39 5.20 7.48 2.16 2.71 3.31 4.19 4.94 6.98 2.12 2.65 3.21 4.03 4.72 6.58

8

9

10

11

12

13

14

E 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR E 1 2 3 G.L. DEL NUMERADOR 4 5 6 7 8 9

Tablas Estadsticas 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 3.07 4.54 6.20 8.68 10.80 16.59 3.05 4.49 6.12 8.53 10.58 16.12 3.03 4.45 6.04 8.40 10.38 15.72 3.01 4.41 5.98 8.29 10.22 15.38 2.99 4.38 5.92 8.18 10.07 15.08 2.97 4.35 5.87 8.10 9.94 14.82 2.96 4.32 5.83 8.02 9.83 14.59 2.70 3.68 4.77 6.36 7.70 11.34 2.67 3.63 4.69 6.23 7.51 10.97 2.64 3.59 4.62 6.11 7.35 10.66 2.62 3.55 4.56 6.01 7.21 10.39 2.61 3.52 4.51 5.93 7.09 10.16 2.59 3.49 4.46 5.85 6.99 9.95 2.57 3.47 4.42 5.78 6.89 9.77 2.49 3.29 4.15 5.42 6.48 9.34 2.46 3.24 4.08 5.29 6.30 9.01 2.44 3.20 4.01 5.19 6.16 8.73 2.42 3.16 3.95 5.09 6.03 8.49 2.40 3.13 3.90 5.01 5.92 8.28 2.38 3.10 3.86 4.94 5.82 8.10 2.36 3.07 3.82 4.87 5.73 7.94 2.36 3.06 3.80 4.89 5.80 8.25 2.33 3.01 3.73 4.77 5.64 7.94 2.31 2.96 3.66 4.67 5.50 7.68 2.29 2.93 3.61 4.58 5.37 7.46 2.27 2.90 3.56 4.50 5.27 7.27 2.25 2.87 3.51 4.43 5.17 7.10 2.23 2.84 3.48 4.37 5.09 6.95 2.27 2.90 3.58 4.56 5.37 7.57 2.24 2.85 3.50 4.44 5.21 7.27 2.22 2.81 3.44 4.34 5.07 7.02 2.20 2.77 3.38 4.25 4.96 6.81 2.18 2.74 3.33 4.17 4.85 6.62 2.16 2.71 3.29 4.10 4.76 6.46 2.14 2.68 3.25 4.04 4.68 6.32 2.21 2.79 3.41 4.32 5.07 7.09 2.18 2.74 3.34 4.20 4.91 6.80 2.15 2.70 3.28 4.10 4.78 6.56 2.13 2.66 3.22 4.01 4.66 6.35 2.11 2.63 3.17 3.94 4.56 6.18 2.09 2.60 3.13 3.87 4.47 6.02 2.08 2.57 3.09 3.81 4.39 5.88 2.16 2.71 3.29 4.14 4.85 6.74 2.13 2.66 3.22 4.03 4.69 6.46 2.10 2.61 3.16 3.93 4.56 6.22 2.08 2.58 3.10 3.84 4.44 6.02 2.06 2.54 3.05 3.77 4.34 5.85 2.04 2.51 3.01 3.70 4.26 5.69 2.02 2.49 2.97 3.64 4.18 5.56

135 2.12 2.64 3.20 4.00 4.67 6.47 2.09 2.59 3.12 3.89 4.52 6.20 2.06 2.55 3.06 3.79 4.39 5.96 2.04 2.51 3.01 3.71 4.28 5.76 2.02 2.48 2.96 3.63 4.18 5.59 2.00 2.45 2.91 3.56 4.09 5.44 1.98 2.42 2.87 3.51 4.01 5.31 2.09 2.59 3.12 3.89 4.54 6.26 2.06 2.54 3.05 3.78 4.38 5.98 2.03 2.49 2.98 3.68 4.25 5.75 2.00 2.46 2.93 3.60 4.14 5.56 1.98 2.42 2.88 3.52 4.04 5.39 1.96 2.39 2.84 3.46 3.96 5.24 1.95 2.37 2.80 3.40 3.88 5.11

15

16

17

18

19

20

21

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR 1 2 3 G.L. DEL NUMERADOR 4 5 6 7 8 9

E

136 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 2.95 4.30 5.79 7.95 9.73 14.38 2.94 4.28 5.75 7.88 9.63 14.20 2.93 4.26 5.72 7.82 9.55 14.03 2.92 4.24 5.69 7.77 9.48 13.88 2.91 4.23 5.66 7.72 9.41 13.74 2.90 4.21 5.63 7.68 9.34 13.61 2.89 4.20 5.61 7.64 9.28 13.50 2.56 3.44 4.38 5.72 6.81 9.61 2.55 3.42 4.35 5.66 6.73 9.47 2.54 3.40 4.32 5.61 6.66 9.34 2.53 3.39 4.29 5.57 6.60 9.22 2.52 3.37 4.27 5.53 6.54 9.12 2.51 3.35 4.24 5.49 6.49 9.02 2.50 3.34 4.22 5.45 6.44 8.93 2.35 3.05 3.78 4.82 5.65 7.80 2.34 3.03 3.75 4.76 5.58 7.67 2.33 3.01 3.72 4.72 5.52 7.55 2.32 2.99 3.69 4.68 5.46 7.45 2.31 2.98 3.67 4.64 5.41 7.36 2.30 2.96 3.65 4.60 5.36 7.27 2.29 2.95 3.63 4.57 5.32 7.19 2.22 2.82 3.44 4.31 5.02 6.81 2.21 2.80 3.41 4.26 4.95 6.70 2.19 2.78 3.38 4.22 4.89 6.59 2.18 2.76 3.35 4.18 4.84 6.49 2.17 2.74 3.33 4.14 4.79 6.41 2.17 2.73 3.31 4.11 4.74 6.33 2.16 2.71 3.29 4.07 4.70 6.25

Estadstica para Ciencias Qumicas 2.13 2.66 3.22 3.99 4.61 6.19 2.11 2.64 3.18 3.94 4.54 6.08 2.10 2.62 3.15 3.90 4.49 5.98 2.09 2.60 3.13 3.85 4.43 5.89 2.08 2.59 3.10 3.82 4.38 5.80 2.07 2.57 3.08 3.78 4.34 5.73 2.06 2.56 3.06 3.75 4.30 5.66 2.06 2.55 3.05 3.76 4.32 5.76 2.05 2.53 3.02 3.71 4.26 5.65 2.04 2.51 2.99 3.67 4.20 5.55 2.02 2.49 2.97 3.63 4.15 5.46 2.01 2.47 2.94 3.59 4.10 5.38 2.00 2.46 2.92 3.56 4.06 5.31 2.00 2.45 2.90 3.53 4.02 5.24 2.01 2.46 2.93 3.59 4.11 5.44 1.99 2.44 2.90 3.54 4.05 5.33 1.98 2.42 2.87 3.50 3.99 5.24 1.97 2.40 2.85 3.46 3.94 5.15 1.96 2.39 2.82 3.42 3.89 5.07 1.95 2.37 2.80 3.39 3.85 5.00 1.94 2.36 2.78 3.36 3.81 4.93 1.97 2.40 2.84 3.45 3.94 5.19 1.95 2.37 2.81 3.41 3.88 5.09 1.94 2.36 2.78 3.36 3.83 4.99 1.93 2.34 2.75 3.32 3.78 4.91 1.92 2.32 2.73 3.29 3.73 4.83 1.91 2.31 2.71 3.26 3.69 4.76 1.90 2.29 2.69 3.23 3.65 4.69 1.93 2.34 2.76 3.35 3.81 4.99 1.92 2.32 2.73 3.30 3.75 4.89 1.91 2.30 2.70 3.26 3.69 4.80 1.89 2.28 2.68 3.22 3.64 4.71 1.88 2.27 2.65 3.18 3.60 4.64 1.87 2.25 2.63 3.15 3.56 4.57 1.87 2.24 2.61 3.12 3.52 4.50

22

23

24

25

26

27

28

Tablas Estadsticas

137

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR 1 2.89 4.18 5.59 7.60 9.23 13.39 2.88 4.17 5.57 7.56 9.18 13.29 2.84 4.08 5.42 7.31 8.83 12.61 2.79 4.00 5.29 7.08 8.49 11.97 2.75 3.92 5.15 6.85 8.18 11.38 2.71 3.84 5.02 6.63 7.88 10.83 2 2.50 3.33 4.20 5.42 6.40 8.85 2.49 3.32 4.18 5.39 6.35 8.77 2.44 3.23 4.05 5.18 6.07 8.25 2.39 3.15 3.93 4.98 5.79 7.77 2.35 3.07 3.80 4.79 5.54 7.32 2.30 3.00 3.69 4.61 5.30 6.91 3 2.28 2.93 3.61 4.54 5.28 7.12 2.28 2.92 3.59 4.51 5.24 7.05 2.23 2.84 3.46 4.31 4.98 6.59 2.18 2.76 3.34 4.13 4.73 6.17 2.13 2.68 3.23 3.95 4.50 5.78 2.08 2.60 3.12 3.78 4.28 5.42 4 2.15 2.70 3.27 4.04 4.66 6.19 2.14 2.69 3.25 4.02 4.62 6.12 2.09 2.61 3.13 3.83 4.37 5.70 2.04 2.53 3.01 3.65 4.14 5.31 1.99 2.45 2.89 3.48 3.92 4.95 1.94 2.37 2.79 3.32 3.72 4.62 5 2.06 2.55 3.04 3.73 4.26 5.59 2.05 2.53 3.03 3.70 4.23 5.53 2.00 2.45 2.90 3.51 3.99 5.13 1.95 2.37 2.79 3.34 3.76 4.76 1.90 2.29 2.67 3.17 3.55 4.42 1.85 2.21 2.57 3.02 3.35 4.10 6 1.99 2.43 2.88 3.50 3.98 5.18 1.98 2.42 2.87 3.47 3.95 5.12 1.93 2.34 2.74 3.29 3.71 4.73 1.87 2.25 2.63 3.12 3.49 4.37 1.82 2.18 2.52 2.96 3.28 4.04 1.77 2.10 2.41 2.80 3.09 3.74 7 1.93 2.35 2.76 3.33 3.77 4.87 1.93 2.33 2.75 3.30 3.74 4.82 1.87 2.25 2.62 3.12 3.51 4.44 1.82 2.17 2.51 2.95 3.29 4.09 1.77 2.09 2.39 2.79 3.09 3.77 1.72 2.01 2.29 2.64 2.90 3.47 8 1.89 2.28 2.67 3.20 3.61 4.64 1.88 2.27 2.65 3.17 3.58 4.58 1.83 2.18 2.53 2.99 3.35 4.21 1.77 2.10 2.41 2.82 3.13 3.86 1.72 2.02 2.30 2.66 2.93 3.55 1.67 1.94 2.19 2.51 2.74 3.27 9 1.86 2.22 2.59 3.09 3.48 4.45 1.85 2.21 2.57 3.07 3.45 4.39 1.79 2.12 2.45 2.89 3.22 4.02 1.74 2.04 2.33 2.72 3.01 3.69 1.68 1.96 2.22 2.56 2.81 3.38 1.63 1.88 2.11 2.41 2.62 3.10

29

30

40

60

120

g

E 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001

138

Estadstica para Ciencias Qumicas

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR G.L. DEL NUMERADOR 10 12 15 20 24 30 40 60 120 g 60.19 60.71 61.22 61.74 62.00 62.26 62.53 62.79 63.06 63.33 241.88 243.90 245.95 248.02 249.05 250.10 251.14 252.20 253.25 254.32 968.63 976.72 984.87 993.08 997.27 1001.40 1005.60 1009.79 1014.04 1018.26 6055.93 6106.68 6156.97 6208.66 6234.27 6260.35 6286.43 6312.97 6339.51 6365.59 24221.84 24426.73 24631.62 24836.51 24937.09 25041.40 25145.71 25253.74 25358.05 25466.08 605583.19 610351.56 616073.61 620841.98 623703.00 626087.19 628471.37 631332.40 634193.42 636577.61 9.39 9.41 9.42 9.44 9.45 9.46 9.47 9.47 9.48 9.49 19.40 19.41 19.43 19.45 19.45 19.46 19.47 19.48 19.49 19.50 39.40 39.41 39.43 39.45 39.46 39.46 39.47 39.48 39.49 39.50 99.40 99.42 99.43 99.45 99.46 99.47 99.48 99.48 99.49 99.50 199.39 199.42 199.43 199.45 199.45 199.48 199.48 199.48 199.49 199.51 999.31 999.31 999.31 999.31 999.31 999.31 999.31 999.31 999.31 999.31 5.23 5.22 5.20 5.18 5.18 5.17 5.16 5.15 5.14 5.13 8.79 8.74 8.70 8.66 8.64 8.62 8.59 8.57 8.55 8.53 14.42 14.34 14.25 14.17 14.12 14.08 14.04 13.99 13.95 13.90 27.23 27.05 26.87 26.69 26.60 26.50 26.41 26.32 26.22 26.13 43.68 43.39 43.08 42.78 42.62 42.47 42.31 42.15 41.99 41.83 129.22 128.32 127.36 126.43 125.93 125.44 124.97 124.45 123.98 123.46 3.92 3.90 3.87 3.84 3.83 3.82 3.80 3.79 3.78 3.76 5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.63 8.84 8.75 8.66 8.56 8.51 8.46 8.41 8.36 8.31 8.26 14.55 14.37 14.20 14.02 13.93 13.84 13.75 13.65 13.56 13.46 20.97 20.70 20.44 20.17 20.03 19.89 19.75 19.61 19.47 19.32 48.05 47.41 46.76 46.10 45.77 45.43 45.08 44.75 44.40 44.05 3.30 3.27 3.24 3.21 3.19 3.17 3.16 3.14 3.12 3.11 4.74 4.68 4.62 4.56 4.53 4.50 4.46 4.43 4.40 4.37 6.62 6.52 6.43 6.33 6.28 6.23 6.18 6.12 6.07 6.02 10.05 9.89 9.72 9.55 9.47 9.38 9.29 9.20 9.11 9.02 13.62 13.38 13.15 12.90 12.78 12.66 12.53 12.40 12.27 12.14 26.91 26.42 25.91 25.39 25.13 24.87 24.60 24.33 24.06 23.79 2.94 2.90 2.87 2.84 2.82 2.80 2.78 2.76 2.74 2.72 4.06 4.00 3.94 3.87 3.84 3.81 3.77 3.74 3.70 3.67 5.46 5.37 5.27 5.17 5.12 5.07 5.01 4.96 4.90 4.85 7.87 7.72 7.56 7.40 7.31 7.23 7.14 7.06 6.97 6.88 10.25 10.03 9.81 9.59 9.47 9.36 9.24 9.12 9.00 8.88 18.41 17.99 17.56 17.12 16.90 16.67 16.44 16.21 15.98 15.75 2.70 2.67 2.63 2.59 2.58 2.56 2.54 2.51 2.49 2.47 3.64 3.57 3.51 3.44 3.41 3.38 3.34 3.30 3.27 3.23 4.76 4.67 4.57 4.47 4.41 4.36 4.31 4.25 4.20 4.14 6.62 6.47 6.31 6.16 6.07 5.99 5.91 5.82 5.74 5.65 8.38 8.18 7.97 7.75 7.64 7.53 7.42 7.31 7.19 7.08 14.08 13.71 13.32 12.93 12.73 12.53 12.33 12.12 11.91 11.70

1

2

3

4

5

6

7

E 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001

Tablas Estadsticas

139

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR 10 2.54 3.35 4.30 5.81 7.21 11.54 2.42 3.14 3.96 5.26 6.42 9.89 2.32 2.98 3.72 4.85 5.85 8.75 2.25 2.85 3.53 4.54 5.42 7.92 2.19 2.75 3.37 4.30 5.09 7.29 2.14 2.67 3.25 4.10 4.82 6.80 2.10 2.60 3.15 3.94 4.60 6.40 12 2.50 3.28 4.20 5.67 7.01 11.19 2.38 3.07 3.87 5.11 6.23 9.57 2.28 2.91 3.62 4.71 5.66 8.45 2.21 2.79 3.43 4.40 5.24 7.63 2.15 2.69 3.28 4.16 4.91 7.00 2.10 2.60 3.15 3.96 4.64 6.52 2.05 2.53 3.05 3.80 4.43 6.13 15 2.46 3.22 4.10 5.52 6.81 10.84 2.34 3.01 3.77 4.96 6.03 9.24 2.24 2.85 3.52 4.56 5.47 8.13 2.17 2.72 3.33 4.25 5.05 7.32 2.10 2.62 3.18 4.01 4.72 6.71 2.05 2.53 3.05 3.82 4.46 6.23 2.01 2.46 2.95 3.66 4.25 5.85 G.L. DEL NUMERADOR 20 24 30 2.42 2.40 2.38 3.15 3.12 3.08 4.00 3.95 3.89 5.36 5.28 5.20 6.61 6.50 6.40 10.48 10.30 10.11 2.30 2.28 2.25 2.94 2.90 2.86 3.67 3.61 3.56 4.81 4.73 4.65 5.83 5.73 5.62 8.90 8.72 8.55 2.20 2.18 2.16 2.77 2.74 2.70 3.42 3.37 3.31 4.41 4.33 4.25 5.27 5.17 5.07 7.80 7.64 7.47 2.12 2.10 2.08 2.65 2.61 2.57 3.23 3.17 3.12 4.10 4.02 3.94 4.86 4.76 4.65 7.01 6.85 6.68 2.06 2.04 2.01 2.54 2.51 2.47 3.07 3.02 2.96 3.86 3.78 3.70 4.53 4.43 4.33 6.40 6.25 6.09 2.01 1.98 1.96 2.46 2.42 2.38 2.95 2.89 2.84 3.66 3.59 3.51 4.27 4.17 4.07 5.93 5.78 5.63 1.96 1.94 1.91 2.39 2.35 2.31 2.84 2.79 2.73 3.51 3.43 3.35 4.06 3.96 3.86 5.56 5.41 5.25 40 2.36 3.04 3.84 5.12 6.29 9.92 2.23 2.83 3.51 4.57 5.52 8.37 2.13 2.66 3.26 4.17 4.97 7.30 2.05 2.53 3.06 3.86 4.55 6.52 1.99 2.43 2.91 3.62 4.23 5.93 1.93 2.34 2.78 3.43 3.97 5.47 1.89 2.27 2.67 3.27 3.76 5.10 60 2.34 3.01 3.78 5.03 6.18 9.73 2.21 2.79 3.45 4.48 5.41 8.19 2.11 2.62 3.20 4.08 4.86 7.12 2.03 2.49 3.00 3.78 4.45 6.35 1.96 2.38 2.85 3.54 4.12 5.76 1.90 2.30 2.72 3.34 3.87 5.30 1.86 2.22 2.61 3.18 3.66 4.94 120 2.32 2.97 3.73 4.95 6.06 9.53 2.18 2.75 3.39 4.40 5.30 8.00 2.08 2.58 3.14 4.00 4.75 6.94 2.00 2.45 2.94 3.69 4.34 6.18 1.93 2.34 2.79 3.45 4.01 5.59 1.88 2.25 2.66 3.25 3.76 5.14 1.83 2.18 2.55 3.09 3.55 4.77

8

9

10

11

12

13

14

E 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001

g 2.29 2.93 3.67 4.86 5.95 9.33 2.16 2.71 3.33 4.31 5.19 7.81 2.06 2.54 3.08 3.91 4.64 6.76 1.97 2.40 2.88 3.60 4.23 6.00 1.90 2.30 2.72 3.36 3.90 5.42 1.85 2.21 2.60 3.17 3.65 4.97 1.80 2.13 2.49 3.00 3.44 4.60

140

Estadstica para Ciencias Qumicas

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR G.L. DEL NUMERADOR 24 30 1.90 1.87 2.29 2.25 2.70 2.64 3.29 3.21 3.79 3.69 5.10 4.95 1.87 1.84 2.24 2.19 2.63 2.57 3.18 3.10 3.64 3.54 4.85 4.70 1.84 1.81 2.19 2.15 2.56 2.50 3.08 3.00 3.51 3.41 4.63 4.48 1.81 1.78 2.15 2.11 2.50 2.44 3.00 2.92 3.40 3.30 4.45 4.30 1.79 1.76 2.11 2.07 2.45 2.39 2.92 2.84 3.31 3.21 4.29 4.14 1.77 1.74 2.08 2.04 2.41 2.35 2.86 2.78 3.22 3.12 4.15 4.00 1.75 1.72 2.05 2.01 2.37 2.31 2.80 2.72 3.15 3.05 4.03 3.88

15

16

17

18

19

20

21

E 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001

10 2.06 2.54 3.06 3.80 4.42 6.08 2.03 2.49 2.99 3.69 4.27 5.81 2.00 2.45 2.92 3.59 4.14 5.58 1.98 2.41 2.87 3.51 4.03 5.39 1.96 2.38 2.82 3.43 3.93 5.22 1.94 2.35 2.77 3.37 3.85 5.08 1.92 2.32 2.73 3.31 3.77 4.95

12 2.02 2.48 2.96 3.67 4.25 5.81 1.99 2.42 2.89 3.55 4.10 5.55 1.96 2.38 2.82 3.46 3.97 5.32 1.93 2.34 2.77 3.37 3.86 5.13 1.91 2.31 2.72 3.30 3.76 4.97 1.89 2.28 2.68 3.23 3.68 4.82 1.87 2.25 2.64 3.17 3.60 4.70

15 1.97 2.40 2.86 3.52 4.07 5.54 1.94 2.35 2.79 3.41 3.92 5.27 1.91 2.31 2.72 3.31 3.79 5.05 1.89 2.27 2.67 3.23 3.68 4.87 1.86 2.23 2.62 3.15 3.59 4.70 1.84 2.20 2.57 3.09 3.50 4.56 1.83 2.18 2.53 3.03 3.43 4.44

20 1.92 2.33 2.76 3.37 3.88 5.25 1.89 2.28 2.68 3.26 3.73 4.99 1.86 2.23 2.62 3.16 3.61 4.78 1.84 2.19 2.56 3.08 3.50 4.59 1.81 2.16 2.51 3.00 3.40 4.43 1.79 2.12 2.46 2.94 3.32 4.29 1.78 2.10 2.42 2.88 3.24 4.17

40 1.85 2.20 2.59 3.13 3.59 4.80 1.81 2.15 2.51 3.02 3.44 4.54 1.78 2.10 2.44 2.92 3.31 4.33 1.75 2.06 2.38 2.84 3.20 4.15 1.73 2.03 2.33 2.76 3.11 3.99 1.71 1.99 2.29 2.69 3.02 3.86 1.69 1.96 2.25 2.64 2.95 3.74

60 1.82 2.16 2.52 3.05 3.48 4.64 1.78 2.11 2.45 2.93 3.33 4.39 1.75 2.06 2.38 2.83 3.21 4.18 1.72 2.02 2.32 2.75 3.10 4.00 1.70 1.98 2.27 2.67 3.00 3.84 1.68 1.95 2.22 2.61 2.92 3.70 1.66 1.92 2.18 2.55 2.84 3.58

120 1.79 2.11 2.46 2.96 3.37 4.48 1.75 2.06 2.38 2.84 3.22 4.23 1.72 2.01 2.32 2.75 3.10 4.02 1.69 1.97 2.26 2.66 2.99 3.84 1.67 1.93 2.20 2.58 2.89 3.68 1.64 1.90 2.16 2.52 2.81 3.54 1.62 1.87 2.11 2.46 2.73 3.42

g 1.76 2.07 2.40 2.87 3.26 4.31 1.72 2.01 2.32 2.75 3.11 4.06 1.69 1.96 2.25 2.65 2.98 3.85 1.66 1.92 2.19 2.57 2.87 3.67 1.63 1.88 2.13 2.49 2.78 3.51 1.61 1.84 2.09 2.42 2.69 3.38 1.59 1.81 2.04 2.36 2.61 3.26

Tablas Estadsticas

141

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR 10 1.90 2.30 2.70 3.26 3.70 4.83 1.89 2.27 2.67 3.21 3.64 4.73 1.88 2.25 2.64 3.17 3.59 4.64 1.87 2.24 2.61 3.13 3.54 4.56 1.86 2.22 2.59 3.09 3.49 4.48 1.85 2.20 2.57 3.06 3.45 4.41 1.84 2.19 2.55 3.03 3.41 4.35 12 1.86 2.23 2.60 3.12 3.54 4.58 1.84 2.20 2.57 3.07 3.47 4.48 1.83 2.18 2.54 3.03 3.42 4.39 1.82 2.16 2.51 2.99 3.37 4.31 1.81 2.15 2.49 2.96 3.33 4.24 1.80 2.13 2.47 2.93 3.28 4.17 1.79 2.12 2.45 2.90 3.25 4.11 15 1.81 2.15 2.50 2.98 3.36 4.33 1.80 2.13 2.47 2.93 3.30 4.23 1.78 2.11 2.44 2.89 3.25 4.14 1.77 2.09 2.41 2.85 3.20 4.06 1.76 2.07 2.39 2.81 3.15 3.99 1.75 2.06 2.36 2.78 3.11 3.92 1.74 2.04 2.34 2.75 3.07 3.86 20 1.76 2.07 2.39 2.83 3.18 4.06 1.74 2.05 2.36 2.78 3.12 3.96 1.73 2.03 2.33 2.74 3.06 3.87 1.72 2.01 2.30 2.70 3.01 3.79 1.71 1.99 2.28 2.66 2.97 3.72 1.70 1.97 2.25 2.63 2.93 3.66 1.69 1.96 2.23 2.60 2.89 3.60 G.L. DEL NUMERADOR 24 30 1.73 1.70 2.03 1.98 2.33 2.27 2.75 2.67 3.08 2.98 3.92 3.78 1.72 1.69 2.01 1.96 2.30 2.24 2.70 2.62 3.02 2.92 3.82 3.68 1.70 1.67 1.98 1.94 2.27 2.21 2.66 2.58 2.97 2.87 3.74 3.59 1.69 1.66 1.96 1.92 2.24 2.18 2.62 2.54 2.92 2.82 3.66 3.52 1.68 1.65 1.95 1.90 2.22 2.16 2.58 2.50 2.87 2.77 3.59 3.44 1.67 1.64 1.93 1.88 2.19 2.13 2.55 2.47 2.83 2.73 3.52 3.38 1.66 1.63 1.91 1.87 2.17 2.11 2.52 2.44 2.79 2.69 3.46 3.32 40 1.67 1.94 2.21 2.58 2.88 3.63 1.66 1.91 2.18 2.54 2.82 3.53 1.64 1.89 2.15 2.49 2.77 3.45 1.63 1.87 2.12 2.45 2.72 3.37 1.61 1.85 2.09 2.42 2.67 3.30 1.60 1.84 2.07 2.38 2.63 3.23 1.59 1.82 2.05 2.35 2.59 3.18 60 1.64 1.89 2.14 2.50 2.77 3.48 1.62 1.86 2.11 2.45 2.71 3.38 1.61 1.84 2.08 2.40 2.66 3.29 1.59 1.82 2.05 2.36 2.61 3.22 1.58 1.80 2.03 2.33 2.56 3.15 1.57 1.79 2.00 2.29 2.52 3.08 1.56 1.77 1.98 2.26 2.48 3.02 120 1.60 1.84 2.08 2.40 2.66 3.32 1.59 1.81 2.04 2.35 2.60 3.22 1.57 1.79 2.01 2.31 2.55 3.14 1.56 1.77 1.98 2.27 2.50 3.06 1.54 1.75 1.95 2.23 2.45 2.99 1.53 1.73 1.93 2.20 2.41 2.92 1.52 1.71 1.91 2.17 2.37 2.86

22

23

24

25

26

27

28

E 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001

g 1.57 1.78 2.00 2.31 2.55 3.15 1.55 1.76 1.97 2.26 2.48 3.05 1.53 1.73 1.94 2.21 2.43 2.97 1.52 1.71 1.91 2.17 2.38 2.89 1.50 1.69 1.88 2.13 2.33 2.82 1.49 1.67 1.85 2.10 2.29 2.75 1.48 1.65 1.83 2.06 2.25 2.69

142

Estadstica para Ciencias Qumicas

TABLA 50 Percentiles de la distribucin F de FisherG.L. ERROR G.L. DEL NUMERADOR 24 30 1.65 1.62 1.90 1.85 2.15 2.09 2.49 2.41 2.76 2.66 3.41 3.27 1.64 1.61 1.89 1.84 2.14 2.07 2.47 2.39 2.73 2.63 3.36 3.22 1.57 1.54 1.79 1.74 2.01 1.94 2.29 2.20 2.50 2.40 3.01 2.87 1.51 1.48 1.70 1.65 1.88 1.82 2.12 2.03 2.29 2.19 2.69 2.55 1.45 1.41 1.61 1.55 1.76 1.69 1.95 1.86 2.09 1.98 2.40 2.26 1.38 1.34 1.52 1.46 1.64 1.57 1.79 1.70 1.90 1.79 2.13 1.99

29

30

40

60

120

g

E 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001 0.100 0.050 0.025 0.010 0.005 0.001

10 1.83 2.18 2.53 3.00 3.38 4.29 1.82 2.16 2.51 2.98 3.34 4.24 1.76 2.08 2.39 2.80 3.12 3.87 1.71 1.99 2.27 2.63 2.90 3.54 1.65 1.91 2.16 2.47 2.71 3.24 1.60 1.83 2.05 2.32 2.52 2.96

12 1.78 2.10 2.43 2.87 3.21 4.05 1.77 2.09 2.41 2.84 3.18 4.00 1.71 2.00 2.29 2.66 2.95 3.64 1.66 1.92 2.17 2.50 2.74 3.32 1.60 1.83 2.05 2.34 2.54 3.02 1.55 1.75 1.94 2.18 2.36 2.74

15 1.73 2.03 2.32 2.73 3.04 3.80 1.72 2.01 2.31 2.70 3.01 3.75 1.66 1.92 2.18 2.52 2.78 3.40 1.60 1.84 2.06 2.35 2.57 3.08 1.55 1.75 1.94 2.19 2.37 2.78 1.49 1.67 1.83 2.04 2.19 2.51

20 1.68 1.94 2.21 2.57 2.86 3.54 1.67 1.93 2.20 2.55 2.82 3.49 1.61 1.84 2.07 2.37 2.60 3.15 1.54 1.75 1.94 2.20 2.39 2.83 1.48 1.66 1.82 2.03 2.19 2.53 1.42 1.57 1.71 1.88 2.00 2.27

40 1.58 1.81 2.03 2.33 2.56 3.12 1.57 1.79 2.01 2.30 2.52 3.07 1.51 1.69 1.88 2.11 2.30 2.73 1.44 1.59 1.74 1.94 2.08 2.41 1.37 1.50 1.61 1.76 1.87 2.11 1.30 1.39 1.48 1.59 1.67 1.84

60 1.55 1.75 1.96 2.23 2.45 2.97 1.54 1.74 1.94 2.21 2.42 2.92 1.47 1.64 1.80 2.02 2.18 2.57 1.40 1.53 1.67 1.84 1.96 2.25 1.32 1.43 1.53 1.66 1.75 1.95 1.24 1.32 1.39 1.47 1.53 1.66

120 1.51 1.70 1.89 2.14 2.33 2.81 1.50 1.68 1.87 2.11 2.30 2.76 1.42 1.58 1.72 1.92 2.06 2.41 1.35 1.47 1.58 1.73 1.83 2.08 1.26 1.35 1.43 1.53 1.61 1.77 1.17 1.22 1.27 1.32 1.36 1.45

g 1.47 1.64 1.81 2.03 2.21 2.64 1.46 1.62 1.79 2.01 2.18 2.59 1.38 1.51 1.64 1.80 1.93 2.23 1.29 1.39 1.48 1.60 1.69 1.89 1.19 1.25 1.31 1.38 1.43 1.54 1.00 1.00 1.00 1.00 1.00 1.00

Tablas Estadsticas

143

TABLA 51 Percentiles de la prueba de rango mltiple de DuncanG.L. ERROR 1 2 3 4 5 6 7 E 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 2 18.0 90.0 6.09 14.0 4.50 8.26 3.93 6.51 3.64 5.70 3.46 5.24 3.35 4.95 3.26 4.74 3.20 4.60 3.15 4.48 3.11 4.39 3.08 4.32 3.06 4.26 3.03 4.21 3.01 4.17 3.00 4.13 2.98 4.10 2.97 4.07 2.96 4.05 2.95 4.02 3 18.0 90.0 6.09 14.0 4.50 8.50 4.01 6.80 3.74 5.96 3.58 5.51 3.47 5.22 3.39 5.00 3.34 4.86 3.30 4.73 3.27 4.63 3.23 4.55 3.21 4.48 3.18 4.42 3.16 4.37 3.15 4.34 3.13 4.30 3.12 4.27 3.11 4.24 3.10 4.22 4 18.0 90.0 6.09 14.0 4.50 8.60 4.02 6.90 3.79 6.11 3.64 5.65 3.54 5.37 3.47 5.14 3.41 4.99 3.37 4.88 3.35 4.77 3.33 4.68 3.30 4.62 3.27 4.55 3.25 4.50 3.23 4.45 3.22 4.41 3.21 4.38 3.19 4.35 3.18 4.33 5 18.0 90.0 6.09 14.0 4.50 8.70 4.02 7.00 3.83 6.18 3.68 5.73 3.58 5.45 3.52 5.23 3.47 5.08 3.43 4.96 3.39 4.86 3.36 4.76 3.35 4.69 3.33 4.63 3.31 4.58 3.30 4.54 3.28 4.50 3.27 4.46 3.26 4.43 3.25 4.40 NUMERO DE MEDIAS CONSIDERADAS 6 7 8 9 10 12 14 18.0 18.0 18.0 18.0 18.0 18.0 18.0 90.0 90.0 90.0 90.0 90.0 90.0 90.0 6.09 14.0 4.50 8.80 4.02 7.10 3.83 6.26 3.68 5.81 3.60 5.53 3.55 5.32 3.50 5.17 3.46 5.06 3.43 4.94 3.40 4.84 3.38 4.74 3.37 4.70 3.36 4.64 3.34 4.60 3.33 4.56 3.32 4.53 3.31 4.50 3.30 4.47 6.09 14.0 4.50 8.90 4.02 7.1 3.83 6.33 3.68 5.88 3.61 5.61 3.56 5.40 3.52 5.25 3.47 5.13 3.44 5.01 3.42 4.92 3.41 4.84 3.39 4.78 3.38 4.72 3.37 4.67 3.36 4.63 3.35 4.59 3.35 4.56 3.34 4.53 6.09 14.0 4.50 8.90 4.02 7.20 3.83 6.40 3.68 5.95 3.61 5.69 3.56 5.47 3.52 5.32 3.47 5.20 3.45 5.06 3.44 4.96 3.42 4.88 3.41 4.83 3.40 4.77 3.39 4.72 3.38 4.68 3.37 4.64 3.37 4.61 3.36 4.58 6.09 14.0 4.50 9.00 4.02 7.20 3.83 6.44 3.68 6.00 3.61 5.73 3.56 5.51 3.52 5.36 3.47 5.24 3.46 5.12 3.44 5.02 3.44 4.94 3.42 4.87 3.42 4.81 3.41 4.76 3.40 4.72 3.39 4.68 3.39 4.64 3.38 4.61 6.09 14.0 4.50 9.00 4.02 7.30 3.83 6.50 3.68 6.00 3.61 5.80 3.56 5.50 3.52 5.40 3.47 5.28 3.46 5.15 3.46 5.07 3.45 4.98 3.44 4.91 3.43 4.84 3.43 4.79 3.42 4.75 3.41 4.71 3.41 4.67 3.40 4.65 6.09 14.0 4.50 9.00 4.02 7.30 3.83 6.60 3.68 6.10 3.61 5.80 3.56 5.60 3.52 5.50 3.47 5.36 3.46 5.24 3.46 5.13 3.45 5.04 3.45 4.96 3.44 4.90 3.44 4.84 3.44 4.80 3.43 4.76 3.43 4.72 3.43 4.69 6.09 14.0 4.50 9.10 4.02 7.40 3.83 6.60 3.68 6.20 3.61 5.90 3.56 5.70 3.52 5.50 3.47 5.42 3.46 5.28 3.46 5.17 3.46 5.08 3.46 5.00 3.45 4.94 3.45 4.88 3.45 4.83 3.45 4.79 3.44 4.76 3.44 4.73 16 18.0 90.0 6.09 14.0 4.50 9.20 4.02 7.40 3.83 6.70 3.68 6.20 3.61 5.90 3.56 5.70 3.52 5.60 3.47 5.48 3.46 5.34 3.46 5.22 3.46 5.13 3.46 5.04 3.46 4.97 3.46 4.91 3.46 4.86 3.46 4.82 3.46 4.79 3.46 4.76 18 18.0 90.0 6.09 14.0 4.50 9.30 4.02 7.50 3.83 6.70 3.68 6.30 3.61 6.00 3.56 5.80 3.52 5.70 3.47 5.54 3.47 5.38 3.47 5.24 3.47 5.14 3.47 5.06 3.47 4.99 3.47 4.93 3.47 4.88 3.47 4.84 3.47 4.81 3.46 4.78 20 18.0 90.0 6.09 14.0 4.50 9.30 4.02 7.50 3.83 6.80 3.68 6.30 3.61 6.00 3.56 5.80 3.52 5.70 3.48 5.55 3.48 5.39 3.48 5.26 3.47 5.15 3.47 5.07 3.47 5.00 3.47 4.94 3.47 4.89 3.47 4.85 3.47 4.82 3.47 4.79

8 9 10 11 12 13 14

15 16 17 18 19 20

144

Estadstica para Ciencias Qumicas

TABLA 51 Percentiles de la prueba de rango mltiple de DuncanG.L. ERROR 22 24 26 28 30 40 60 100 g E 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 2 2.93 3.99 2.92 3.96 2.91 3.93 2.90 3.91 2.89 3.89 2.86 3.82 2.83 3.76 2.80 3.71 2.77 3.64 3 3.08 4.17 3.07 4.14 3.06 4.11 3.04 4.08 3.04 4.06 3.01 3.99 2.98 3.92 2.95 3.86 2.92 3.80 4 3.17 4.28 3.15 4.24 3.14 4.21 3.13 4.18 3.12 4.16 3.10 4.10 3.08 4.03 3.05 3.98 3.02 3.90 5 3.24 4.36 3.22 4.33 3.21 4.30 3.20 4.28 3.20 4.22 3.17 4.17 3.14 4.12 3.12 4.06 3.09 3.98 NUMERO DE MEDIAS CONSIDERADAS 6 7 8 9 10 12 14 3.29 3.32 3.35 3.37 3.39 3.42 3.44 4.42 4.48 4.53 4.57 4.60 4.65 4.64 3.28 4.39 3.27 4.36 3.26 4.34 3.25 4.32 3.22 4.24 3.20 4.17 3.18 4.11 3.15 4.04 3.31 4.44 3.30 4.41 3.30 4.39 3.29 4.36 3.27 4.30 3.24 4.23 3.22 4.17 3.19 4.09 3.34 4.49 3.34 4.46 3.33 4.43 3.32 4.41 3.30 4.34 3.28 4.27 3.26 4.21 3.23 4.14 3.37 4.53 3.36 4.50 3.35 4.47 3.35 4.45 3.33 4.37 3.31 4.31 3.29 4.25 3.26 4.17 3.38 4.57 3.38 4.53 3.37 4.51 3.37 4.48 3.35 4.41 3.33 4.34 3.32 4.29 3.29 4.20 3.41 4.62 3.41 4.58 3.40 4.56 3.40 4.54 3.39 4.46 3.37 4.39 3.36 4.35 3.34 4.26 3.44 4.64 3.43 4.62 3.43 4.60 3.43 4.58 3.42 4.51 3.40 4.44 3.40 4.38 3.38 4.31 16 3.45 4.71 3.45 4.67 3.45 4.65 3.45 4.62 3.44 4.61 3.44 4.54 3.43 4.47 3.42 4.42 3.41 4.34 18 3.46 4.74 3.46 4.70 3.46 4.67 3.46 4.65 3.46 4.63 3.46 4.54 3.45 4.50 3.45 4.45 3.44 4.38 20 3.47 4.75 3.47 4.72 3.47 4.69 3.47 4.67 3.47 4.65 3.47 4.59 3.47 4.53 3.47 4.48 3.47 4.41

Tablas Estadsticas

145

TABLA 52 Percentiles de la Distribucin Chi -Cuadrado.G.L. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 50 60 70 80 90 100 120 0.995 0.001 0.01 0.07 0.21 0.41 0.68 0.99 1.34 1.73 2.16 2.60 3.07 3.57 4.07 4.60 5.14 5.70 6.26 6.84 7.434 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 83.85 0.990 0.001 0.02 0.11 0.30 0.55 0.87 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 8.260 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 86.92 0.975 0.950 0.900 0.750 0.001 0.004 0.02 0.10 0.05 0.10 0.21 0.58 0.22 0.35 0.58 1.21 0.48 0.71 1.06 1.92 0.83 1.15 1.61 2.67 1.24 1.64 2.20 3.45 1.69 2.17 2.83 4.25 2.18 2.73 3.49 5.07 2.70 3.33 4.17 5.90 3.25 3.94 4.87 6.74 3.82 4.57 5.58 7.58 4.40 5.23 6.30 8.44 5.01 5.89 7.04 9.30 5.63 6.57 7.79 10.17 6.26 7.26 8.55 11.04 6.91 7.96 9.31 11.91 7.56 8.67 10.09 12.79 8.23 9.39 10.86 13.68 8.91 10.12 11.65 14.56 9.591 10.851 12.44 15.45 10.28 11.59 13.24 16.34 10.98 12.34 14.04 17.24 11.69 13.09 14.85 18.14 12.40 13.85 15.66 19.04 13.12 14.61 16.47 19.94 13.84 15.38 17.29 20.84 14.57 16.15 18.11 21.75 15.31 16.93 18.94 22.66 16.05 17.71 19.77 23.57 16.79 18.49 20.60 24.48 24.43 26.51 29.05 33.66 32.36 34.76 37.69 42.94 40.48 43.19 46.46 52.29 48.76 51.74 55.33 61.70 57.15 60.39 64.28 71.14 65.65 69.13 73.29 80.62 74.22 77.93 82.36 90.13 91.57 95.70 100.62 109.22 0.500 0.45 1.39 2.37 3.36 4.35 5.35 6.35 7.34 8.34 9.34 10.34 11.34 12.34 13.34 14.34 15.34 16.34 17.34 18.34 19.34 20.34 21.34 22.34 23.34 24.34 25.34 26.34 27.34 28.34 29.34 39.34 49.33 59.33 69.33 79.33 89.33 99.33 119.33 0.250 1.32 2.77 4.11 5.39 6.63 7.84 9.04 10.22 11.39 12.55 13.70 14.85 15.98 17.12 18.25 19.37 20.49 21.60 22.72 23.83 24.93 26.04 27.14 28.24 29.34 30.43 31.53 32.62 33.71 34.80 45.62 56.33 66.98 77.58 88.13 98.65 109.14 130.05 0.100 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 96.58 107.57 118.50 140.23 0.050 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 90.53 101.88 113.15 124.34 146.57 0.025 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 95.02 106.63 118.14 129.56 152.21 0.010 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 88.38 100.43 112.33 124.12 135.81 158.95 0.005 7.88 10.60 12.84 14.86 16.75 18.55 20.28 21.95 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 49.65 50.99 52.34 53.67 66.77 79.49 91.95 104.21 116.32 128.30 140.17 163.65 0.001 10.83 13.82 16.27 18.47 20.51 22.46 24.32 26.12 27.88 29.59 31.26 32.91 34.53 36.12 37.70 39.25 40.79 42.31 43.82 45.31 46.80 48.27 49.73 51.18 52.62 54.05 55.48 56.89 58.30 59.70 73.40 86.66 99.61 112.32 124.84 137.21 149.45 173.62

146

Estadstica para Ciencias Qumicas

TABLA 53 Arcoseno de la raz cuadrada de datos expresados en porcentaje.% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 0 0.00 5.74 8.13 9.97 11.54 12.92 14.18 15.34 16.43 17.46 18.43 19.37 20.27 21.13 21.97 22.79 23.58 24.35 25.10 25.84 26.56 27.27 27.97 28.66 29.33 30.00 30.66 31.31 31.95 32.58 33.21 33.83 34.45 35.06 35.67 36.27 36.87 37.46 38.06 38.65 39.23 39.82 40.40 40.98 41.55 42.13 1 1.81 6.02 8.33 10.14 11.68 13.05 14.30 15.45 16.54 17.56 18.53 19.46 20.36 21.22 22.06 22.87 23.66 24.43 25.18 25.91 26.64 27.34 28.04 28.73 29.40 30.07 30.72 31.37 32.01 32.65 33.27 33.89 34.51 35.12 35.73 36.33 36.93 37.52 38.12 38.70 39.29 39.87 40.45 41.03 41.61 42.19 2 2.56 6.29 8.53 10.30 11.83 13.18 14.42 15.56 16.64 17.66 18.63 19.55 20.44 21.30 22.14 22.95 23.73 24.50 25.25 25.99 26.71 27.42 28.11 28.79 29.47 30.13 30.79 31.44 32.08 32.71 33.34 33.96 34.57 35.18 35.79 36.39 36.99 37.58 38.17 38.76 39.35 39.93 40.51 41.09 41.67 42.25 3 3.14 6.55 8.72 10.47 11.97 13.31 14.54 15.68 16.74 17.76 18.72 19.64 20.53 21.39 22.22 23.03 23.81 24.58 25.33 26.06 26.78 27.49 28.18 28.86 29.53 30.20 30.85 31.50 32.14 32.77 33.40 34.02 34.63 35.24 35.85 36.45 37.05 37.64 38.23 38.82 39.41 39.99 40.57 41.15 41.73 42.30 4 3.63 6.80 8.91 10.63 12.11 13.44 14.65 15.79 16.85 17.85 18.81 19.73 20.62 21.47 22.30 23.11 23.89 24.65 25.40 26.13 26.85 27.56 28.25 28.93 29.60 30.26 30.92 31.56 32.20 32.83 33.46 34.08 34.70 35.30 35.91 36.51 37.11 37.70 38.29 38.88 39.47 40.05 40.63 41.21 41.78 42.36 5 4.05 7.03 9.10 10.78 12.25 13.56 14.77 15.89 16.95 17.95 18.91 19.82 20.70 21.56 22.38 23.18 23.97 24.73 25.47 26.21 26.92 27.62 28.32 29.00 29.67 30.33 30.98 31.63 32.27 32.90 33.52 34.14 34.76 35.37 35.97 36.57 37.17 37.76 38.35 38.94 39.52 40.11 40.69 41.27 41.84 42.42 6 4.44 7.27 9.28 10.94 12.38 13.69 14.89 16.00 17.05 18.05 19.00 19.91 20.79 21.64 22.46 23.26 24.04 24.80 25.55 26.28 26.99 27.69 28.38 29.06 29.73 30.40 31.05 31.69 32.33 32.96 33.58 34.20 34.82 35.43 36.03 36.63 37.23 37.82 38.41 39.00 39.58 40.16 40.74 41.32 41.90 42.48 7 4.80 7.49 9.46 11.09 12.52 13.81 15.00 16.11 17.15 18.15 19.09 20.00 20.88 21.72 22.54 23.34 24.12 24.88 25.62 26.35 27.06 27.76 28.45 29.13 29.80 30.46 31.11 31.76 32.39 33.02 33.65 34.27 34.88 35.49 36.09 36.69 37.29 37.88 38.47 39.06 39.64 40.22 40.80 41.38 41.96 42.53 8 5.13 7.71 9.63 11.24 12.66 13.94 15.12 16.22 17.26 18.24 19.19 20.09 20.96 21.81 22.63 23.42 24.20 24.95 25.70 26.42 27.13 27.83 28.52 29.20 29.87 30.53 31.18 31.82 32.46 33.09 33.71 34.33 34.94 35.55 36.15 36.75 37.35 37.94 38.53 39.11 39.70 40.28 40.86 41.44 42.02 42.59 9 5.44 7.92 9.80 11.39 12.79 14.06 15.23 16.32 17.36 18.34 19.28 20.18 21.05 21.89 22.71 23.50 24.27 25.03 25.77 26.49 27.20 27.90 28.59 29.27 29.93 30.59 31.24 31.88 32.52 33.15 33.77 34.39 35.00 35.61 36.21 36.81 37.41 38.00 38.59 39.17 39.76 40.34 40.92 41.50 42.07 42.65

Tablas Estadsticas

147

TABLA 53 Arcoseno de la raz cuadrad a de datos expresados en porcentaje.% 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 0 42.71 43.28 43.85 44.43 45.00 45.57 46.15 46.72 47.29 47.87 48.45 49.02 49.60 50.18 50.77 51.35 51.94 52.53 53.13 53.73 54.33 54.94 55.55 56.17 56.79 57.42 58.05 58.69 59.34 60.00 60.67 61.34 62.03 62.73 63.43 64.16 64.90 65.65 66.42 67.21 68.03 68.87 69.73 70.63 71.56 72.54 1 42.76 43.34 43.91 44.48 45.06 45.63 46.20 46.78 47.35 47.93 48.50 49.08 49.66 50.24 50.83 51.41 52.00 52.59 53.19 53.79 54.39 55.00 55.61 56.23 56.85 57.48 58.12 58.76 59.41 60.07 60.73 61.41 62.10 62.80 63.51 64.23 64.97 65.73 66.50 67.29 68.11 68.95 69.82 70.72 71.66 72.64 2 42.82 43.39 43.97 44.54 45.11 45.69 46.26 46.83 47.41 47.98 48.56 49.14 49.72 50.30 50.89 51.47 52.06 52.65 53.25 53.85 54.45 55.06 55.67 56.29 56.91 57.54 58.18 58.82 59.47 60.13 60.80 61.48 62.17 62.87 63.58 64.30 65.05 65.80 66.58 67.37 68.19 69.04 69.91 70.81 71.76 72.74 3 42.88 43.45 44.03 44.60 45.17 45.74 46.32 46.89 47.47 48.04 48.62 49.20 49.78 50.36 50.94 51.53 52.12 52.71 53.31 53.91 54.51 55.12 55.73 56.35 56.98 57.61 58.24 58.89 59.54 60.20 60.87 61.55 62.24 62.94 63.65 64.38 65.12 65.88 66.66 67.46 68.28 69.12 70.00 70.91 71.85 72.84 4 42.94 43.51 44.08 44.66 45.23 45.80 46.38 46.95 47.52 48.10 48.68 49.26 49.84 50.42 51.00 51.59 52.18 52.77 53.37 53.97 54.57 55.18 55.80 56.41 57.04 57.67 58.31 58.95 59.60 60.27 60.94 61.61 62.31 63.01 63.72 64.45 65.20 65.96 66.74 67.54 68.36 69.21 70.09 71.00 71.95 72.95 5 42.99 43.57 44.14 44.71 45.29 45.86 46.43 47.01 47.58 48.16 48.73 49.31 49.89 50.48 51.06 51.65 52.24 52.83 53.43 54.03 54.63 55.24 55.86 56.48 57.10 57.73 58.37 59.02 59.67 60.33 61.00 61.68 62.37 63.08 63.79 64.52 65.27 66.03 66.81 67.62 68.44 69.30 70.18 71.09 72.05 73.05 6 43.05 43.62 44.20 44.77 45.34 45.92 46.49 47.06 47.64 48.22 48.79 49.37 49.95 50.53 51.12 51.71 52.30 52.89 53.49 54.09 54.69 55.30 55.92 56.54 57.17 57.80 58.44 59.08 59.74 60.40 61.07 61.75 62.44 63.15 63.87 64.60 65.35 66.11 66.89 67.70 68.53 69.38 70.27 71.19 72.15 73.15 7 43.11 43.68 44.25 44.83 45.40 45.97 46.55 47.12 47.70 48.27 48.85 49.43 50.01 50.59 51.18 51.77 52.36 52.95 53.55 54.15 54.76 55.37 55.98 56.60 57.23 57.86 58.50 59.15 59.80 60.47 61.14 61.82 62.51 63.22 63.94 64.67 65.42 66.19 66.97 67.78 68.61 69.47 70.36 71.28 72.24 73.26 8 43.17 43.74 44.31 44.89 45.46 46.03 46.61 47.18 47.75 48.33 48.91 49.49 50.07 50.65 51.24 51.83 52.42 53.01 53.61 54.21 54.82 55.43 56.04 56.66 57.29 57.92 58.56 59.21 59.87 60.53 61.21 61.89 62.58 63.29 64.01 64.75 65.50 66.27 67.05 67.86 68.70 69.56 70.45 71.37 72.34 73.36 9 43.22 43.80 44.37 44.94 45.52 46.09 46.66 47.24 47.81 48.39 48.97 49.55 50.13 50.71 51.30 51.88 52.48 53.07 53.67 54.27 54.88 55.49 56.10 56.73 57.35 57.99 58.63 59.28 59.93 60.60 61.27 61.96 62.65 63.36 64.08 64.82 65.57 66.34 67.13 67.94 68.78 69.64 70.54 71.47 72.44 73.46

148

Estadstica para Ciencias Qumicas

TABLA 53 Arcoseno de la raz cuadrad a de datos expresados en porcentaje.% 92 93 94 95 96 97 98 99 100 0 73.57 74.66 75.82 77.08 78.46 80.03 81.87 84.26 90.00 1 73.68 74.77 75.94 77.21 78.61 80.19 82.08 84.56 2 73.78 74.88 76.06 77.34 78.76 80.37 82.29 84.87 3 73.89 75.00 76.19 77.48 78.91 80.54 82.51 85.20 4 74.00 75.11 76.31 77.62 79.06 80.72 82.73 85.56 5 74.11 75.23 76.44 77.75 79.22 80.90 82.96 85.94 6 74.21 75.35 76.56 77.89 79.37 81.09 83.20 86.37 7 74.32 75.46 76.69 78.03 79.53 81.28 83.45 86.86 8 74.44 75.58 76.82 78.17 79.69 81.47 83.71 87.44 9 74.55 75.70 76.95 78.32 79.86 81.67 83.98 88.19

Tablas Estadsticas

149

TABLA 54 Coeficientes de Correlacin.G.L. del Error 1 2 3 4 5 6 7 8 9 19 20 21 22 23 24 25 26 27 Variables independientes 4 1 0.999 10 0.576 1.000 0.708 0.987 11 0.553 0.998 0.684 0.961 12 0.532 0.987 0.661 0.930 13 0.514 0.970 0.641 0.898 14 0.497 0.949 0.623 0.867 15 0.482 0.927 0.606 0.838 16 0.468 0.904 0.590 0.811 17 0.456 0.882 0.575 0.786 18 0.444 0.861 0.561 0.615 28 0.361 0.698 0.463 0.604 29 0.355 0.685 0.456 0.592 30 0.349 0.674 0.449 0.582 35 0.325 0.663 0.418 0.572 40 0.304 0.652 0.393 0.562 45 0.288 0.642 0.372 0.553 50 0.273 0.633 0.354 0.545 60 0.250 0.624 0.325 0.536 70 0.232 0.615 0.302

E 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01

1 0.997 1.000 0.950 0.990 0.878 0.959 0.811 0.917 0.754 0.874 0.707 0.834 0.666 0.798 0.632 0.765 0.602 0.735 0.433 0.549 0.423 0.537 0.413 0.526 0.404 0.515 0.396 0.505 0.388 0.496 0.381 0.487 0.374 0.478 0.367 0.470

2 0.999 1.000 0.975 0.995 0.930 0.976 0.881 0.949 0.836 0.917 0.795 0.886 0.758 0.855 0.726 0.827 0.697 0.800 0.520 0.620 0.509 0.608 0.498 0.596 0.488 0.585 0.479 0.574 0.470 0.565 0.462 0.555 0.454 0.546 0.446 0.538

3 0.999 1.000 0.983 0.997 0.950 0.983 0.912 0.962 0.874 0.937 0.839 0.911 0.807 0.885 0.777 0.860 0.750 0.836 0.575 0.665 0.563 0.652 0.522 0.641 0.542 0.630 0.532 0.619 0.523 0.609 0.514 0.600 0.506 0.590 0.498 0.582

2 0.671 0.776 0.648 0.753 0.627 0.732 0.608 0.712 0.590 0.694 0.574 0.677 0.559 0.662 0.545 0.647 0.532 0.633 0.439 0.530 0.432 0.522 0.426 0.514 0.397 0.481 0.373 0.454 0.353 0.430 0.336 0.410 0.308 0.377 0.286 0.351

3 0.726 0.814 0.703 0.793 0.683 0.773 0.664 0.755 0.646 0.737 0.630 0.721 0.615 0.706 0.601 0.691 0.587 0.678 0.490 0.573 0.482 0.565 0.476 0.558 0.445 0.523 0.419 0.494 0.397 0.470 0.379 0.449 0.348 0.414 0.324 0.386

4 0.763 0.840 0.741 0.821 0.722 0.802 0.703 0.785 0.686 0.768 0.670 0.752 0.655 0.738 0.641 0.724 0.628 0.710 0.529 0.605 0.521 0.598 0.514 0.591 0.482 0.556 0.455 0.526 0.432 0.501 0.412 0.479 0.380 0.442 0.354 0.413

150

Estadstica para Ciencias Qumicas

TABLA 54 Coeficientes de CorrelacinG.L. del Error 80 90 100 150 200 300 400 500 1000 1 0.217 0.283 0.205 0.267 0.195 0.254 0.159 0.208 0.138 0.181 0.113 0.148 0.098 0.128 0.088 0.115 0.062 0.081 Variables independientes 2 3 0.269 0.304 0.330 0.362 0.254 0.288 0.312 0.343 0.241 0.274 0.297 0.327 0.198 0.225 0.244 0.270 0.172 0.196 0.212 0.234 0.141 0.160 0.174 0.192 0.122 0.139 0.151 0.167 0.109 0.124 0.135 0.150 0.077 0.088 0.096 0.106 4 0.332 0.389 0.315 0.368 0.300 0.351 0.247 0.290 0.215 0.253 0.176 0.208 0.153 0.180 0.137 0.162 0.097 0.115

E 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01


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