Source code for simplestatistics.statistics.chi_squared_dist_table

[docs]def chi_squared_dist_table(k=0, p=0): """ From `Wikipedia <https://en.wikipedia.org/wiki/Chi-squared_distribution>`_. The p-value is the probability of observing a test statistic at least as extreme in a chi-squared distribution. Accordingly, since the cumulative distribution function (CDF) for the appropriate degrees of freedom (df) gives the probability of having obtained a value less extreme than this point, subtracting the CDF value from 1 gives the p-value. The table below gives a number of p-values matching to :math:`\\chi^2` for the first 10 degrees of freedom. The ``chi_squared_dist_table`` function can either return the full table of :math:`\\chi^2` vs. *p* values, or it can perform a lookup for a certain value if given *k* (degrees of freedom: df) or *k* and *p* values. *k* has to be one of the following values: 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 *p* has to be one of the following values: .005, .01, .025, .05, .1, .5, .9, .95, .975, .99, .995 Args: k: (optional) int of *k* representing degrees of freedom. p: (optiona, but *k* is required) float of *p* representing probability. Returns: Entire table as dict where the key is degree of freedom and value is another dict of keys representing *p* and values representing test statistic. If only *k* is provided, the function returns a dict of *p*: test statistic pairs. If both *k* and *p* are provided, the function will return the specific test statistic. Examples: >>> chi_squared_dist_table(5, .01) 15.09 >>> x = chi_squared_dist_table() >>> sorted(x.keys()) [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] >>> k60 = chi_squared_dist_table(60) >>> for p in sorted(k60.keys()): print({p: k60[p]}) {0.005: 91.95} {0.01: 88.38} {0.025: 83.3} {0.05: 79.08} {0.1: 74.4} {0.5: 59.33} {0.9: 46.46} {0.95: 43.19} {0.975: 40.48} {0.99: 37.48} {0.995: 35.53} >>> chi_squared_dist_table(5, 0.4) Traceback (most recent call last): ... ValueError: If you provide a p value, it has to be one of 11 values. See documentation for more information. >>> chi_squared_dist_table(95) Traceback (most recent call last): ... ValueError: If you are providing k and/or p values, they have to be chosen from a list of values. See documentation for more information """ chi_table = { 1: { 0.995: 0, 0.99: 0, 0.975: 0, 0.95: 0, 0.9: 0.02, 0.5: 0.45, 0.1: 2.71, 0.05: 3.84, 0.025: 5.02, 0.01: 6.63, 0.005: 7.88 }, 2: { 0.995: 0.01, 0.99: 0.02, 0.975: 0.05, 0.95: 0.1, 0.9: 0.21, 0.5: 1.39, 0.1: 4.61, 0.05: 5.99, 0.025: 7.38, 0.01: 9.21, 0.005: 10.6 }, 3: { 0.995: 0.07, 0.99: 0.11, 0.975: 0.22, 0.95: 0.35, 0.9: 0.58, 0.5: 2.37, 0.1: 6.25, 0.05: 7.81, 0.025: 9.35, 0.01: 11.34, 0.005: 12.84 }, 4: { 0.995: 0.21, 0.99: 0.3, 0.975: 0.48, 0.95: 0.71, 0.9: 1.06, 0.5: 3.36, 0.1: 7.78, 0.05: 9.49, 0.025: 11.14, 0.01: 13.28, 0.005: 14.86 }, 5: { 0.995: 0.41, 0.99: 0.55, 0.975: 0.83, 0.95: 1.15, 0.9: 1.61, 0.5: 4.35, 0.1: 9.24, 0.05: 11.07, 0.025: 12.83, 0.01: 15.09, 0.005: 16.75 }, 6: { 0.995: 0.68, 0.99: 0.87, 0.975: 1.24, 0.95: 1.64, 0.9: 2.2, 0.5: 5.35, 0.1: 10.65, 0.05: 12.59, 0.025: 14.45, 0.01: 16.81, 0.005: 18.55 }, 7: { 0.995: 0.99, 0.99: 1.25, 0.975: 1.69, 0.95: 2.17, 0.9: 2.83, 0.5: 6.35, 0.1: 12.02, 0.05: 14.07, 0.025: 16.01, 0.01: 18.48, 0.005: 20.28 }, 8: { 0.995: 1.34, 0.99: 1.65, 0.975: 2.18, 0.95: 2.73, 0.9: 3.49, 0.5: 7.34, 0.1: 13.36, 0.05: 15.51, 0.025: 17.53, 0.01: 20.09, 0.005: 21.96 }, 9: { 0.995: 1.73, 0.99: 2.09, 0.975: 2.7, 0.95: 3.33, 0.9: 4.17, 0.5: 8.34, 0.1: 14.68, 0.05: 16.92, 0.025: 19.02, 0.01: 21.67, 0.005: 23.59 }, 10: { 0.995: 2.16, 0.99: 2.56, 0.975: 3.25, 0.95: 3.94, 0.9: 4.87, 0.5: 9.34, 0.1: 15.99, 0.05: 18.31, 0.025: 20.48, 0.01: 23.21, 0.005: 25.19 }, 11: { 0.995: 2.6, 0.99: 3.05, 0.975: 3.82, 0.95: 4.57, 0.9: 5.58, 0.5: 10.34, 0.1: 17.28, 0.05: 19.68, 0.025: 21.92, 0.01: 24.72, 0.005: 26.76 }, 12: { 0.995: 3.07, 0.99: 3.57, 0.975: 4.4, 0.95: 5.23, 0.9: 6.3, 0.5: 11.34, 0.1: 18.55, 0.05: 21.03, 0.025: 23.34, 0.01: 26.22, 0.005: 28.3 }, 13: { 0.995: 3.57, 0.99: 4.11, 0.975: 5.01, 0.95: 5.89, 0.9: 7.04, 0.5: 12.34, 0.1: 19.81, 0.05: 22.36, 0.025: 24.74, 0.01: 27.69, 0.005: 29.82 }, 14: { 0.995: 4.07, 0.99: 4.66, 0.975: 5.63, 0.95: 6.57, 0.9: 7.79, 0.5: 13.34, 0.1: 21.06, 0.05: 23.68, 0.025: 26.12, 0.01: 29.14, 0.005: 31.32 }, 15: { 0.995: 4.6, 0.99: 5.23, 0.975: 6.27, 0.95: 7.26, 0.9: 8.55, 0.5: 14.34, 0.1: 22.31, 0.05: 25, 0.025: 27.49, 0.01: 30.58, 0.005: 32.8 }, 16: { 0.995: 5.14, 0.99: 5.81, 0.975: 6.91, 0.95: 7.96, 0.9: 9.31, 0.5: 15.34, 0.1: 23.54, 0.05: 26.3, 0.025: 28.85, 0.01: 32, 0.005: 34.27 }, 17: { 0.995: 5.7, 0.99: 6.41, 0.975: 7.56, 0.95: 8.67, 0.9: 10.09, 0.5: 16.34, 0.1: 24.77, 0.05: 27.59, 0.025: 30.19, 0.01: 33.41, 0.005: 35.72 }, 18: { 0.995: 6.26, 0.99: 7.01, 0.975: 8.23, 0.95: 9.39, 0.9: 10.87, 0.5: 17.34, 0.1: 25.99, 0.05: 28.87, 0.025: 31.53, 0.01: 34.81, 0.005: 37.16 }, 19: { 0.995: 6.84, 0.99: 7.63, 0.975: 8.91, 0.95: 10.12, 0.9: 11.65, 0.5: 18.34, 0.1: 27.2, 0.05: 30.14, 0.025: 32.85, 0.01: 36.19, 0.005: 38.58 }, 20: { 0.995: 7.43, 0.99: 8.26, 0.975: 9.59, 0.95: 10.85, 0.9: 12.44, 0.5: 19.34, 0.1: 28.41, 0.05: 31.41, 0.025: 34.17, 0.01: 37.57, 0.005: 40 }, 21: { 0.995: 8.03, 0.99: 8.9, 0.975: 10.28, 0.95: 11.59, 0.9: 13.24, 0.5: 20.34, 0.1: 29.62, 0.05: 32.67, 0.025: 35.48, 0.01: 38.93, 0.005: 41.4 }, 22: { 0.995: 8.64, 0.99: 9.54, 0.975: 10.98, 0.95: 12.34, 0.9: 14.04, 0.5: 21.34, 0.1: 30.81, 0.05: 33.92, 0.025: 36.78, 0.01: 40.29, 0.005: 42.8 }, 23: { 0.995: 9.26, 0.99: 10.2, 0.975: 11.69, 0.95: 13.09, 0.9: 14.85, 0.5: 22.34, 0.1: 32.01, 0.05: 35.17, 0.025: 38.08, 0.01: 41.64, 0.005: 44.18 }, 24: { 0.995: 9.89, 0.99: 10.86, 0.975: 12.4, 0.95: 13.85, 0.9: 15.66, 0.5: 23.34, 0.1: 33.2, 0.05: 36.42, 0.025: 39.36, 0.01: 42.98, 0.005: 45.56 }, 25: { 0.995: 10.52, 0.99: 11.52, 0.975: 13.12, 0.95: 14.61, 0.9: 16.47, 0.5: 24.34, 0.1: 34.28, 0.05: 37.65, 0.025: 40.65, 0.01: 44.31, 0.005: 46.93 }, 26: { 0.995: 11.16, 0.99: 12.2, 0.975: 13.84, 0.95: 15.38, 0.9: 17.29, 0.5: 25.34, 0.1: 35.56, 0.05: 38.89, 0.025: 41.92, 0.01: 45.64, 0.005: 48.29 }, 27: { 0.995: 11.81, 0.99: 12.88, 0.975: 14.57, 0.95: 16.15, 0.9: 18.11, 0.5: 26.34, 0.1: 36.74, 0.05: 40.11, 0.025: 43.19, 0.01: 46.96, 0.005: 49.65 }, 28: { 0.995: 12.46, 0.99: 13.57, 0.975: 15.31, 0.95: 16.93, 0.9: 18.94, 0.5: 27.34, 0.1: 37.92, 0.05: 41.34, 0.025: 44.46, 0.01: 48.28, 0.005: 50.99 }, 29: { 0.995: 13.12, 0.99: 14.26, 0.975: 16.05, 0.95: 17.71, 0.9: 19.77, 0.5: 28.34, 0.1: 39.09, 0.05: 42.56, 0.025: 45.72, 0.01: 49.59, 0.005: 52.34 }, 30: { 0.995: 13.79, 0.99: 14.95, 0.975: 16.79, 0.95: 18.49, 0.9: 20.6, 0.5: 29.34, 0.1: 40.26, 0.05: 43.77, 0.025: 46.98, 0.01: 50.89, 0.005: 53.67 }, 40: { 0.995: 20.71, 0.99: 22.16, 0.975: 24.43, 0.95: 26.51, 0.9: 29.05, 0.5: 39.34, 0.1: 51.81, 0.05: 55.76, 0.025: 59.34, 0.01: 63.69, 0.005: 66.77 }, 50: { 0.995: 27.99, 0.99: 29.71, 0.975: 32.36, 0.95: 34.76, 0.9: 37.69, 0.5: 49.33, 0.1: 63.17, 0.05: 67.5, 0.025: 71.42, 0.01: 76.15, 0.005: 79.49 }, 60: { 0.995: 35.53, 0.99: 37.48, 0.975: 40.48, 0.95: 43.19, 0.9: 46.46, 0.5: 59.33, 0.1: 74.4, 0.05: 79.08, 0.025: 83.3, 0.01: 88.38, 0.005: 91.95 }, 70: { 0.995: 43.28, 0.99: 45.44, 0.975: 48.76, 0.95: 51.74, 0.9: 55.33, 0.5: 69.33, 0.1: 85.53, 0.05: 90.53, 0.025: 95.02, 0.01: 100.42, 0.005: 104.22 }, 80: { 0.995: 51.17, 0.99: 53.54, 0.975: 57.15, 0.95: 60.39, 0.9: 64.28, 0.5: 79.33, 0.1: 96.58, 0.05: 101.88, 0.025: 106.63, 0.01: 112.33, 0.005: 116.32 }, 90: { 0.995: 59.2, 0.99: 61.75, 0.975: 65.65, 0.95: 69.13, 0.9: 73.29, 0.5: 89.33, 0.1: 107.57, 0.05: 113.14, 0.025: 118.14, 0.01: 124.12, 0.005: 128.3 }, 100: { 0.995: 67.33, 0.99: 70.06, 0.975: 74.22, 0.95: 77.93, 0.9: 82.36, 0.5: 99.33, 0.1: 118.5, 0.05: 124.34, 0.025: 129.56, 0.01: 135.81, 0.005: 140.17 } } krange = list(range(1, 30)) + list(range(30, 110, 10)) prange = [.005, .01, .025, .05, .1, .5, .9, .95, .975, .99, .995] if k == 0 and p == 0: return(chi_table) elif k in krange: if p != 0 and p in prange: return(chi_table[k][p]) elif p == 0: return(chi_table[k]) else: raise ValueError('If you provide a p value, it has to be one of 11 values. See documentation for more information.') else: raise ValueError('If you are providing k and/or p values, they have to be chosen from a list of values. See documentation for more information')