description | Python code | Details |
---|---|---|

cum. distribution function | pbinom(x, n, p) | $P(X \le x);f(x)= \binom{n}{x}p^xq^{n-x)}$ |

critical value | onesidedcritbinom(n,p,alpha) | $ P(X\le xrit) \le \alpha$ |

critical values | twosidedcritbinom(n,p,alpha) | $ P(xcrit1\le X\le xcrit2) \le \alpha$ |

exact test of proportion | exactproptest(p0, x, n, alpha, side = 0) | test using binomial pdf |

approx test of prop. | normproptest(p0, x, n, alpha, side = 0) | test using normal approximation. |

comparison of two prop. | twosampleproptest(x1,n1, x2,n2,alpha,side) | two sample test of prop. |

test cases | Walpole(),Walpole_normaltests() | Test cases from "Intro. to statistics,3e" book. |

""" file: testofproportions.py author: ernesto p. adorio UP Clarkfield Pampanga version 0.0.1 april, 3, 2010 """ from math import * from rstats import * import scipy.stats as stat def ztest(samplestat, se, alpha =0.05, side=0): """ Normal test of a sample statistic. Arguments: teststat- teststatistic se - standard error of sample statistic alpha - significance level side - -1 left-sided test 0 double sided test +1 right-sided test """ Ztest = samplestat/se print "Ztest=", Ztest if side ==0: pvalue = pnorm(Ztest) if Ztest > 0.0: pvalue = 1.0 -pvalue pvalue *= 2.0 zcrit1 = qnorm(alpha/2) zcrit2 = qnorm(1-alpha/2.0) return pvalue, Ztest, (zcrit1,zcrit2) elif side == -1: pvalue = pnorm(Ztest) zcrit = qnorm(alpha) return pvalue, Ztest, zcrit else: pvalue = 1- pnorm(Ztest) zcrit = qnorm(1.0-alpha) return pvalue, Ztest, zcrit def pbinom(x, n, p): """ Computest the cumulative probability density function of the binomial distribution up : P(X <= x) """ #print "input to pbinom:", x, n, p q = 1.0 - p pdf = cdf = q ** n f = p/q for i in range (1, x+1): pdf *= ((n -i + 1.0)/i * f) cdf += pdf return cdf def onesidedcritbinom(n, p, alpha): """ Determines critical value xcrit such that P(X <= xcrit) < alpha """ q = 1.0 - p pdf = cdf = q ** n f = p/q xcrit = None for i in range (1, x+1): if xcrit is None and cdf >= alpha: xcrit = i - 1 pdf *= ((n -i + 1.0)/i * f) cdf += pdf return xcrit def twosidedcritbinom(n, p, alpha): """ Determines value xrit1, xrit2 such that P(X < xcrit1) = alpha/2 andP(X>xcrit2) = alpha/2 """ if not (0 <= alpha <= 1.0): return None q = 1.0 - p pdf = cdf = q ** n f = p/q xcrit1 = None xcrit2 = None alpha1 = alpha/2.0 alpha2 = 1.0- alpha1 for i in range (1, n+1): if xcrit1 is None and cdf > alpha1: print cdf, alpha1 xcrit1 = i - 1 if xcrit2 is None and cdf > alpha2: xcrit2 = i-1 break pdf *= ((n -i + 1.0)/i * f) cdf += pdf return (xcrit1, xcrit2) def exactproptest(p0, x, n, alpha, side = 0): """ p0- assumed population proportion x - number of success of desired characteristic in sample n - sample size Returns pvalue, teststatistic, critical value """ p = float(x) / n if side == 0: pvalue = pbinom(x, n, p0) if pvalue > 0.5: pvalue = 1 - pvalue return pvalue, x, twosidedcritbinom(n, p0, alpha) elif side == -1: pvalue = pbinom(x, n, p0) return pvalue, x, onesidedcritbinom(n, p0, alpha) elif side == 1: pvalue = 1-0, pbinom(x, n, 1.0-p0) return pvalue, x, onesidedcritbinom(n, p0, alpha) def normproptest(p0, x, n, alpha, side = 0): print "inputargs:", p0, x, n, alpha, side samplestat = x - n * p0 se = sqrt(n * p0 * (1-p0)) print "normproptest:", samplestat, "se=", samplestat, se return ztest(samplestat, se, alpha, side) def twosampleproptest(x1, n1, x2, n2, alpha, side): p1hat = float(x1)/n1 p2hat = float(x2)/n2 phat = float(x1 +x2)/(n1+n2) print "p1hat, p2hat", p1hat, p2hat samplestat = p1hat - p2hat se = sqrt(phat*(1.0-phat) * (1.0/n1 + 1.0/n2)) return ztest(samplestat, se, alpha, side) def Walpole_tests(): print "Example 10, p.326" p0 = 0.7 alpha = 0.10 side = 0 x = 8 n = 15 return exactproptest(p0, x, n, alpha, side) def Walpole_normaltests(): print "Example 11, p.329" p0 = 0.6 alpha = 0.05 side = 1 x = 70 n = 100 print normproptest(p0, x, n, alpha, side) print print "Example12, p. 330" x1, n1 = 120, 200 x2, n2 = 240, 500 alpha = 0.025 side = 1 print twosampleproptest(x1, n1, x2, n2, alpha, side) if __name__ == "__main__": print 'testing pbinom' print Walpole_tests() print Walpole_normaltests()

When Python(via the Eric Python IDE) runs the script file above, it outputs the following:

Python 2.6.4 (r264:75706, Dec 7 2009, 18:43:55) [GCC 4.4.1] on toto-laptop, Standard >>> testing pbinom Example 10, p.326 0.0500125400538 0.05 (0.13114257338312119, 8, (7, 13)) Example 11, p.329 inputargs: 0.6 70 100 0.05 1 normproptest: 10.0 se= 10.0 4.89897948557 Ztest= 2.04124145232 (0.020613416668581852, 2.0412414523193152, 1.6448536269514722) Example12, p. 330 p1hat, p2hat 0.6 0.48 Ztest= 2.86972021592 (0.0020541757121497195, 2.8697202159177571, 1.959963984540054) None

We will explain further in the days ahead how to test proportions as we are at the moment focusing on writing the codes.

This comment has been removed by the author.

ReplyDelete