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SciPy Reference Guide, Release 0.8.dev Examples >>> from scipy import stats >>> import numpy as np >>> #fix seed to get the same result >>> np.random.seed(7654567) >>> rvs = stats.norm.rvs(loc=5,scale=10,size=(50,2)) test if mean of random sample is equal to true mean, and different mean. We reject the null hypothesis in the second case and don’t reject it in the first case >>> stats.ttest_1samp(rvs,5.0) (array([-0.68014479, -0.04323899]), array([ 0.49961383, 0.96568674])) >>> stats.ttest_1samp(rvs,0.0) (array([ 2.77025808, 4.11038784]), array([ 0.00789095, 0.00014999])) examples using axis and non-scalar dimension for population mean >>> stats.ttest_1samp(rvs,[5.0,0.0]) (array([-0.68014479, 4.11038784]), array([ 4.99613833e-01, 1.49986458e-04])) >>> stats.ttest_1samp(rvs.T,[5.0,0.0],axis=1) (array([-0.68014479, 4.11038784]), array([ 4.99613833e-01, 1.49986458e-04])) >>> stats.ttest_1samp(rvs,[[5.0],[0.0]]) (array([[-0.68014479, -0.04323899], [ 2.77025808, 4.11038784]]), array([[ 4.99613833e-01, 9.65686743e-01], [ 7.89094663e-03, 1.49986458e-04]])) ttest_rel(a, b, axis=None) Calculates the T-test on TWO RELATED samples of scores, a and b. This is a two-sided test for the null hypothesis that 2 related or repeated samples have identical average (expected) values. Notes Parameters a, b : sequence of ndarrays The arrays must have the same shape. axis : int, optional, (default axis=0) Axis can equal None (ravel array first), or an integer (the axis over which to operate on a and b). Returns t : float or array t-statistic prob : float or array two-tailed p-value Examples for the use are scores of the same set of student in different exams, or repeated sampling from the same units. The test measures whether the average score differs significantly across samples (e.g. exams). If we observe a large p-value, for example greater than 0.05 or 0.1 then we cannot reject the null hypothesis of identical average scores. If the p-value is smaller than the threshold, e.g. 1%, 5% or 10%, then we reject the null hypothesis of equal averages. Small p-values are associated with large t-statistics. 694 Chapter 3. Reference
Examples SciPy Reference Guide, Release 0.8.dev >>> from scipy import stats >>> np.random.seed(12345678) # fix random seed to get same numbers >>> rvs1 = stats.norm.rvs(loc=5,scale=10,size=500) >>> rvs2 = (stats.norm.rvs(loc=5,scale=10,size=500) + ... stats.norm.rvs(scale=0.2,size=500)) >>> stats.ttest_rel(rvs1,rvs2) (0.24101764965300962, 0.80964043445811562) >>> rvs3 = (stats.norm.rvs(loc=8,scale=10,size=500) + ... stats.norm.rvs(scale=0.2,size=500)) >>> stats.ttest_rel(rvs1,rvs3) (-3.9995108708727933, 7.3082402191726459e-005) tvar(a, limits=None, inclusive=(True, True)) Compute the trimmed variance This function computes the sample variance of an array of values, while ignoring values which are outside of given limits. Parameters a : array_like array of values limits : None or (lower limit, upper limit), optional Values in the input array less than the lower limit or greater than the upper limit will be ignored. When limits is None, then all values are used. Either of the limit values in the tuple can also be None representing a half-open interval. The default value is None. inclusive : (bool, bool), optional Returns tvar : float A tuple consisting of the (lower flag, upper flag). These flags determine whether values exactly equal to the lower or upper limits are included. The default value is (True, True). var(a, axis=None) Returns the estimated population variance of the values in the passed array (i.e., N-1). Axis can equal None (ravel array first), or an integer (the axis over which to operate). variation(a, axis=0) Computes the coefficient of variation, the ratio of the biased standard deviation to the mean. Parameters a : array References axis : int or None [CRCProbStat2000] Section 2.2.20 [CRCProbStat2000] winsorize(a, limits=None, inclusive=(True, True), inplace=False, axis=None) Returns a Winsorized version of the input array. 3.18. Statistical functions (scipy.stats) 695
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