Multivariate Pattern Analysis in Python

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# mvpa2.clfs.stats.kstest

`mvpa2.clfs.stats.``kstest`(rvs, cdf, args=(), N=20, alternative='two-sided', mode='approx')

  Perform the Kolmogorov-Smirnov test for goodness of fit.

  This performs a test of the distribution G(x) of an observed random variable against a given distribution F(x). Under the null hypothesis the two distributions are identical, G(x)=F(x). The alternative hypothesis can be either ‘two-sided’ (default), ‘less’ or ‘greater’. The KS test is only valid for continuous distributions.

  Parameters:

  rvs : str, array or callable

  > If a string, it should be the name of a distribution in `scipy.stats`. If an array, it should be a 1-D array of observations of random variables. If a callable, it should be a function to generate random variables; it is required to have a keyword argument `size`.

  cdf : str or callable

  > If a string, it should be the name of a distribution in `scipy.stats`. If `rvs` is a string then `cdf` can be False or the same as `rvs`. If a callable, that callable is used to calculate the cdf.

  args : tuple, sequence, optional

  > Distribution parameters, used if `rvs` or `cdf` are strings.

  N : int, optional

  > Sample size if `rvs` is string or callable. Default is 20.

  alternative : {‘two-sided’, ‘less’,’greater’}, optional

  > Defines the alternative hypothesis (see explanation above). Default is ‘two-sided’.

  mode : ‘approx’ (default) or ‘asymp’, optional

  > Defines the distribution used for calculating the p-value.

  > > - ‘approx’ : use approximation to exact distribution of test statistic
  > > - ‘asymp’ : use asymptotic distribution of test statistic

  Returns:

  D : float

  > KS test statistic, either D, D+ or D-.

  p-value : float

  > One-tailed or two-tailed p-value.

  Notes

  In the one-sided test, the alternative is that the empirical cumulative distribution function of the random variable is “less” or “greater” than the cumulative distribution function F(x) of the hypothesis, `G(x)<=F(x)`, resp. `G(x)>=F(x)`.

  Examples

      >>> from scipy import stats

      >>> x = np.linspace(-15, 15, 9)
      >>> stats.kstest(x, 'norm')
      (0.44435602715924361, 0.038850142705171065)

      >>> np.random.seed(987654321) # set random seed to get the same result
      >>> stats.kstest('norm', False, N=100)
      (0.058352892479417884, 0.88531190944151261)

  The above lines are equivalent to:

      >>> np.random.seed(987654321)
      >>> stats.kstest(stats.norm.rvs(size=100), 'norm')
      (0.058352892479417884, 0.88531190944151261)

  Test against one-sided alternative hypothesis

  Shift distribution to larger values, so that `cdf_dgp(x) < norm.cdf(x)`:

      >>> np.random.seed(987654321)
      >>> x = stats.norm.rvs(loc=0.2, size=100)
      >>> stats.kstest(x,'norm', alternative = 'less')
      (0.12464329735846891, 0.040989164077641749)

  Reject equal distribution against alternative hypothesis: less

      >>> stats.kstest(x,'norm', alternative = 'greater')
      (0.0072115233216311081, 0.98531158590396395)

  Don’t reject equal distribution against alternative hypothesis: greater

      >>> stats.kstest(x,'norm', mode='asymp')
      (0.12464329735846891, 0.08944488871182088)

  Testing t distributed random variables against normal distribution

  With 100 degrees of freedom the t distribution looks close to the normal distribution, and the K-S test does not reject the hypothesis that the sample came from the normal distribution:

      >>> np.random.seed(987654321)
      >>> stats.kstest(stats.t.rvs(100,size=100),'norm')
      (0.072018929165471257, 0.67630062862479168)

  With 3 degrees of freedom the t distribution looks sufficiently different from the normal distribution, that we can reject the hypothesis that the sample came from the normal distribution at the 10% level:

      >>> np.random.seed(987654321)
      >>> stats.kstest(stats.t.rvs(3,size=100),'norm')
      (0.131016895759829, 0.058826222555312224)

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