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SciPy Reference Guide, Release 0.8.dev References [R28], [R29] obrientransform(*args) Computes a transform on input data (any number of columns). Used to test for homogeneity of variance prior to running one-way stats. Each array in *args is one level of a factor. If an F_oneway() run on the transformed data and found significant, variances are unequal. From Maxwell and Delaney, p.112. Returns: transformed data for use in an ANOVA pearsonr(x, y) Calculates a Pearson correlation coefficient and the p-value for testing non-correlation. The Pearson correlation coefficient measures the linear relationship between two datasets. Strictly speaking, Pearson’s correlation requires that each dataset be normally distributed. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship. Positive correlations imply that as x increases, so does y. Negative correlations imply that as x increases, y decreases. The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets. The p-values are not entirely reliable but are probably reasonable for datasets larger than 500 or so. Parameters x : 1D array y : 1D array the same length as x Returns (Pearson’s correlation coefficient, : References 2-tailed p-value) http://www.statsoft.com/textbook/glosp.html#Pearson%20Correlation plotting_positions(data, alpha=0.40000000000000002, beta=0.40000000000000002) Returns the plotting positions (or empirical percentile points) for the data. Plotting positions are defined as (i-alpha)/(n-alpha-beta), where: • i is the rank order statistics • n is the number of unmasked values along the given axis • alpha and beta are two parameters. Typical values for alpha and beta are: • (0,1) : p(k) = k/n : linear interpolation of cdf (R, type 4) • (.5,.5) : p(k) = (k-1/2.)/n : piecewise linear function (R, type 5) • (0,0) : p(k) = k/(n+1) : Weibull (R type 6) • (1,1) : p(k) = (k-1)/(n-1). In this case, p(k) = mode[F(x[k])]. That’s R default (R type 7) • (1/3,1/3): p(k) = (k-1/3)/(n+1/3). Then p(k) ~ median[F(x[k])]. The resulting quantile estimates are approximately median-unbiased regardless of the distribution of x. (R type 8) 682 Chapter 3. Reference
SciPy Reference Guide, Release 0.8.dev • (3/8,3/8): p(k) = (k-3/8)/(n+1/4). Blom. The resulting quantile estimates are approximately unbiased if x is normally distributed (R type 9) • (.4,.4) : approximately quantile unbiased (Cunnane) • (.35,.35): APL, used with PWM Parameters x : sequence pointbiserialr(x, y) Input data, as a sequence or array of dimension at most 2. prob [sequence] List of quantiles to compute. alpha [{0.4, float} optional] Plotting positions parameter. beta [{0.4, float} optional] Plotting positions parameter. Calculates a point biserial correlation coefficient and the associated p-value. Notes The point biserial correlation is used to measure the relationship between a binary variable, x, and a continuous variable, y. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply a determinative relationship. Parameters x : array of bools y : array of floats Returns (point-biserial r, : 2-tailed p-value) Missing values are considered pair-wise: if a value is missing in x, the corresponding value in y is masked. rankdata(data, axis=None, use_missing=False) Returns the rank (also known as order statistics) of each data point along the given axis. If some values are tied, their rank is averaged. If some values are masked, their rank is set to 0 if use_missing is False, or set to the average rank of the unmasked values if use_missing is True. Parameters data : sequence Input data. The data is transformed to a masked array axis [{None,int} optional] Axis along which to perform the ranking. If None, the array is first flattened. An exception is raised if the axis is specified for arrays with a dimension larger than 2 3.18. Statistical functions (<strong>scipy</strong>.stats) 683
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