Module stats

Calculates the geometric mean of the values in the passed list. That is: n-th root of (x1 * x2 * ... * xn). Assumes a '1D' list.

Usage: lgeometricmean(inlist)

Calculates the harmonic mean of the values in the passed list. That is: n / (1/x1 + 1/x2 + ... + 1/xn). Assumes a '1D' list.

Usage: lharmonicmean(inlist)

Returns the arithematic mean of the values in the passed list. Assumes a '1D' list, but will function on the 1st dim of an array(!).

Usage: lmean(inlist)

Returns the computed median value of a list of numbers, given the number of bins to use for the histogram (more bins brings the computed value closer to the median score, default number of bins = 1000). See G.W. Heiman's Basic Stats (1st Edition), or CRC Probability & Statistics.

Usage: lmedian (inlist, numbins=1000)

Returns the 'middle' score of the passed list. If there is an even number of scores, the mean of the 2 middle scores is returned.

Usage: lmedianscore(inlist)

Returns a list of the modal (most common) score(s) in the passed list. If there is more than one such score, all are returned. The bin-count for the mode(s) is also returned.

Usage: lmode(inlist) Returns: bin-count for mode(s), a list of modal value(s)

Calculates the nth moment about the mean for a sample (defaults to the 1st moment). Used to calculate coefficients of skewness and kurtosis.

Usage: lmoment(inlist,moment=1) Returns: appropriate moment (r) from ... 1/n * SUM((inlist(i)-mean)**r)

Returns the coefficient of variation, as defined in CRC Standard Probability and Statistics, p.6.

Usage: lvariation(inlist)

Returns the skewness of a distribution, as defined in Numerical Recipies (alternate defn in CRC Standard Probability and Statistics, p.6.)

Usage: lskew(inlist)

Returns the kurtosis of a distribution, as defined in Numerical Recipies (alternate defn in CRC Standard Probability and Statistics, p.6.)

Usage: lkurtosis(inlist)

Returns some descriptive statistics of the passed list (assumed to be 1D).

Usage: ldescribe(inlist) Returns: n, mean, standard deviation, skew, kurtosis

Returns a list of pairs. Each pair consists of one of the scores in inlist and it's frequency count. Assumes a 1D list is passed.

Usage: litemfreq(inlist) Returns: a 2D frequency table (col [0:n-1]=scores, col n=frequencies)

Returns the score at a given percentile relative to the distribution given by inlist.

Usage: lscoreatpercentile(inlist,percent)

Returns the percentile value of a score relative to the distribution given by inlist. Formula depends on the values used to histogram the data(!).

Usage: lpercentileofscore(inlist,score,histbins=10,defaultlimits=None)

Returns (i) a list of histogram bin counts, (ii) the smallest value of the histogram binning, and (iii) the bin width (the last 2 are not necessarily integers). Default number of bins is 10. If no sequence object is given for defaultreallimits, the routine picks (usually non-pretty) bins spanning all the numbers in the inlist.

Usage: lhistogram (inlist, numbins=10, defaultreallimits=None,suppressoutput=0) Returns: list of bin values, lowerreallimit, binsize, extrapoints

Returns a cumulative frequency histogram, using the histogram function.

Usage: lcumfreq(inlist,numbins=10,defaultreallimits=None) Returns: list of cumfreq bin values, lowerreallimit, binsize, extrapoints

Returns a relative frequency histogram, using the histogram function.

Usage: lrelfreq(inlist,numbins=10,defaultreallimits=None) Returns: list of cumfreq bin values, lowerreallimit, binsize, extrapoints

Computes a transform on input data (any number of columns). Used to test for homogeneity of variance prior to running one-way stats. From Maxwell and Delaney, p.112.

Usage: lobrientransform(*args) Returns: transformed data for use in an ANOVA

Returns the variance of the values in the passed list using N for the denominator (i.e., DESCRIBES the sample variance only).

Usage: lsamplevar(inlist)

Returns the standard deviation of the values in the passed list using N for the denominator (i.e., DESCRIBES the sample stdev only).

Usage: lsamplestdev(inlist)

Returns the variance of the values in the passed list using N-1 for the denominator (i.e., for estimating population variance).

Usage: lvar(inlist)

Returns the standard deviation of the values in the passed list using N-1 in the denominator (i.e., to estimate population stdev).

Usage: lstdev(inlist)

Returns the standard error of the values in the passed list using N-1 in the denominator (i.e., to estimate population standard error).

Usage: lsterr(inlist)

Returns the estimated standard error of the mean (sx-bar) of the values in the passed list. sem = stdev / sqrt(n)

Usage: lsem(inlist)

Returns the z-score for a given input score, given that score and the list from which that score came. Not appropriate for population calculations.

Usage: lz(inlist, score)

Returns a list of z-scores, one for each score in the passed list.

Usage: lzs(inlist)

Slices off the passed proportion of items from BOTH ends of the passed list (i.e., with proportiontocut=0.1, slices 'leftmost' 10% AND 'rightmost' 10% of scores. Assumes list is sorted by magnitude. Slices off LESS if proportion results in a non-integer slice index (i.e., conservatively slices off proportiontocut).

Usage: ltrimboth (l,proportiontocut) Returns: trimmed version of list l

Slices off the passed proportion of items from ONE end of the passed list (i.e., if proportiontocut=0.1, slices off 'leftmost' or 'rightmost' 10% of scores). Slices off LESS if proportion results in a non-integer slice index (i.e., conservatively slices off proportiontocut).

Usage: ltrim1 (l,proportiontocut,tail='right') or set tail='left' Returns: trimmed version of list l

Interactively determines the type of data and then runs the appropriated statistic for paired group data.

Usage: lpaired(x,y) Returns: appropriate statistic name, value, and probability

Calculates a Pearson correlation coefficient and the associated probability value. Taken from Heiman's Basic Statistics for the Behav. Sci (2nd), p.195.

Usage: lpearsonr(x,y) where x and y are equal-length lists Returns: Pearson's r value, two-tailed p-value

Calculates a Spearman rank-order correlation coefficient. Taken from Heiman's Basic Statistics for the Behav. Sci (1st), p.192.

Usage: lspearmanr(x,y) where x and y are equal-length lists Returns: Spearman's r, two-tailed p-value

Calculates a point-biserial correlation coefficient and the associated probability value. Taken from Heiman's Basic Statistics for the Behav. Sci (1st), p.194.

Usage: lpointbiserialr(x,y) where x,y are equal-length lists Returns: Point-biserial r, two-tailed p-value

Calculates Kendall's tau ... correlation of ordinal data. Adapted from function kendl1 in Numerical Recipies. Needs good test-routine.@@@

Usage: lkendalltau(x,y) Returns: Kendall's tau, two-tailed p-value

Calculates a regression line on x,y pairs.

Usage: llinregress(x,y) x,y are equal-length lists of x-y coordinates Returns: slope, intercept, r, two-tailed prob, sterr-of-estimate

Calculates the t-obtained for the independent samples T-test on ONE group of scores a, given a population mean. If printit=1, results are printed to the screen. If printit='filename', the results are output to 'filename' using the given writemode (default=append). Returns t-value, and prob.

Usage: lttest_1samp(a,popmean,Name='Sample',printit=0,writemode='a') Returns: t-value, two-tailed prob

Calculates the t-obtained T-test on TWO INDEPENDENT samples of scores a, and b. From Numerical Recipies, p.483. If printit=1, results are printed to the screen. If printit='filename', the results are output to 'filename' using the given writemode (default=append). Returns t-value, and prob.

Usage: lttest_ind(a,b,printit=0,name1='Samp1',name2='Samp2',writemode='a') Returns: t-value, two-tailed prob

Calculates the t-obtained T-test on TWO RELATED samples of scores, a and b. From Numerical Recipies, p.483. If printit=1, results are printed to the screen. If printit='filename', the results are output to 'filename' using the given writemode (default=append). Returns t-value, and prob.

Usage: lttest_rel(a,b,printit=0,name1='Sample1',name2='Sample2',writemode='a') Returns: t-value, two-tailed prob

Calculates a one-way chi square for list of observed frequencies and returns the result. If no expected frequencies are given, the total N is assumed to be equally distributed across all groups.

Usage: lchisquare(f_obs, f_exp=None) f_obs = list of observed cell freq. Returns: chisquare-statistic, associated p-value

Computes the Kolmogorov-Smirnof statistic on 2 samples. From Numerical Recipies in C, page 493.

Usage: lks_2samp(data1,data2) data1&2 are lists of values for 2 conditions Returns: KS D-value, associated p-value

Calculates a Mann-Whitney U statistic on the provided scores and returns the result. Use only when the n in each condition is < 20 and you have 2 independent samples of ranks. NOTE: Mann-Whitney U is significant if the u-obtained is LESS THAN or equal to the critical value of U found in the tables. Equivalent to Kruskal-Wallis H with just 2 groups.

Usage: lmannwhitneyu(data) Returns: u-statistic, one-tailed p-value (i.e., p(z(U)))

Corrects for ties in Mann Whitney U and Kruskal Wallis H tests. See Siegel, S. (1956) Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill. Code adapted from |Stat rankind.c code.

Usage: ltiecorrect(rankvals) Returns: T correction factor for U or H

Calculates the rank sums statistic on the provided scores and returns the result. Use only when the n in each condition is > 20 and you have 2 independent samples of ranks.

Usage: lranksums(x,y) Returns: a z-statistic, two-tailed p-value

Calculates the Wilcoxon T-test for related samples and returns the result. A non-parametric T-test.

Usage: lwilcoxont(x,y) Returns: a t-statistic, two-tail probability estimate

The Kruskal-Wallis H-test is a non-parametric ANOVA for 3 or more groups, requiring at least 5 subjects in each group. This function calculates the Kruskal-Wallis H-test for 3 or more independent samples and returns the result.

Usage: lkruskalwallish(*args) Returns: H-statistic (corrected for ties), associated p-value

Friedman Chi-Square is a non-parametric, one-way within-subjects ANOVA. This function calculates the Friedman Chi-square test for repeated measures and returns the result, along with the associated probability value. It assumes 3 or more repeated measures. Only 3 levels requires a minimum of 10 subjects in the study. Four levels requires 5 subjects per level(??).

Usage: lfriedmanchisquare(*args) Returns: chi-square statistic, associated p-value

Returns the (1-tailed) probability value associated with the provided chi-square value and df. Adapted from chisq.c in Gary Perlman's |Stat.

Usage: lchisqprob(chisq,df)

Returns the complementary error function erfc(x) with fractional error everywhere less than 1.2e-7. Adapted from Numerical Recipies.

Usage: lerfcc(x)

Returns the area under the normal curve 'to the left of' the given z value.
Thus, 
    for z<0, zprob(z) = 1-tail probability
    for z>0, 1.0-zprob(z) = 1-tail probability
    for any z, 2.0*(1.0-zprob(abs(z))) = 2-tail probability
Adapted from z.c in Gary Perlman's |Stat.

Usage:   lzprob(z)

Computes a Kolmolgorov-Smirnov t-test significance level. Adapted from Numerical Recipies.

Usage: lksprob(alam)

Returns the (1-tailed) significance level (p-value) of an F statistic given the degrees of freedom for the numerator (dfR-dfF) and the degrees of freedom for the denominator (dfF).

Usage: lfprob(dfnum, dfden, F) where usually dfnum=dfbn, dfden=dfwn

This function evaluates the continued fraction form of the incomplete Beta function, betai. (Adapted from: Numerical Recipies in C.)

Usage: lbetacf(a,b,x)

Returns the gamma function of xx.
    Gamma(z) = Integral(0,infinity) of t^(z-1)exp(-t) dt.
(Adapted from: Numerical Recipies in C.)

Usage:   lgammln(xx)

Returns the incomplete beta function:

    I-sub-x(a,b) = 1/B(a,b)*(Integral(0,x) of t^(a-1)(1-t)^(b-1) dt)

where a,b>0 and B(a,b) = G(a)*G(b)/(G(a+b)) where G(a) is the gamma
function of a.  The continued fraction formulation is implemented here,
using the betacf function.  (Adapted from: Numerical Recipies in C.)

Usage:   lbetai(a,b,x)

Performs a 1-way ANOVA, returning an F-value and probability given
any number of groups.  From Heiman, pp.394-7.

Usage:   F_oneway(*lists)    where *lists is any number of lists, one per
                                  treatment group
Returns: F value, one-tailed p-value

Returns an F-statistic given the following:
        ER  = error associated with the null hypothesis (the Restricted model)
        EF  = error associated with the alternate hypothesis (the Full model)
        dfR-dfF = degrees of freedom of the numerator
        dfF = degrees of freedom associated with the denominator/Full model

Usage:   lF_value(ER,EF,dfnum,dfden)

Writes a list of lists to a file in columns, customized by the max size of items within the columns (max size of items in col, +2 characters) to specified file. File-overwrite is the default.

Usage: writecc (listoflists,file,writetype='w',extra=2) Returns: None

Simulate a counting system from an n-dimensional list.

Usage: lincr(l,cap) l=list to increment, cap=max values for each list pos'n Returns: next set of values for list l, OR -1 (if overflow)

Returns the sum of the items in the passed list.

Usage: lsum(inlist)

Returns a list consisting of the cumulative sum of the items in the passed list.

Usage: lcumsum(inlist)

Squares each value in the passed list, adds up these squares and returns the result.

Usage: lss(inlist)

Multiplies elements in list1 and list2, element by element, and returns the sum of all resulting multiplications. Must provide equal length lists.

Usage: lsummult(list1,list2)

Takes pairwise differences of the values in lists x and y, squares these differences, and returns the sum of these squares.

Usage: lsumdiffsquared(x,y) Returns: sum[(x[i]-y[i])**2]

Adds the values in the passed list, squares the sum, and returns the result.

Usage: lsquare_of_sums(inlist) Returns: sum(inlist[i])**2

Shellsort algorithm. Sorts a 1D-list.

Usage: lshellsort(inlist) Returns: sorted-inlist, sorting-index-vector (for original list)

Ranks the data in inlist, dealing with ties appropritely. Assumes a 1D inlist. Adapted from Gary Perlman's |Stat ranksort.

Usage: lrankdata(inlist) Returns: a list of length equal to inlist, containing rank scores

Prints or write to a file stats for two groups, using the name, n,
mean, sterr, min and max for each group, as well as the statistic name,
its value, and the associated p-value.

Usage:   outputpairedstats(fname,writemode,
                           name1,n1,mean1,stderr1,min1,max1,
                           name2,n2,mean2,stderr2,min2,max2,
                           statname,stat,prob)
Returns: None

Returns an integer representing a binary vector, where 1=within- subject factor, 0=between. Input equals the entire data 2D list (i.e., column 0=random factor, column -1=measured values (those two are skipped). Note: input data is in |Stat format ... a list of lists ("2D list") with one row per measured value, first column=subject identifier, last column= score, one in-between column per factor (these columns contain level designations on each factor). See also stats.anova.__doc__.

Usage: lfindwithin(data) data in |Stat format

Calculates the geometric mean of the values in the passed array. That is: n-th root of (x1 * x2 * ... * xn). Defaults to ALL values in the passed array. Use dimension=None to flatten array first. REMEMBER: if dimension=0, it collapses over dimension 0 ('rows' in a 2D array) only, and if dimension is a sequence, it collapses over all specified dimensions. If keepdims is set to 1, the resulting array will have as many dimensions as inarray, with only 1 'level' per dim that was collapsed over.

Usage: ageometricmean(inarray,dimension=None,keepdims=0) Returns: geometric mean computed over dim(s) listed in dimension

Calculates the harmonic mean of the values in the passed array. That is: n / (1/x1 + 1/x2 + ... + 1/xn). Defaults to ALL values in the passed array. Use dimension=None to flatten array first. REMEMBER: if dimension=0, it collapses over dimension 0 ('rows' in a 2D array) only, and if dimension is a sequence, it collapses over all specified dimensions. If keepdims is set to 1, the resulting array will have as many dimensions as inarray, with only 1 'level' per dim that was collapsed over.

Usage: aharmonicmean(inarray,dimension=None,keepdims=0) Returns: harmonic mean computed over dim(s) in dimension

Calculates the arithmatic mean of the values in the passed array. That is: 1/n * (x1 + x2 + ... + xn). Defaults to ALL values in the passed array. Use dimension=None to flatten array first. REMEMBER: if dimension=0, it collapses over dimension 0 ('rows' in a 2D array) only, and if dimension is a sequence, it collapses over all specified dimensions. If keepdims is set to 1, the resulting array will have as many dimensions as inarray, with only 1 'level' per dim that was collapsed over.

Usage: amean(inarray,dimension=None,keepdims=0) Returns: arithematic mean calculated over dim(s) in dimension

Calculates the COMPUTED median value of an array of numbers, given the number of bins to use for the histogram (more bins approaches finding the precise median value of the array; default number of bins = 1000). From G.W. Heiman's Basic Stats, or CRC Probability & Statistics. NOTE: THIS ROUTINE ALWAYS uses the entire passed array (flattens it first).

Usage: amedian(inarray,numbins=1000) Returns: median calculated over ALL values in inarray

Returns the 'middle' score of the passed array. If there is an even number of scores, the mean of the 2 middle scores is returned. Can function with 1D arrays, or on the FIRST dimension of 2D arrays (i.e., dimension can be None, to pre-flatten the array, or else dimension must equal 0).

Usage: amedianscore(inarray,dimension=None) Returns: 'middle' score of the array, or the mean of the 2 middle scores

Returns an array of the modal (most common) score in the passed array. If there is more than one such score, ONLY THE FIRST is returned. The bin-count for the modal values is also returned. Operates on whole array (dimension=None), or on a given dimension.

Usage: amode(a, dimension=None) Returns: array of bin-counts for mode(s), array of corresponding modal values

Returns the arithmetic mean of all values in an array, ignoring values strictly outside the sequence passed to 'limits'. Note: either limit in the sequence, or the value of limits itself, can be set to None. The inclusive list/tuple determines whether the lower and upper limiting bounds (respectively) are open/exclusive (0) or closed/inclusive (1).

Usage: atmean(a,limits=None,inclusive=(1,1))

Returns the sample variance of values in an array, (i.e., using N-1), ignoring values strictly outside the sequence passed to 'limits'. Note: either limit in the sequence, or the value of limits itself, can be set to None. The inclusive list/tuple determines whether the lower and upper limiting bounds (respectively) are open/exclusive (0) or closed/inclusive (1).

Usage: atvar(a,limits=None,inclusive=(1,1))

Returns the minimum value of a, along dimension, including only values less than (or equal to, if inclusive=1) lowerlimit. If the limit is set to None, all values in the array are used.

Usage: atmin(a,lowerlimit=None,dimension=None,inclusive=1)

Returns the maximum value of a, along dimension, including only values greater than (or equal to, if inclusive=1) upperlimit. If the limit is set to None, a limit larger than the max value in the array is used.

Usage: atmax(a,upperlimit,dimension=None,inclusive=1)

Returns the standard deviation of all values in an array, ignoring values strictly outside the sequence passed to 'limits'. Note: either limit in the sequence, or the value of limits itself, can be set to None. The inclusive list/tuple determines whether the lower and upper limiting bounds (respectively) are open/exclusive (0) or closed/inclusive (1).

Usage: atstdev(a,limits=None,inclusive=(1,1))

Returns the standard error of the mean for the values in an array, (i.e., using N for the denominator), ignoring values strictly outside the sequence passed to 'limits'. Note: either limit in the sequence, or the value of limits itself, can be set to None. The inclusive list/tuple determines whether the lower and upper limiting bounds (respectively) are open/exclusive (0) or closed/inclusive (1).

Usage: atsem(a,limits=None,inclusive=(1,1))

Calculates the nth moment about the mean for a sample (defaults to the 1st moment). Generally used to calculate coefficients of skewness and kurtosis. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions).

Usage: amoment(a,moment=1,dimension=None) Returns: appropriate moment along given dimension

Returns the coefficient of variation, as defined in CRC Standard Probability and Statistics, p.6. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions).

Usage: avariation(a,dimension=None)

Returns the skewness of a distribution (normal ==> 0.0; >0 means extra weight in left tail). Use askewtest() to see if it's close enough. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions).

Usage: askew(a, dimension=None) Returns: skew of vals in a along dimension, returning ZERO where all vals equal

Returns the kurtosis of a distribution (normal ==> 3.0; >3 means heavier in the tails, and usually more peaked). Use akurtosistest() to see if it's close enough. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions).

Usage: akurtosis(a,dimension=None) Returns: kurtosis of values in a along dimension, and ZERO where all vals equal

Returns several descriptive statistics of the passed array. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions).

Usage: adescribe(inarray,dimension=None) Returns: n, (min,max), mean, standard deviation, skew, kurtosis

Tests whether the skew is significantly different from a normal distribution. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions).

Usage: askewtest(a,dimension=None) Returns: z-score and 2-tail z-probability

Tests whether a dataset has normal kurtosis (i.e., kurtosis=3(n-1)/(n+1)) Valid only for n>20. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions).

Usage: akurtosistest(a,dimension=None) Returns: z-score and 2-tail z-probability, returns 0 for bad pixels

Tests whether skew and/OR kurtosis of dataset differs from normal curve. Can operate over multiple dimensions. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions).

Usage: anormaltest(a,dimension=None) Returns: z-score and 2-tail probability

Returns a 2D array of item frequencies. Column 1 contains item values, column 2 contains their respective counts. Assumes a 1D array is passed.

Usage: aitemfreq(a) Returns: a 2D frequency table (col [0:n-1]=scores, col n=frequencies)

Note: result of this function depends on the values used to histogram the data(!).

Usage: apercentileofscore(inarray,score,histbins=10,defaultlimits=None) Returns: percentile-position of score (0-100) relative to inarray

Returns (i) an array of histogram bin counts, (ii) the smallest value of the histogram binning, and (iii) the bin width (the last 2 are not necessarily integers). Default number of bins is 10. Defaultlimits can be None (the routine picks bins spanning all the numbers in the inarray) or a 2-sequence (lowerlimit, upperlimit). Returns all of the following: array of bin values, lowerreallimit, binsize, extrapoints.

Usage: ahistogram(inarray,numbins=10,defaultlimits=None,printextras=1) Returns: (array of bin counts, bin-minimum, min-width, #-points-outside-range)

Returns a cumulative frequency histogram, using the histogram function. Defaultreallimits can be None (use all data), or a 2-sequence containing lower and upper limits on values to include.

Usage: acumfreq(a,numbins=10,defaultreallimits=None) Returns: array of cumfreq bin values, lowerreallimit, binsize, extrapoints

Returns a relative frequency histogram, using the histogram function. Defaultreallimits can be None (use all data), or a 2-sequence containing lower and upper limits on values to include.

Usage: arelfreq(a,numbins=10,defaultreallimits=None) Returns: array of cumfreq bin values, lowerreallimit, binsize, extrapoints

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.

Usage: aobrientransform(*args) *args = 1D arrays, one per level of factor Returns: transformed data for use in an ANOVA

Returns the sample standard deviation of the values in the passed array (i.e., using N). Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). Set keepdims=1 to return an array with the same number of dimensions as inarray.

Usage: asamplevar(inarray,dimension=None,keepdims=0)

Returns the sample standard deviation of the values in the passed array (i.e., using N). Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). Set keepdims=1 to return an array with the same number of dimensions as inarray.

Usage: asamplestdev(inarray,dimension=None,keepdims=0)

Calculates signal-to-noise.  Dimension can equal None (ravel array
first), an integer (the dimension over which to operate), or a
sequence (operate over multiple dimensions).

Usage:   asignaltonoise(instack,dimension=0):
Returns: array containing the value of (mean/stdev) along dimension,
         or 0 when stdev=0

Returns the estimated population variance of the values in the passed array (i.e., N-1). Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). Set keepdims=1 to return an array with the same number of dimensions as inarray.

Usage: avar(inarray,dimension=None,keepdims=0)

Returns the estimated population standard deviation of the values in the passed array (i.e., N-1). Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). Set keepdims=1 to return an array with the same number of dimensions as inarray.

Usage: astdev(inarray,dimension=None,keepdims=0)

Returns the estimated population standard error of the values in the passed array (i.e., N-1). Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). Set keepdims=1 to return an array with the same number of dimensions as inarray.

Usage: asterr(inarray,dimension=None,keepdims=0)

Returns the standard error of the mean (i.e., using N) of the values in the passed array. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). Set keepdims=1 to return an array with the same number of dimensions as inarray.

Usage: asem(inarray,dimension=None, keepdims=0)

Returns the z-score of a given input score, given thearray from which that score came. Not appropriate for population calculations, nor for arrays > 1D.

Usage: az(a, score)

Returns a 1D array of z-scores, one for each score in the passed array, computed relative to the passed array.

Usage: azs(a)

Returns an array of z-scores the shape of scores (e.g., [x,y]), compared to array passed to compare (e.g., [time,x,y]). Assumes collapsing over dim 0 of the compare array.

Usage: azs(scores, compare, dimension=0)

Rounds all values in array a to 'digits' decimal places.

Usage: around(a,digits) Returns: a, where each value is rounded to 'digits' decimals

Like Numeric.clip() except that values <threshmid or >threshmax are replaced by newval instead of by threshmin/threshmax (respectively).

Usage: athreshold(a,threshmin=None,threshmax=None,newval=0) Returns: a, with values <threshmin or >threshmax replaced with newval

Slices off the passed proportion of items from BOTH ends of the passed array (i.e., with proportiontocut=0.1, slices 'leftmost' 10% AND 'rightmost' 10% of scores. You must pre-sort the array if you want "proper" trimming. Slices off LESS if proportion results in a non-integer slice index (i.e., conservatively slices off proportiontocut).

Usage: atrimboth (a,proportiontocut) Returns: trimmed version of array a

Slices off the passed proportion of items from ONE end of the passed array (i.e., if proportiontocut=0.1, slices off 'leftmost' or 'rightmost' 10% of scores). Slices off LESS if proportion results in a non-integer slice index (i.e., conservatively slices off proportiontocut).

Usage: atrim1(a,proportiontocut,tail='right') or set tail='left' Returns: trimmed version of array a

Computes the covariance matrix of a matrix X. Requires a 2D matrix input.

Usage: acovariance(X) Returns: covariance matrix of X

Computes the correlation matrix of a matrix X. Requires a 2D matrix input.

Usage: acorrelation(X) Returns: correlation matrix of X

Interactively determines the type of data in x and y, and then runs the appropriated statistic for paired group data.

Usage: apaired(x,y) x,y = the two arrays of values to be compared Returns: appropriate statistic name, value, and probability

Calculates a Pearson correlation coefficient and returns p. Taken from Heiman's Basic Statistics for the Behav. Sci (2nd), p.195.

Usage: apearsonr(x,y,verbose=1) where x,y are equal length arrays Returns: Pearson's r, two-tailed p-value

Calculates a Spearman rank-order correlation coefficient. Taken from Heiman's Basic Statistics for the Behav. Sci (1st), p.192.

Usage: aspearmanr(x,y) where x,y are equal-length arrays Returns: Spearman's r, two-tailed p-value

Calculates a point-biserial correlation coefficient and the associated probability value. Taken from Heiman's Basic Statistics for the Behav. Sci (1st), p.194.

Usage: apointbiserialr(x,y) where x,y are equal length arrays Returns: Point-biserial r, two-tailed p-value

Calculates Kendall's tau ... correlation of ordinal data. Adapted from function kendl1 in Numerical Recipies. Needs good test-cases.@@@

Usage: akendalltau(x,y) Returns: Kendall's tau, two-tailed p-value

Calculates a regression line on two arrays, x and y, corresponding to x,y pairs. If a single 2D array is passed, alinregress finds dim with 2 levels and splits data into x,y pairs along that dim.

Usage: alinregress(*args) args=2 equal-length arrays, or one 2D array Returns: slope, intercept, r, two-tailed prob, sterr-of-the-estimate

Calculates the t-obtained for the independent samples T-test on ONE group of scores a, given a population mean. If printit=1, results are printed to the screen. If printit='filename', the results are output to 'filename' using the given writemode (default=append). Returns t-value, and prob.

Usage: attest_1samp(a,popmean,Name='Sample',printit=0,writemode='a') Returns: t-value, two-tailed prob

Calculates the t-obtained T-test on TWO INDEPENDENT samples of scores
a, and b.  From Numerical Recipies, p.483.  If printit=1, results are
printed to the screen.  If printit='filename', the results are output
to 'filename' using the given writemode (default=append).  Dimension
can equal None (ravel array first), or an integer (the dimension over
which to operate on a and b).

Usage:   attest_ind (a,b,dimension=None,printit=0,
                     Name1='Samp1',Name2='Samp2',writemode='a')
Returns: t-value, two-tailed p-value

Calculates the t-obtained T-test on TWO RELATED samples of scores, a
and b.  From Numerical Recipies, p.483.  If printit=1, results are
printed to the screen.  If printit='filename', the results are output
to 'filename' using the given writemode (default=append).  Dimension
can equal None (ravel array first), or an integer (the dimension over
which to operate on a and b).

Usage:   attest_rel(a,b,dimension=None,printit=0,
                    name1='Samp1',name2='Samp2',writemode='a')
Returns: t-value, two-tailed p-value

Calculates a one-way chi square for array of observed frequencies and returns the result. If no expected frequencies are given, the total N is assumed to be equally distributed across all groups.

Usage: achisquare(f_obs, f_exp=None) f_obs = array of observed cell freq. Returns: chisquare-statistic, associated p-value

Computes the Kolmogorov-Smirnof statistic on 2 samples. Modified from Numerical Recipies in C, page 493. Returns KS D-value, prob. Not ufunc- like.

Usage: aks_2samp(data1,data2) where data1 and data2 are 1D arrays Returns: KS D-value, p-value

Calculates a Mann-Whitney U statistic on the provided scores and returns the result. Use only when the n in each condition is < 20 and you have 2 independent samples of ranks. REMEMBER: Mann-Whitney U is significant if the u-obtained is LESS THAN or equal to the critical value of U.

Usage: amannwhitneyu(x,y) where x,y are arrays of values for 2 conditions Returns: u-statistic, one-tailed p-value (i.e., p(z(U)))

Tie-corrector for ties in Mann Whitney U and Kruskal Wallis H tests. See Siegel, S. (1956) Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill. Code adapted from |Stat rankind.c code.

Usage: atiecorrect(rankvals) Returns: T correction factor for U or H

Calculates the rank sums statistic on the provided scores and returns the result.

Usage: aranksums(x,y) where x,y are arrays of values for 2 conditions Returns: z-statistic, two-tailed p-value

Calculates the Wilcoxon T-test for related samples and returns the result. A non-parametric T-test.

Usage: awilcoxont(x,y) where x,y are equal-length arrays for 2 conditions Returns: t-statistic, two-tailed p-value

The Kruskal-Wallis H-test is a non-parametric ANOVA for 3 or more groups, requiring at least 5 subjects in each group. This function calculates the Kruskal-Wallis H and associated p-value for 3 or more independent samples.

Usage: akruskalwallish(*args) args are separate arrays for 3+ conditions Returns: H-statistic (corrected for ties), associated p-value

Friedman Chi-Square is a non-parametric, one-way within-subjects ANOVA. This function calculates the Friedman Chi-square test for repeated measures and returns the result, along with the associated probability value. It assumes 3 or more repeated measures. Only 3 levels requires a minimum of 10 subjects in the study. Four levels requires 5 subjects per level(??).

Usage: afriedmanchisquare(*args) args are separate arrays for 2+ conditions Returns: chi-square statistic, associated p-value

Returns the (1-tail) probability value associated with the provided chi-square value and df. Heavily modified from chisq.c in Gary Perlman's |Stat. Can handle multiple dimensions.

Usage: achisqprob(chisq,df) chisq=chisquare stat., df=degrees of freedom

Returns the complementary error function erfc(x) with fractional error everywhere less than 1.2e-7. Adapted from Numerical Recipies. Can handle multiple dimensions.

Usage: aerfcc(x)

Returns the area under the normal curve 'to the left of' the given z value.
Thus, 
    for z<0, zprob(z) = 1-tail probability
    for z>0, 1.0-zprob(z) = 1-tail probability
    for any z, 2.0*(1.0-zprob(abs(z))) = 2-tail probability
Adapted from z.c in Gary Perlman's |Stat.  Can handle multiple dimensions.

Usage:   azprob(z)    where z is a z-value

Returns the probability value for a K-S statistic computed via ks_2samp. Adapted from Numerical Recipies. Can handle multiple dimensions.

Usage: aksprob(alam)

Returns the 1-tailed significance level (p-value) of an F statistic given the degrees of freedom for the numerator (dfR-dfF) and the degrees of freedom for the denominator (dfF). Can handle multiple dims for F.

Usage: afprob(dfnum, dfden, F) where usually dfnum=dfbn, dfden=dfwn

Evaluates the continued fraction form of the incomplete Beta function, betai. (Adapted from: Numerical Recipies in C.) Can handle multiple dimensions for x.

Usage: abetacf(a,b,x,verbose=1)

Returns the gamma function of xx.
    Gamma(z) = Integral(0,infinity) of t^(z-1)exp(-t) dt.
Adapted from: Numerical Recipies in C.  Can handle multiple dims ... but
probably doesn't normally have to.

Usage:   agammln(xx)

Returns the incomplete beta function:

    I-sub-x(a,b) = 1/B(a,b)*(Integral(0,x) of t^(a-1)(1-t)^(b-1) dt)

where a,b>0 and B(a,b) = G(a)*G(b)/(G(a+b)) where G(a) is the gamma
function of a.  The continued fraction formulation is implemented
here, using the betacf function.  (Adapted from: Numerical Recipies in
C.)  Can handle multiple dimensions.

Usage:   abetai(a,b,x,verbose=1)

Calculates a linear model fit ... anova/ancova/lin-regress/t-test/etc. Taken
from:
    Peterson et al. Statistical limitations in functional neuroimaging
    I. Non-inferential methods and statistical models.  Phil Trans Royal Soc
    Lond B 354: 1239-1260.

Usage:   aglm(data,para)
Returns: statistic, p-value ???

Performs a 1-way ANOVA, returning an F-value and probability given
any number of groups.  From Heiman, pp.394-7.

Usage:   aF_oneway (*args)    where *args is 2 or more arrays, one per
                                  treatment group
Returns: f-value, probability

Returns an F-statistic given the following:
        ER  = error associated with the null hypothesis (the Restricted model)
        EF  = error associated with the alternate hypothesis (the Full model)
        dfR = degrees of freedom the Restricted model
        dfF = degrees of freedom associated with the Restricted model

An alternative to the Numeric.add.reduce function, which allows one to (1) collapse over multiple dimensions at once, and/or (2) to retain all dimensions in the original array (squashing one down to size. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). If keepdims=1, the resulting array will have as many dimensions as the input array.

Usage: asum(a, dimension=None, keepdims=0) Returns: array summed along 'dimension'(s), same _number_ of dims if keepdims=1

Returns an array consisting of the cumulative sum of the items in the passed array. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions, but this last one just barely makes sense).

Usage: acumsum(a,dimension=None)

Squares each value in the passed array, adds these squares & returns the result. Unfortunate function name. :-) Defaults to ALL values in the array. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). Set keepdims=1 to maintain the original number of dimensions.

Usage: ass(inarray, dimension=None, keepdims=0) Returns: sum-along-'dimension' for (inarray*inarray)

Multiplies elements in array1 and array2, element by element, and returns the sum (along 'dimension') of all resulting multiplications. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). A trivial function, but included for completeness.

Usage: asummult(array1,array2,dimension=None,keepdims=0)

Adds the values in the passed array, squares that sum, and returns the result. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). If keepdims=1, the returned array will have the same NUMBER of dimensions as the original.

Usage: asquare_of_sums(inarray, dimension=None, keepdims=0) Returns: the square of the sum over dim(s) in dimension

Takes pairwise differences of the values in arrays a and b, squares these differences, and returns the sum of these squares. Dimension can equal None (ravel array first), an integer (the dimension over which to operate), or a sequence (operate over multiple dimensions). keepdims=1 means the return shape = len(a.shape) = len(b.shape)

Usage: asumdiffsquared(a,b) Returns: sum[ravel(a-b)**2]

Shellsort algorithm. Sorts a 1D-array.

Usage: ashellsort(inarray) Returns: sorted-inarray, sorting-index-vector (for original array)

Ranks the data in inarray, dealing with ties appropritely. Assumes a 1D inarray. Adapted from Gary Perlman's |Stat ranksort.

Usage: arankdata(inarray) Returns: array of length equal to inarray, containing rank scores

Returns a binary vector, 1=within-subject factor, 0=between. Input equals the entire data array (i.e., column 1=random factor, last column = measured values.

Usage: afindwithin(data) data in |Stat format

geometricmean

Value:

Dispatch((lgeometricmean, (ListType, TupleType)), (ageometricmean, (N. ArrayType,)))

harmonicmean

Value:

Dispatch((lharmonicmean, (ListType, TupleType)), (aharmonicmean, (N.Ar rayType,)))

mean

Value:

Dispatch((lmean, (ListType, TupleType)), (amean, (N.ArrayType,)))

median

Value:

Dispatch((lmedian, (ListType, TupleType)), (amedian, (N.ArrayType,)))

medianscore

Value:

Dispatch((lmedianscore, (ListType, TupleType)), (amedianscore, (N.Arra yType,)))

mode

Value:

Dispatch((lmode, (ListType, TupleType)), (amode, (N.ArrayType,)))

moment

Value:

Dispatch((lmoment, (ListType, TupleType)), (amoment, (N.ArrayType,)))

variation

Value:

Dispatch((lvariation, (ListType, TupleType)), (avariation, (N.ArrayTyp e,)))

skew

Value:

Dispatch((lskew, (ListType, TupleType)), (askew, (N.ArrayType,)))

kurtosis

Value:

Dispatch((lkurtosis, (ListType, TupleType)), (akurtosis, (N.ArrayType, )))

describe

Value:

Dispatch((ldescribe, (ListType, TupleType)), (adescribe, (N.ArrayType, )))

skewtest

Value:

Dispatch((askewtest, (ListType, TupleType)), (askewtest, (N.ArrayType, )))

kurtosistest

Value:

Dispatch((akurtosistest, (ListType, TupleType)), (akurtosistest, (N.Ar rayType,)))

normaltest

Value:

Dispatch((anormaltest, (ListType, TupleType)), (anormaltest, (N.ArrayT ype,)))

itemfreq

Value:

Dispatch((litemfreq, (ListType, TupleType)), (aitemfreq, (N.ArrayType, )))

scoreatpercentile

Value:

Dispatch((lscoreatpercentile, (ListType, TupleType)), (ascoreatpercent ile, (N.ArrayType,)))

percentileofscore

Value:

Dispatch((lpercentileofscore, (ListType, TupleType)), (apercentileofsc ore, (N.ArrayType,)))

histogram

Value:

Dispatch((lhistogram, (ListType, TupleType)), (ahistogram, (N.ArrayTyp e,)))

cumfreq

Value:

Dispatch((lcumfreq, (ListType, TupleType)), (acumfreq, (N.ArrayType,)) )

relfreq

Value:

Dispatch((lrelfreq, (ListType, TupleType)), (arelfreq, (N.ArrayType,)) )

obrientransform

Value:

Dispatch((lobrientransform, (ListType, TupleType)), (aobrientransform, (N.ArrayType,)))

samplevar

Value:

Dispatch((lsamplevar, (ListType, TupleType)), (asamplevar, (N.ArrayTyp e,)))

samplestdev

Value:

Dispatch((lsamplestdev, (ListType, TupleType)), (asamplestdev, (N.Arra yType,)))

var

Value:

Dispatch((lvar, (ListType, TupleType)), (avar, (N.ArrayType,)))

stdev

Value:

Dispatch((lstdev, (ListType, TupleType)), (astdev, (N.ArrayType,)))

sterr

Value:

Dispatch((lsterr, (ListType, TupleType)), (asterr, (N.ArrayType,)))

sem

Value:

Dispatch((lsem, (ListType, TupleType)), (asem, (N.ArrayType,)))

zs

Value:

Dispatch((lzs, (ListType, TupleType)), (azs, (N.ArrayType,)))

trimboth

Value:

Dispatch((ltrimboth, (ListType, TupleType)), (atrimboth, (N.ArrayType, )))

trim1

Value:

Dispatch((ltrim1, (ListType, TupleType)), (atrim1, (N.ArrayType,)))

paired

Value:

Dispatch((lpaired, (ListType, TupleType)), (apaired, (N.ArrayType,)))

pearsonr

Value:

Dispatch((lpearsonr, (ListType, TupleType)), (apearsonr, (N.ArrayType, )))

spearmanr

Value:

Dispatch((lspearmanr, (ListType, TupleType)), (aspearmanr, (N.ArrayTyp e,)))

pointbiserialr

Value:

Dispatch((lpointbiserialr, (ListType, TupleType)), (apointbiserialr, ( N.ArrayType,)))

kendalltau

Value:

Dispatch((lkendalltau, (ListType, TupleType)), (akendalltau, (N.ArrayT ype,)))

linregress

Value:

Dispatch((llinregress, (ListType, TupleType)), (alinregress, (N.ArrayT ype,)))

ttest_1samp

Value:

Dispatch((lttest_1samp, (ListType, TupleType)), (attest_1samp, (N.Arra yType,)))

ttest_ind

Value:

Dispatch((lttest_ind, (ListType, TupleType)), (attest_ind, (N.ArrayTyp e,)))

ttest_rel

Value:

Dispatch((lttest_rel, (ListType, TupleType)), (attest_rel, (N.ArrayTyp e,)))

chisquare

Value:

Dispatch((lchisquare, (ListType, TupleType)), (achisquare, (N.ArrayTyp e,)))

ks_2samp

Value:

Dispatch((lks_2samp, (ListType, TupleType)), (aks_2samp, (N.ArrayType, )))

mannwhitneyu

Value:

Dispatch((lmannwhitneyu, (ListType, TupleType)), (amannwhitneyu, (N.Ar rayType,)))

tiecorrect

Value:

Dispatch((ltiecorrect, (ListType, TupleType)), (atiecorrect, (N.ArrayT ype,)))

ranksums

Value:

Dispatch((lranksums, (ListType, TupleType)), (aranksums, (N.ArrayType, )))

wilcoxont

Value:

Dispatch((lwilcoxont, (ListType, TupleType)), (awilcoxont, (N.ArrayTyp e,)))

kruskalwallish

Value:

Dispatch((lkruskalwallish, (ListType, TupleType)), (akruskalwallish, ( N.ArrayType,)))

friedmanchisquare

Value:

Dispatch((lfriedmanchisquare, (ListType, TupleType)), (afriedmanchisqu are, (N.ArrayType,)))

chisqprob

Value:

Dispatch((lchisqprob, (IntType, FloatType)), (achisqprob, (N.ArrayType ,)))

zprob

Value:

Dispatch((lzprob, (IntType, FloatType)), (azprob, (N.ArrayType,)))

ksprob

Value:

Dispatch((lksprob, (IntType, FloatType)), (aksprob, (N.ArrayType,)))

fprob

Value:

Dispatch((lfprob, (IntType, FloatType)), (afprob, (N.ArrayType,)))

betacf

Value:

Dispatch((lbetacf, (IntType, FloatType)), (abetacf, (N.ArrayType,)))

betai

Value:

Dispatch((lbetai, (IntType, FloatType)), (abetai, (N.ArrayType,)))

erfcc

Value:

Dispatch((lerfcc, (IntType, FloatType)), (aerfcc, (N.ArrayType,)))

gammln

Value:

Dispatch((lgammln, (IntType, FloatType)), (agammln, (N.ArrayType,)))

F_oneway

Value:

Dispatch((lF_oneway, (ListType, TupleType)), (aF_oneway, (N.ArrayType, )))

F_value

Value:

Dispatch((lF_value, (ListType, TupleType)), (aF_value, (N.ArrayType,)) )

sum

Value:

Dispatch((lsum, (ListType, TupleType)), (asum, (N.ArrayType,)))

cumsum

Value:

Dispatch((lcumsum, (ListType, TupleType)), (acumsum, (N.ArrayType,)))

ss

Value:

Dispatch((lss, (ListType, TupleType)), (ass, (N.ArrayType,)))

summult

Value:

Dispatch((lsummult, (ListType, TupleType)), (asummult, (N.ArrayType,)) )

square_of_sums

Value:

Dispatch((lsquare_of_sums, (ListType, TupleType)), (asquare_of_sums, ( N.ArrayType,)))

sumdiffsquared

Value:

Dispatch((lsumdiffsquared, (ListType, TupleType)), (asumdiffsquared, ( N.ArrayType,)))

shellsort

Value:

Dispatch((lshellsort, (ListType, TupleType)), (ashellsort, (N.ArrayTyp e,)))

rankdata

Value:

Dispatch((lrankdata, (ListType, TupleType)), (arankdata, (N.ArrayType, )))

findwithin

Value:

Dispatch((lfindwithin, (ListType, TupleType)), (afindwithin, (N.ArrayT ype,)))