A Python module implementing a class which can be used for computing numerical statistics for a given data set.

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"""Descriptive statistical analysis tool.
"""
__author__ = "Chad J. Schroeder"
__revision__ = "$Id$"
__version__ = "0.1"
__all__ = [ "StatisticsException", "Statistics" ]
class StatisticsException(Exception):
"""Statistics Exception class."""
pass
class Statistics(object):
"""Class for descriptive statistical analysis.
Behavior:
Computes numerical statistics for a given data set.
Available public methods:
None
Available instance attributes:
N: total number of elements in the data set
sum: sum of all values (n) in the data set
min: smallest value of the data set
max: largest value of the data set
mode: value(s) that appear(s) most often in the data set
mean: arithmetic average of the data set
range: difference between the largest and smallest value in the data set
median: value which is in the exact middle of the data set
variance: measure of the spread of the data set about the mean
stddev: standard deviation - measure of the dispersion of the data set
based on variance
identification: Instance ID
Raised Exceptions:
StatisticsException
Bases Classes:
object (builtin)
Example Usage:
x = [ -1, 0, 1 ]
try:
stats = Statistics(x)
except StatisticsException, mesg:
<handle exception>
print "N: %s" % stats.N
print "SUM: %s" % stats.sum
print "MIN: %s" % stats.min
print "MAX: %s" % stats.max
print "MODE: %s" % stats.mode
print "MEAN: %0.2f" % stats.mean
print "RANGE: %s" % stats.range
print "MEDIAN: %0.2f" % stats.median
print "VARIANCE: %0.5f" % stats.variance
print "STDDEV: %0.5f" % stats.stddev
print "DATA LIST: %s" % stats.sample
"""
def __init__(self, sample=[], population=False):
"""Statistics class initializer method."""
# Raise an exception if the data set is empty.
if (not sample):
raise StatisticsException, "Empty data set!: %s" % sample
# The data set (a list).
self.sample = sample
# Sample/Population variance determination flag.
self.population = population
self.N = len(self.sample)
self.sum = float(sum(self.sample))
self.min = min(self.sample)
self.max = max(self.sample)
self.range = self.max - self.min
self.mean = self.sum/self.N
# Inplace sort (list is now in ascending order).
self.sample.sort()
self.__getMode()
self.__getMedian()
self.__getVariance()
self.__getStandardDeviation()
# Instance identification attribute.
self.identification = id(self)
def __getMode(self):
"""Determine the most repeated value(s) in the data set."""
# Initialize a dictionary to store frequency data.
frequency = {}
# Build dictionary: key - data set values; item - data frequency.
for x in self.sample:
if (x in frequency):
frequency[x] += 1
else:
frequency[x] = 1
# Create a new list containing the values of the frequency dict. Convert
# the list, which may have duplicate elements, into a set. This will
# remove duplicate elements. Convert the set back into a sorted list
# (in descending order). The first element of the new list now contains
# the frequency of the most repeated values(s) in the data set.
# mode = sorted(list(set(frequency.values())), reverse=True)[0]
# Or use the builtin - max(), which returns the largest item of a
# non-empty sequence.
mode = max(frequency.values())
# If the value of mode is 1, there is no mode for the given data set.
if (mode == 1):
self.mode = []
return
# Step through the frequency dictionary, looking for values equaling
# the current value of mode. If found, append the value and its
# associated key to the self.mode list.
self.mode = [(x, mode) for x in frequency if (mode == frequency[x])]
def __getMedian(self):
"""Determine the value which is in the exact middle of the data set."""
if (self.N%2): # Number of elements in data set is odd.
self.median = float(self.sample[self.N/2])
else:
midpt = self.N/2 # Number of elements in data set is even.
self.median = (self.sample[midpt-1] + self.sample[midpt])/2.0
def __getVariance(self):
"""Determine the measure of the spread of the data set about the mean.
Sample variance is determined by default; population variance can be
determined by setting population attribute to True.
"""
x = 0 # Summation variable.
# Subtract the mean from each data item and square the difference.
# Sum all the squared deviations.
for item in self.sample:
x += (item - self.mean)**2.0
try:
if (not self.population):
# Divide sum of squares by N-1 (sample variance).
self.variance = x/(self.N-1)
else:
# Divide sum of squares by N (population variance).
self.variance = x/self.N
except:
self.variance = 0
def __getStandardDeviation(self):
"""Determine the measure of the dispersion of the data set based on the
variance.
"""
from math import sqrt # Mathematical functions.
# Take the square root of the variance.
self.stddev = sqrt(self.variance)
if __name__ == "__main__":
import os # Miscellaneous OS interfaces.
import sys # System-specific parameters and functions.
# Self-test
a = [ -1, 0, 1 ]
b = [ -1.0, 0.0, 1.1 ]
c = []
d = [ 12.23 ]
e = [ 12.23, 99.543, 66.08 ]
f = [ -1, 0, 2, -2, 1, 3, 0, -3, 2 ]
g = [ 0, 9, 1, 8, 2, 7, 3, 6, 4, 5 ]
h = [ -1, -1 ]
for x in a, b, c, d, e, f, g, h:
try:
stats = Statistics(x)
except StatisticsException, mesg:
print; print "Exception caught: %s" % mesg; print
continue
print
print "N: %s" % stats.N
print "SUM: %s" % stats.sum
print "MIN: %s" % stats.min
print "MAX: %s" % stats.max
print "MODE: %s" % stats.mode
print "MEAN: %0.2f" % stats.mean
print "RANGE: %s" % stats.range
print "MEDIAN: %0.2f" % stats.median
print "VARIANCE: %0.5f" % stats.variance
print "STDDEV: %0.5f" % stats.stddev
print "DATA LIST: %s\n" % stats.sample
print
sys.exit(0)
``` |

This recipe implements a descriptive statistical analysis class. It's intended to aid in computing numerical statistics for a given data set. It's well documented and hopefully useful. Any corrections, ideas, or suggestions are welcome. Enjoy.

Tags: programs

Preexisting solutions.Very useful, but ...There is a similar module in development within the python cvs tree: python/nondist/sandbox/statistics/statistics.py

There is also a nice stats module at http://www.nmr.mgh.harvard.edu/Neural_Systems_Group/gary/python.html

SciPy (http://www.scipy.org) also has some statistics-related functions: http://www.scipy.org/documentation/apidocs/scipy/scipy.stats.html

Bug in variance computation.You use x both as loop variable and summation variable, so that the result is bogus. E.g. Statistics([-1, -1]) gives a negative variance (and thus an exception from sqrt).Also, computing the mode is more complicated than necessary: why not use

(Converting to a set does not save anything; one must touch all the elements of the list anyway, so it's O(n). And even if one wants to do list(set(lst)) first, max(lst) is faster than sorted(lst)[-1] or sorted(lst, reverse=True)[0].)

Mode and variance.Thanks for pointing out the summation oversight and mode computation improvement. Modifications have been merged.Chad, thanks for the code. I had a project in VBA for ArcGIS that I'm moving to Python, this was what I needed. However, when I call it from the main module (terms may not be right since new to Python) I get the same stats for the 2nd - n runs as the 1st.

My code generates a list named lstYield of points within a specific polygon

stat_analysis.Statistics(lstYield)

then the median, max, and std dev will be saved to the table for that record in the polygon's attribute table, but like I said I get one viable run, then it repeats the same N and stats. I've checked the list going in, and it is changing. I tried setting the stats.N, stats.median, etc to 0 before getting the next list of points, then all variables return as 0. Any thoughts would be greatly appreciated. Kim

Chad, figured it out, had to say blockStats = stat_analysis.Statistics(lstYield), then it ran just fine. Sorry for jumping the gun in posting question, but thanks again for the code!