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QuickStart Samples

Mean Tests QuickStart Sample (IronPython)

Illustrates how to use various tests for the mean of one or more sanples using classes in the Extreme.Statistics.Tests namespace in IronPython.

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import numerics

from Extreme.Mathematics import *
from Extreme.Statistics import *
from Extreme.Statistics.Tests import *

#/ Demonstrates how to use hypothesis tests for the mean 
#/ of one or two distributions.

# This QuickStart Sample uses the scores obtained by the students
# in two groups of students on a national test.
# 
# We want to know if the scores for these two groups of students
# are significantly different from the national average, and
# from each other.

# The mean and standard deviation of the complete population:
nationalMean = 79.3
nationalStandardDeviation = 7.3

print "Tests for group 1"

# First we create a NumericalVariable that holds the test scores.
group1Data = Vector([ \
	62, 77, 61, 94, 75, 82, 86, 83, 64, 84, \
    68, 82, 72, 71, 85, 66, 61, 79, 81, 73 ])
group1Results = NumericalVariable("Class 1", group1Data)
			
# We can get the mean and standard deviation of the group right away:
print "Mean for the group: {0:.1f}".format(group1Results.Mean)
print "Standard deviation: {0:.1f}".format(group1Results.StandardDeviation)
			
#
# One Sample z-test
#

print "\nUsing z-test:"
# We know the population standard deviation, so we can use the z-test, # implemented by the OneSampleZTest group. We pass the sample variable
# and the population parameters to the constructor.
zTest = OneSampleZTest(group1Results, nationalMean, nationalStandardDeviation)
# We can obtan the value of the test statistic through the Statistic property, # and the corresponding P-value through the Probability property:
print "Test statistic: {0:.4f}".format(zTest.Statistic)
print "P-value:        {0:.4f}".format(zTest.PValue)

# The significance level is the default value of 0.05:
print "Significance level:     {0:F2}".format(zTest.SignificanceLevel)
# We can now print the test scores:
print "Reject null hypothesis?", "yes" if zTest.Reject() else "no"
# We can get a confidence interval for the current significance level:
meanInterval = zTest.GetConfidenceInterval()
print "95% Confidence interval for the mean: {0:.1f} - {1:.1f}".format(meanInterval.LowerBound, meanInterval.UpperBound)

# We can get the same scores for the 0.01 significance level by explicitly
# passing the significance level as a parameter to these methods:
print "Significance level:     {0:F2}".format(0.01)
print "Reject null hypothesis?", "yes" if zTest.Reject(0.01) else "no"
# The GetConfidenceInterval method needs the confidence level, which equals
# 1 - the significance level:
meanInterval = zTest.GetConfidenceInterval(0.99)
print "99% Confidence interval for the mean: {0:.1f} - {1:.1f}".format(meanInterval.LowerBound, meanInterval.UpperBound)


# 
# One sample t-test
#

print "\nUsing t-test:"
# Suppose we only know the mean of the national scores, # not the standard deviation. In this case, a t-test is 
# the appropriate test to use.
tTest = OneSampleTTest(group1Results, nationalMean)
# We can obtan the value of the test statistic through the Statistic property, # and the corresponding P-value through the Probability property:
print "Test statistic: {0:.4f}".format(tTest.Statistic)
print "P-value:        {0:.4f}".format(tTest.PValue)

# The significance level is the default value of 0.05:
print "Significance level:     {0:.2f}".format(tTest.SignificanceLevel)
# We can now print the test scores:
print "Reject null hypothesis?", "yes" if tTest.Reject() else "no"
# We can get a confidence interval for the current significance level:
meanInterval = tTest.GetConfidenceInterval()
print "95% Confidence interval for the mean: {0:.1f} - {1:.1f}".format(meanInterval.LowerBound, meanInterval.UpperBound)

			
# 
# Two sample t-test
#

print "\nUsing two-sample t-test:"
# We want to compare the scores of the first group to the scores 
# of a second group from the same school. Once again, we start
# by creating a NumericalVariable containing the scores:
group2Data = Vector([ \
	61, 80, 98, 90, 94, 65, 79, 75, 74, 86, \
    76, 85, 78, 72, 76, 79, 65, 92, 76, 80 ])
group2Results = NumericalVariable("Class 2", group2Data)

# To compare the means of the two groups, we need the two sample
# t test, implemented by the TwoSampleTTest group:
tTest2 = TwoSampleTTest(group1Results, group2Results, SamplePairing.Paired, VarianceAssumption.None)
# We can obtan the value of the test statistic through the Statistic property, # and the corresponding P-value through the Probability property:
print "Test statistic: {0:.4f}".format(tTest2.Statistic)
print "P-value:        {0:.4f}".format(tTest2.PValue)

# The significance level is the default value of 0.05:
print "Significance level:     {0:.2f}".format(tTest2.SignificanceLevel)
# We can now print the test scores:
print "Reject null hypothesis?", "yes" if tTest2.Reject() else "no"