Variance Tests QuickStart Sample (IronPython)

```Python
import numerics

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

#/ Demonstrates how to use hypothesis tests for the variance 
#/ 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 variance of the scores is greater than
# a specific value. We use the one sample Chi-square test for this
# purpose.

print "Tests for class 1"

# First we create a NumericalVariable that holds the test results.
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 class right away:
print "Mean for the class: {0:.1f}".format(group1Results.Mean)
print "Standard deviation: {0:.1f}".format(group1Results.StandardDeviation)
			
#
# One Sample Chi-square Test
#

print "\nUsing chi-square test:"

# We want to know if the standard deviation is larger than 15.
# Therefore, we use a one-tailed chi-square test:
chiSquareTest = OneSampleChiSquareTest(group1Results, 225, HypothesisType.OneTailedUpper)
			
# 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(chiSquareTest.Statistic)
print "P-value:        {0:.4f}".format(chiSquareTest.PValue)

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

# We can get the same results for the 0.01 significance level by explicitly
# passing the significance level as a parameter to these methods:
print "Significance level:     {0:.2f}".format(0.01)
print "Reject null hypothesis?", "yes" if chiSquareTest.Reject(0.01) else "no"
			
# The GetConfidenceInterval method needs the confidence level, which equals
# 1 - the significance level:
varianceInterval = chiSquareTest.GetConfidenceInterval(0.99)
print "99% Confidence interval for the variance: {0:.1f} - {1:.1f}".format( \
    varianceInterval.LowerBound, varianceInterval.UpperBound)

# 
# Two sample F-test
#

print "\nUsing F-test:"
# We want to compare the scores of the first group to the scores 
# of a second group from another school. We want to verify that the
# variances of the scores from the two schools are equal. Once again, # we start by creating a NumericalVariable, this time containing 
# the scores for the second group:
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 variances of the two groups, we need the two sample
# F test, implemented by the FTest class:
fTest = FTest(group1Results, group2Results)
# 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(fTest.Statistic)
print "P-value:        {0:.4f}".format(fTest.PValue)

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