# Mean Tests in IronPython QuickStart Sample

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

View this sample in: C# Visual Basic F#

``````Python
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"
``````