# 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.

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```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" ```