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Tests Commands

  

The Statistics package provides various parametric and non-parametric tools for performing hypothesis testing and statistical inference.

  

 

ChiSquareGoodnessOfFitTest

apply the chi-square test for goodness-of-fit

ChiSquareIndependenceTest

apply the chi-square test for independence in a matrix

ChiSquareSuitableModelTest

apply the chi-square suitable model test

OneSampleChiSquareTest

apply the one sample chi-square test for the population standard deviation

OneSampleTTest

apply the one sample t-test for the population mean

OneSampleZTest

apply the one sample z-test for the population mean

ShapiroWilkWTest

apply Shapiro and Wilk's W-test for normality

TwoSampleFTest

apply the two sample F-test for population variances

TwoSamplePairedTTest

apply the paired t-test for population means

TwoSampleTTest

apply the two sample t-test for population means

TwoSampleZTest

apply the two sample z-test for population means

 

Notes

Examples

Notes

• 

All tests generate a complete report of all calculations in the form of a userinfo message.  In order to access these reports when applying tests, specify infolevel[Statistics] := 1 or use the summarize option.

Examples

withStatistics:

Build a sample from a Rayleigh distribution and compare with the population mean and population standard deviation.

SSampleRayleigh7,100:

evalfMeanRayleigh7

8.773198959

(1)

evalfStandardDeviationRayleigh7

4.585954642

(2)

Test that the sample S is drawn from a population with mean equal to 8 and standard deviation equal to 5.

OneSampleZTestS,8,5

hypothesis=false,confidenceinterval=8.19465579918747..10.1546197837269,distribution=Normal0,1,pvalue=0.0188099792028316,statistic=2.34927558291438

(3)

Test that the sample S is drawn from a population with mean equal to 8 with unknown standard deviation.

OneSampleTTestS,8

hypothesis=false,confidenceinterval=8.26546145701860..10.0838141258958,distribution=StudentT99,pvalue=0.0118640683436966,statistic=2.56356894641468

(4)

Test that S is drawn from a normal distribution and return an embedded report.

ShapiroWilkWTestS,summarize=embed

hypothesis=false,pvalue=0.00138375156142846,statistic=0.947243047976463

(5)

Null Hypothesis:

Sample drawn from a population that follows a normal distribution

Alternative Hypothesis:

Sample drawn from population that does not follow a normal distribution

Sample Size

Computed Statistic

Computed p-value

100.

0.947243

0.00138375

Result:

Rejected: This statistical test provides evidence that the null hypothesis is false.

Test that Normal(8.77,4.59) is a suitable model for the population of S.

ChiSquareSuitableModelTestS,Normal8.77,4.59,level=0.01

hypothesis=true,criticalvalue=21.6659943178256,distribution=ChiSquare9,pvalue=0.474985626461966,statistic=8.600000000

(6)

Test for independence in a 3x2 table.

XMatrix32.,12.,14.,22.,6.,9.:

ChiSquareIndependenceTestX,level=0.05

hypothesis=false,criticalvalue=5.99146454710798,distribution=ChiSquare2,pvalue=0.00471928013399603,statistic=10.71219801

(7)

Return a report for the test above:

ChiSquareIndependenceTestX,level=0.05,summarize=true

Chi-Square Test for Independence
--------------------------------
Null Hypothesis:
Two attributes within a population are independent of one another
Alt. Hypothesis:
Two attributes within a population are not independent of one another
 
Dimensions:              3

Total Elements:          95
Distribution:            ChiSquare(2)
Computed Statistic:      10.71219801
Computed p-value:        .00471928013399603
Critical Values:         5.99146454710798
 
Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false.

hypothesis=false,criticalvalue=5.99146454710798,distribution=ChiSquare2,pvalue=0.00471928013399603,statistic=10.71219801

(8)

See Also

Statistics

Statistics[Computation]

 


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