Overview of the Student Statistics Subpackage Calling SequenceDescriptionQuantitiesHypothesis TestingInteractive explorationReference TablesGetting Help with a Command in the PackageExample WorksheetCompatibility
<Text-field style="Heading 2" layout="Heading 2" bookmark="info">Description</Text-field> The Student:-Statistics subpackage is designed to help teachers present and students understand the basic material of a standard course in statistics. There are three components to the subpackage: quantities (including visualization and formulas), hypothesis testing, and interactive exploration. These components are described in the following sections. Each command in the Student:-Statistics subpackage can be accessed by using either the long form or the short form of the command name in the command calling sequence. The long form, Student:-Statistics:-command, is always available. The short form can be used after loading the package. Most of the commands and tutors in the Student:-Statistics package can be accessed through the context menu. These commands are consolidated under the Student:-Statistics name.
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk0">Quantities</Text-field> In this subpackage, we can work with random variables taken from various distributions:
BernoulliRandomVariableBetaRandomVariableBinomialRandomVariableCauchyRandomVariableChiSquareRandomVariableDiscreteUniformRandomVariableEmpiricalRandomVariableExponentialRandomVariableFRatioRandomVariableGammaRandomVariableGeometricRandomVariableHypergeometricRandomVariableLogNormalRandomVariableNegativeBinomialRandomVariableNormalRandomVariablePoissonRandomVariableStudentTRandomVariableUniformRandomVariable
For more information, see RandomVariable. We can also work with data samples. Data samples within this subpackage are of the form of list, Vector, or Matrix. Data stored in a list and data stored in a Vector are interpreted the same way. For example, [1,2,3] and <1,2,3> represent the same data sample. For data stored in a Matrix, we treat the Matrix as a collection of data samples where each column of the Matrix represents an individual list or Vector data sample. We can use the following commands to work with these random variables and data samples: CorrelationCovarianceDataSummaryDecileExpectedValueInterquartileRangeKurtosisMeanMedianModeMomentPercentileQuantileQuartileSkewnessStandardDeviationVariance
These commands only work for random variables: CDFMGFProbabilityPDFProbabilityFunctionSample
<Text-field style="Heading 3" layout="Heading 3" bookmark="bkmrk1">Visualization</Text-field> Some of the commands mentioned above are designed to give a visual demonstration to help users better understand the material. To return a plot from one of the commands listed below, specify the optional parameter output=plot, for example: CDF(X,2,output=plot) where NiNJIlhHNiI= is a NiMtSTdCaW5vbWlhbFJhbmRvbVZhcmlhYmxlRzYiNiQiIiYjIiIiIiIj. Commands able to generate such a visualization are: CDFDataSummaryDecileExpectedValueInterquartileRangeMeanMedianModePDFProbabilityFunctionPercentileQuantileQuartileSampleStandardDeviation
<Text-field style="Heading 3" layout="Heading 3" bookmark="bkmrk2">Formulas</Text-field> Some of the commands can give a formula for the quantity they compute, rather than the end result. To obtain such a formula, use the command on a random variable (or an expression involving random variables) and specify the optional parameter inert. For example, define Y := PoissonRandomVariable(lambda) and then compute Variance(Y, inert). Commands that are able to return a formula are: CDFCorrelationCovarianceExpectedValueKurtosisMeanMomentMGFProbabilityPDFProbabilityFunctionSkewnessStandardDeviationVariance
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk3">Hypothesis Testing</Text-field> This section contains commands for some commonly used hypothesis tests. The command TestsGuide can be used to select an appropriate test from among the options Maple offers. It explains the assumptions the test makes and the hypothesis it tests. For more information, see HypothesisTest.
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk4">Interactive exploration</Text-field> To explore a random variable interactively, you can use the ExploreRV command. It takes a random variable, or an expression involving one or more random variables, and inserts sliders and graphs into the current worksheet, so that you can see how many quantities and the PDF and CDF change when you change the parameters of the distribution.
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk5">Reference Tables</Text-field> The Student Statistics package also contains two commands to generate and read values from statistical reference tables. CriticalTableProbabilityTable
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk6">Getting Help with a Command in the Package</Text-field> To display the help page for a particular Student:-Statistics command, see Getting Help with a Command in a Package.
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk7">Example Worksheet</Text-field> For introductory examples, see Statistics Example Worksheet.