The ChiSquareSuitableModelTest function performs the chi-square suitable model test upon an observed data sample against a known random variable or probability distribution. It works by determining bins for a histogram from the probability distribution, then classifying the entries of X into these bins, and finally testing whether the resulting histogram matches the histogram for the probability distribution.

The first parameter X is a data sample of observed data to use in the analysis.

The second parameter F is a random variable or probability distribution that is compared to the observed data sample.

This test is only appropriate if there is prior knowledge of any parameters in the distribution. If any of the parameters in the distribution have been fitted to the data sample in question, then an adjustment of the degrees-of-freedom parameter is necessary. This adjustment is not available in the current implementation.

The options argument can contain one or more of the options shown below.

bins='deduce' or posint

This option indicates the number of bins to use when categorizing data from X and probabilities from F.  If set to 'deduce' (default), the function attempts to determine a reasonable value for this option. This parameter is ignored if the distribution is discrete.

range='deduce' or range

This option indicates the range to use when considering data values - data outside of the range is discarded during processing.  If set to 'deduce' (default), the function attempts to determine a suitable range.

level=float

This option is used to specify the level of the analysis (minimum criteria for the observed data to be considered well-fit to the expected data).  By default, this value is 0.05.

output=report or plot or both

If the option output is not included or is specified to be output=report, then the function will return a report. If output=plot is specified, then the function will return a plot of the sample test. If output=both is specified, then both the report and the plot will be returned.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Statistics}\right]\right)\:$

$X≔\mathrm{Sample}\left(\mathrm{NormalRandomVariable}\left(0\,1\right)\,100\right)\:$

$\mathrm{ChiSquareSuitableModelTest}\left(X\,\mathrm{UniformRandomVariable}\left(0\,1\right)\,\mathrm{bins}=10\right)$

Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution
 
Bins:                    10
Degrees of Freedom:      9
Distribution:            ChiSquare(9)
Computed Statistic:      301.6000000
Computed p-value:        0.
Critical Values:         16.9189774487099
 
Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false.

$\left[\mathrm{hypothesis}=\mathrm{false}\,\mathrm{criticalvalue}=16.9189774487099\,\mathrm{distribution}=\mathrm{ChiSquare}\left(9\right)\,\mathrm{pvalue}=0.\,\mathrm{statistic}=301.6000000\right]$

$\mathrm{ChiSquareSuitableModelTest}\left(X\,\mathrm{NormalRandomVariable}\left(0\,1\right)\,\mathrm{bins}=10\right)$

Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution
 
Bins:                    10
Degrees of Freedom:      9
Distribution:            ChiSquare(9)
Computed Statistic:      14.80000000
Computed p-value:        .0965781731648307
Critical Values:         16.9189774487099
 
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false.

$\left[\mathrm{hypothesis}=\mathrm{true}\,\mathrm{criticalvalue}=16.9189774487099\,\mathrm{distribution}=\mathrm{ChiSquare}\left(9\right)\,\mathrm{pvalue}=0.0965781731648307\,\mathrm{statistic}=14.80000000\right]$

$\mathrm{ChiSquareSuitableModelTest}\left(X\,\mathrm{NormalRandomVariable}\left(0\,1\right)\,\mathrm{bins}=10\,\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{report},\mathrm{graph}≔\mathrm{ChiSquareSuitableModelTest}\left(X\,\mathrm{NormalRandomVariable}\left(0\,1\right)\,\mathrm{bins}=10\,\mathrm{output}=\mathrm{both}\right)\:$

Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution
 
Bins:                    10
Degrees of Freedom:      9
Distribution:            ChiSquare(9)
Computed Statistic:      14.80000000
Computed p-value:        .0965781731648307
Critical Values:         16.9189774487099
 
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false.
Histogram Type:  default
Data Range:      -1.6348567543439 .. 2.21337958939036
Bin Width:       .128274544791142
Number of Bins:  30
Frequency Scale: relative

$\mathrm{report}$

$\left[\mathrm{hypothesis}=\mathrm{true}\,\mathrm{criticalvalue}=16.9189774487099\,\mathrm{distribution}=\mathrm{ChiSquare}\left(9\right)\,\mathrm{pvalue}=0.0965781731648307\,\mathrm{statistic}=14.80000000\right]$

$\mathrm{graph}$

Kanju, Gopal K. 100 Statistical Tests. London: SAGE Publications Ltd., 1994.

Sheskin, David J. Handbook of Parametric and Nonparametric Statistical Procedures. London: CRC Press, 1997.

The Student[Statistics][ChiSquareSuitableModelTest] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.