The TwoSampleFTest function computes the two sample F-test upon datasets X1 and X2. This tests whether the population standard deviation of X1, divided by the population standard deviation of X2, is equal to beta, under the assumption that both populations are normally distributed.

The first parameter X1 is the first data sample to use in the analysis.

The second parameter X2 is the second data sample to use in the analysis.

The third parameter beta is the assumed ratio of population variances (assumed population variance of X1 divided by the assumed population variance of X2), specified as a real constant.

confidence=float

This option is used to specify the confidence level of the interval and must be a floating-point value between 0 and 1.  By default this is set to 0.95.

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.

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

$X≔\left[9\,10\,8\,4\,8\,3\,0\,10\,15\,9\right]\:$

$Y≔\left[6\,3\,10\,11\,9\,8\,13\,4\,4\,4\right]\:$

$\frac{\mathrm{Variance}\left(X\right)}{\mathrm{Variance}\left(Y\right)}$

$\frac{203}{137}$

$\mathrm{TwoSampleFTest}\left(X\,Y\,1\,\mathrm{confidence}=0.95\right)$

F-Ratio Test on Two Samples
---------------------------
Null Hypothesis:
Sample drawn from populations with ratio of variances equal to 1
Alt. Hypothesis:
Sample drawn from population with ratio of variances not equal to 1
 
Sample Sizes:            10, 10
Sample Variances:        18.0444, 12.1778
Ratio of Variances:      1.48175
Distribution:            FRatio(9,9)
Computed Statistic:      1.48175182481752
Computed p-value:        .567367926580979
Confidence Interval:     .368046193452367 .. 5.96552419074047
                         (ratio of population variances)
 
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false.

$\left[\mathrm{hypothesis}=\mathrm{true}\,\mathrm{confidenceinterval}=0.368046193452367..5.96552419074047\,\mathrm{distribution}=\mathrm{FRatio}\left(9\,9\right)\,\mathrm{pvalue}=0.567367926580979\,\mathrm{statistic}=1.48175182481752\right]$

$\mathrm{TwoSampleFTest}\left(X\,Y\,1\,\mathrm{confidence}=0.95\,\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{report},\mathrm{graph}≔\mathrm{TwoSampleFTest}\left(X\,Y\,1\,\mathrm{confidence}=0.95\,\mathrm{output}=\mathrm{both}\right)\:$

F-Ratio Test on Two Samples
---------------------------
Null Hypothesis:
Sample drawn from populations with ratio of variances equal to 1
Alt. Hypothesis:
Sample drawn from population with ratio of variances not equal to 1
 
Sample Sizes:            10, 10
Sample Variances:        18.0444, 12.1778
Ratio of Variances:      1.48175
Distribution:            FRatio(9,9)
Computed Statistic:      1.48175182481752
Computed p-value:        .567367926580979
Confidence Interval:     .368046193452367 .. 5.96552419074047
                         (ratio of population variances)
 
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false.
Histogram Type:  default
Data Range:      0 .. 15
Bin Width:       1/2
Number of Bins:  30
Frequency Scale: relative
Histogram Type:  default
Data Range:      3 .. 13
Bin Width:       1/3
Number of Bins:  30
Frequency Scale: relative

$\mathrm{report}$

$\left[\mathrm{hypothesis}=\mathrm{true}\,\mathrm{confidenceinterval}=0.368046193452367..5.96552419074047\,\mathrm{distribution}=\mathrm{FRatio}\left(9\,9\right)\,\mathrm{pvalue}=0.567367926580979\,\mathrm{statistic}=1.48175182481752\right]$

$\mathrm{graph}$

Kanji, 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][TwoSampleFTest] command was introduced in Maple 18.

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