 TwoSampleFTest - Maple Help

Student[Statistics]

 TwoSampleFTest
 apply the two sample F-test for population variances Calling Sequence TwoSampleFTest(X1, X2, beta, confidence_option, output_option) Parameters

 X1 - first data sample X2 - second data sample beta - realcons; the test value for the ratio of the two variances confidence_option - (optional) equation of the form confidence=float. output_option - (optional) equation of the form output=x where x is report, plot, or both Description

 • 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. Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{Statistics}}\right):$

Specify the data sample.

 > $X≔\left[9,10,8,4,8,3,0,10,15,9\right]:$
 > $Y≔\left[6,3,10,11,9,8,13,4,4,4\right]:$
 > $\frac{\mathrm{Variance}\left(X\right)}{\mathrm{Variance}\left(Y\right)}$
 $\frac{{203}}{{137}}$ (1)

Calculate the two sample F-test on a list of values, assuming equal variances.

 > $\mathrm{TwoSampleFTest}\left(X,Y,1,\mathrm{confidence}=0.95\right)$
 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.
 $\left[{\mathrm{hypothesis}}{=}{\mathrm{true}}{,}{\mathrm{confidenceinterval}}{=}{0.368046193452367}{..}{5.96552419074047}{,}{\mathrm{distribution}}{=}{\mathrm{FRatio}}{}\left({9}{,}{9}\right){,}{\mathrm{pvalue}}{=}{0.567367926580979}{,}{\mathrm{statistic}}{=}{1.48175182481752}\right]$ (2)

If the output=plot option is included, then a plot will be returned.

 > $\mathrm{TwoSampleFTest}\left(X,Y,1,\mathrm{confidence}=0.95,\mathrm{output}=\mathrm{plot}\right)$ If the output=both option is included, then both a report and a plot will be returned.

 > $\mathrm{report},\mathrm{graph}≔\mathrm{TwoSampleFTest}\left(X,Y,1,\mathrm{confidence}=0.95,\mathrm{output}=\mathrm{both}\right):$
 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
 > $\mathrm{report}$
 $\left[{\mathrm{hypothesis}}{=}{\mathrm{true}}{,}{\mathrm{confidenceinterval}}{=}{0.368046193452367}{..}{5.96552419074047}{,}{\mathrm{distribution}}{=}{\mathrm{FRatio}}{}\left({9}{,}{9}\right){,}{\mathrm{pvalue}}{=}{0.567367926580979}{,}{\mathrm{statistic}}{=}{1.48175182481752}\right]$ (3)
 > $\mathrm{graph}$  References

 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. Compatibility

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