The TwoSamplePairedTTest function computes the paired t-test upon datasets X1 and X2. This means that every entry of the population of X1 is related to an entry of the population of X2; in the samples, X1[i] is related to X2[i]; and the procedure tests whether the mean of the population of differences between related pairs, X1[i] minus X2[i], is equal to beta, under the assumption that these differences are normally distributed. No assumptions are made on the standard deviation.

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 difference in population means (assumed population mean of X1 minus the assumed population mean 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.

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

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

$Y≔\left[10\,11\,7\,3\,10\,5\,2\,12\,14\,10\right]\:$

$\mathrm{Mean}\left(X\right)-\mathrm{Mean}\left(Y\right)$

$-\frac{4}{5}$

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

Standard T-Test with Paired Samples
-----------------------------------
Null Hypothesis:
Sample drawn from populations with difference of means equal to 1
Alt. Hypothesis:
Sample drawn from population with difference of means not equal to 1
 
Sample Size:             10
Difference in Means:     -0.8
Difference Std. Dev.:    1.31656
Distribution:            StudentT(9)
Computed Statistic:      -4.32346015250714
Computed p-value:        .00192341172347674
Confidence Interval:     -1.7418108909393 .. .141810890939296
                         (difference of population means)
 
Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false.

$\left[\mathrm{hypothesis}=\mathrm{false}\,\mathrm{confidenceinterval}=\mathrm{-1.74181089093930}..0.141810890939296\,\mathrm{distribution}=\mathrm{StudentT}\left(9\right)\,\mathrm{pvalue}=0.00192341172347674\,\mathrm{statistic}=\mathrm{-4.32346015250714}\right]$

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

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

Standard T-Test with Paired Samples
-----------------------------------
Null Hypothesis:
Sample drawn from populations with difference of means equal to 1
Alt. Hypothesis:
Sample drawn from population with difference of means not equal to 1
 
Sample Size:             10
Difference in Means:     -0.8
Difference Std. Dev.:    1.31656
Distribution:            StudentT(9)
Computed Statistic:      -4.32346015250714
Computed p-value:        .00192341172347674
Confidence Interval:     -1.7418108909393 .. .141810890939296
                         (difference of population means)
 
Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false.
Histogram Type:  default
Data Range:      -2 .. 1
Bin Width:       1/10
Number of Bins:  30
Frequency Scale: relative

$\mathrm{report}$

$\left[\mathrm{hypothesis}=\mathrm{false}\,\mathrm{confidenceinterval}=\mathrm{-1.74181089093930}..0.141810890939296\,\mathrm{distribution}=\mathrm{StudentT}\left(9\right)\,\mathrm{pvalue}=0.00192341172347674\,\mathrm{statistic}=\mathrm{-4.32346015250714}\right]$

$\mathrm{graph}$

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][TwoSamplePairedTTest] command was introduced in Maple 18.

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