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Student[Statistics]

  

TwoSamplePairedTTest

  

apply the paired t-test for population means

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

TwoSamplePairedTTest(X1, X2, beta, confidence_option, output_option)

Parameters

X1

-

first data sample

X2

-

second data sample

beta

-

realcons; the test value for the difference between the two means

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 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.

Examples

withStudent[Statistics]:

Specify the data sample.

X9,10,8,4,8,3,0,10,15,9:

Y10,11,7,3,10,5,2,12,14,10:

MeanXMeanY

45

(1)

Calculate the paired t-test on a list of values.

TwoSamplePairedTTestX,Y,1,confidence=0.95

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.

hypothesis=false,confidenceinterval=1.74181089093930..0.141810890939296,distribution=StudentT9,pvalue=0.00192341172347674,statistic=4.32346015250714

(2)

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

TwoSamplePairedTTestX,Y,1,confidence=0.95,output=plot

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

report,graphTwoSamplePairedTTestX,Y,1,confidence=0.95,output=both:

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
Number of Bins:  30
Frequency Scale: relative

report

hypothesis=false,confidenceinterval=1.74181089093930..0.141810890939296,distribution=StudentT9,pvalue=0.00192341172347674,statistic=4.32346015250714

(3)

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][TwoSamplePairedTTest] command was introduced in Maple 18.

• 

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

See Also

Statistics[TwoSamplePairedTTest]

Student

Student/Statistics/TwoSamplePairedTTest/overview

Student[Statistics]

Student[Statistics][HypothesisTest]

Student[Statistics][OneSampleTTest]

Student[Statistics][TwoSampleTTest]

 


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