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Statistics

  

OneWayANOVA

  

generate a one-way ANOVA table

 

Calling Sequence

Parameters

Options

Description

Examples

References

Compatibility

Calling Sequence

OneWayANOVA(X, options)

Parameters

X

-

list(Vector) or Matrix; observations

options

-

(optional) equation(s) of the form option=value where option is headers; specify options for the OneWayANOVA command

Options

• 

headers : truefalse; display header information. The default is true.

Description

• 

The OneWayANOVA command generates a Matrix that represents the standard analysis-of-variance (ANOVA) table for a one-way classification. Suppose one performs experiments varying only one factor.  Each value of the factor results in one group of observations.  The ANOVA table generated by analyzing all the observations can help in determining whether changing the factor has any significant influence.

• 

The parameter X is a list of Vectors, each containing the observations for a single group.  If each group contains the same number of observations, then X can be a Matrix in which each column contains observations for one group. The data sets for the groups can also be supplied as lists; see the Input Forms help page for more details.

• 

The OneWayANOVA command returns a Matrix with 4 rows and 5 columns. The first row displays the heading for the contents of each column (see Options). The second row contains variance between groups, the third contains variance within groups, and the fourth contains total variance.

• 

The first column of the ANOVA table contains the degrees of freedom for each source of variance, the second column contains the sum of squares, and the third contains the mean square.  The final two columns show the F-statistic (ratio of the mean squares) and the p-value for the null hypothesis that there is no difference between means of the groups.

Examples

withStatistics:

Consider three groups of observations.

G1Vector10,11,8,datatype=float:

G2Vector9,9,9,11,datatype=float:

G3Vector10,11,7,12,datatype=float:

Generate the one-way ANOVA table.

OneWayANOVAG1,G2,G3

DFSum of SquaresMean SquareF-Statisticp-value20.5151515151515150.2575757575757580.09510489510489510.910290149152349821.66666666666672.70833333333333NULLNULL1022.1818181818182NULLNULLNULL

(1)

When all groups have equal numbers of observations, the observations can be placed in a Matrix.

MMatrix60,55,57,69,65,60,58,69,52,67,66,50,54,51,53,69,66,52,66,56,51,61,66,54,52,64,53,57,63,63,58,66,51,58,70,52,51,54,52,58,54,63,69,65,68,52,58,62:

OneWayANOVAM,headers=false

397.833333333333432.61111111111110.7915172688547700.505164016846382441812.8333333333341.2007575757576NULLNULL471910.66666666667NULLNULLNULL

(2)

References

  

Draper, Norman R., and Smith, Harry. Applied Regression Analysis. 3rd ed. New York: Wiley, 1998.

Compatibility

• 

The Statistics[OneWayANOVA] command was updated in Maple 2016.

• 

The headers option was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

Statistics

Statistics/Regression

Statistics/Regression/InputForms

 


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