One Way ANOVA - Maple Help

Statistics

 OneWayANOVA
 generate a one-way ANOVA table

 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

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

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

Consider three groups of observations.

 > $\mathrm{G1}≔\mathrm{Vector}\left(\left[10,11,8\right],\mathrm{datatype}=\mathrm{float}\right):$
 > $\mathrm{G2}≔\mathrm{Vector}\left(\left[9,9,9,11\right],\mathrm{datatype}=\mathrm{float}\right):$
 > $\mathrm{G3}≔\mathrm{Vector}\left(\left[10,11,7,12\right],\mathrm{datatype}=\mathrm{float}\right):$

Generate the one-way ANOVA table.

 > $\mathrm{OneWayANOVA}\left(\left[\mathrm{G1},\mathrm{G2},\mathrm{G3}\right]\right)$
 $\left[\begin{array}{ccccc}\mathrm{DF}& \mathrm{Sum of Squares}& \mathrm{Mean Square}& \mathrm{F-Statistic}& \mathrm{p-value}\\ 2& 0.5151515151515154& 0.2575757575757577& 0.09510489510489514& 0.9102901491523487\\ 8& 21.666666666666668& 2.7083333333333335& \mathrm{NULL}& \mathrm{NULL}\\ 10& 22.181818181818183& \mathrm{NULL}& \mathrm{NULL}& \mathrm{NULL}\end{array}\right]$ (1)

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

 > $M≔\mathrm{Matrix}\left(\left[\left[60,55,57,69\right],\left[65,60,58,69\right],\left[52,67,66,50\right],\left[54,51,53,69\right],\left[66,52,66,56\right],\left[51,61,66,54\right],\left[52,64,53,57\right],\left[63,63,58,66\right],\left[51,58,70,52\right],\left[51,54,52,58\right],\left[54,63,69,65\right],\left[68,52,58,62\right]\right]\right):$
 > $\mathrm{OneWayANOVA}\left(M,\mathrm{headers}=\mathrm{false}\right)$
 $\left[\begin{array}{ccccc}3& 97.83333333333337& 32.61111111111112& 0.7915172688547703& 0.5051640168463818\\ 44& 1812.8333333333335& 41.20075757575758& \mathrm{NULL}& \mathrm{NULL}\\ 47& 1910.666666666667& \mathrm{NULL}& \mathrm{NULL}& \mathrm{NULL}\end{array}\right]$ (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.