Documentation

manova

Class:RepeatedMeasuresModel

Multivariate analysis of variance

expand all in page

Syntax

manovatbl = manova(rm)
manovatbl = manova(rm,Name,Value)
[manovatbl,A,C,D] = manova(___)

Description

example

manovatbl= manova(rm)returns the results of multivariate analysis of variance (manova) for the repeated measures modelrm.

example

manovatbl= manova(rm,Name,Value)also returns manova results with additional options, specified by one or moreName,Valuepair arguments.

example

[manovatbl,A,C,D] = manova(___)also returns arraysA,C, andDfor the hypotheses tests of the formA*B*C = D, whereDis zero.

Input Arguments

expand all

Repeated measures model, returned as aRepeatedMeasuresModel对象。

For properties and methods of this object, seeRepeatedMeasuresModel.

Name-Value Pair Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name andValueis the corresponding value.Namemust appear inside single quotes (' '). You can specify several name and value pair arguments in any order asName1,Value1,...,NameN,ValueN.

expand all

Model specifying the within-subjects hypothesis test, specified as one of the following:

  • 'separatemeans'— Compute a separate mean for each group, and test for equality among the means.

  • Model specification — This is a model specification in the within-subject factors. Test each term in the model. In this case,tblcontains a separate manova for each term in the formula, with the multivariate response equal to the vector of coefficients of that term.

  • Anr-by-ncmatrix,C, specifyingnccontrasts among therrepeated measures. IfYrepresents the matrix of repeated measures you use in the repeated measures modelrm, then the outputtblcontains a separate manova for each column ofY*C.

Example:“WithinModel”,'separatemeans'

Single between-subjects factor, specified as the comma-separated pair consisting of'By'and a character vector.manovaperforms a separate test of the within-subjects model for each value of this factor.

For example, if you have a between-subjects factor, Drug, then you can specify that factor to perform manova as follows.

Example:“通过”、“药物”

Output Arguments

expand all

Results of multivariate analysis of variance for the repeated measures modelrm, returned as atable.

manovauses these methods to measure the contributions of the model terms to the overall covariance:

  • Wilks' Lambda

  • Pillai's trace

  • Hotelling-Lawley trace

  • Roy's maximum root statistic

For details, seeMultivariate Analysis of Variance for Repeated Measures.

manovareturns the results for these tests for each group.manovatblcontains the following columns.

Column Name Definition
Within Within-subject terms
Between Between-subject terms
Statistic Name of the statistic computed
Value Value of the corresponding statistic
F F-statistic value
RSquare Measure for variance explained
df1 Numerator degrees of freedom
df2 Denominator degrees of freedom
pValue p-value for the correspondingF-statistic value

Data Types:table

Specification based on the between-subjects model, returned as a matrix or a cell array. It permits the hypothesis on the elements within given columns ofB(within time hypothesis). Ifmanovatblcontains multiple hypothesis tests,Amight be a cell array.

Data Types:single|double|cell

Specification based on the within-subjects model, returned as a matrix or a cell array. It permits the hypotheses on the elements within given rows ofB(between time hypotheses). Ifmanovatblcontains multiple hypothesis tests,Cmight be a cell array.

Data Types:single|double|cell

Hypothesis value, returned as 0.

Examples

expand all

Open Script

Load the sample data.

loadfisheriris

The column vectorspeciesconsists of iris flowers of three different species: setosa, versicolor, virginica. The double matrixmeasconsists of four types of measurements on the flowers: the length and width of sepals and petals in centimeters, respectively.

Store the data in a table array.

t = table(species,meas(:,1),meas(:,2),meas(:,3),meas(:,4),...'VariableNames',{'species','meas1','meas2','meas3','meas4'}); Meas = table([1 2 3 4]','VariableNames',{'Measurements'});

Fit a repeated measures model where the measurements are the responses and the species is the predictor variable.

rm = fitrm(t,'meas1-meas4~species','WithinDesign',Meas);

执行变量的多变量分析iance.

manova(rm)
ans = 8×9表统计价值之间在F RSquare df1 df2 pValue ________ ___________ _________ _________ ______ _______ ___ ___ ___________ Constant (Intercept) Pillai 0.99013 4847.5 0.99013 3 145 3.7881e-145 Constant (Intercept) Wilks 0.0098724 4847.5 0.99013 3 145 3.7881e-145 Constant (Intercept) Hotelling 100.29 4847.5 0.99013 3 145 3.7881e-145 Constant (Intercept) Roy 100.29 4847.5 0.99013 3 145 3.7881e-145 Constant species Pillai 0.96909 45.749 0.48455 6 292 2.4729e-39 Constant species Wilks 0.041153 189.92 0.79714 6 290 2.3958e-97 Constant species Hotelling 23.051 555.17 0.92016 6 288 4.6662e-155 Constant species Roy 23.04 1121.3 0.9584 3 146 1.4771e-100

执行多元一个ova separately for each species.

manova(rm,'By','species')
ans = 12×9 table Within Between Statistic Value F RSquare df1 df2 pValue ________ __________________ _________ ________ ______ _______ ___ ___ ___________ Constant species=setosa Pillai 0.9823 2682.7 0.9823 3 145 9.0223e-127 Constant species=setosa Wilks 0.017698 2682.7 0.9823 3 145 9.0223e-127 Constant species=setosa Hotelling 55.504 2682.7 0.9823 3 145 9.0223e-127 Constant species=setosa Roy 55.504 2682.7 0.9823 3 145 9.0223e-127 Constant species=versicolor Pillai 0.97 1562.8 0.97 3 145 3.7058e-110 Constant species=versicolor Wilks 0.029999 1562.8 0.97 3 145 3.7058e-110 Constant species=versicolor Hotelling 32.334 1562.8 0.97 3 145 3.7058e-110 Constant species=versicolor Roy 32.334 1562.8 0.97 3 145 3.7058e-110 Constant species=virginica Pillai 0.97261 1716.1 0.97261 3 145 5.1113e-113 Constant species=virginica Wilks 0.027394 1716.1 0.97261 3 145 5.1113e-113 Constant species=virginica Hotelling 35.505 1716.1 0.97261 3 145 5.1113e-113 Constant species=virginica Roy 35.505 1716.1 0.97261 3 145 5.1113e-113
Open Script

Load the sample data.

loadfisheriris

The column vectorspeciesconsists of iris flowers of three different species: setosa, versicolor, virginica. The double matrixmeasconsists of four types of measurements on the flowers: the length and width of sepals and petals in centimeters, respectively.

Store the data in a table array.

t = table(species,meas(:,1),meas(:,2),meas(:,3),meas(:,4),...'VariableNames',{'species','meas1','meas2','meas3','meas4'}); Meas = dataset([1 2 3 4]','VarNames',{'Measurements'});

Fit a repeated measures model where the measurements are the responses and the species is the predictor variable.

rm = fitrm(t,'meas1-meas4~species','WithinDesign',Meas);

执行变量的多变量分析iance. Also return the arrays for constructing the hypothesis test.

[manovatbl,A,C,D] = manova(rm)
manovatbl = 8×9 table Within Between Statistic Value F RSquare df1 df2 pValue ________ ___________ _________ _________ ______ _______ ___ ___ ___________ Constant (Intercept) Pillai 0.99013 4847.5 0.99013 3 145 3.7881e-145 Constant (Intercept) Wilks 0.0098724 4847.5 0.99013 3 145 3.7881e-145 Constant (Intercept) Hotelling 100.29 4847.5 0.99013 3 145 3.7881e-145 Constant (Intercept) Roy 100.29 4847.5 0.99013 3 145 3.7881e-145 Constant species Pillai 0.96909 45.749 0.48455 6 292 2.4729e-39 Constant species Wilks 0.041153 189.92 0.79714 6 290 2.3958e-97 Constant species Hotelling 23.051 555.17 0.92016 6 288 4.6662e-155 Constant species Roy 23.04 1121.3 0.9584 3 146 1.4771e-100 A = 2×1 cell array [1×3 double] [2×3 double] C = 1 0 0 -1 1 0 0 -1 1 0 0 -1 D = 0

Index into matrix A.

A{1}
ans = 1 0 0
A{2}
ans = 0 1 0 0 0 1

Tips

  • The multivariate response for each observation (subject) is the vector of repeated measures.

  • To test a more general hypothesisA*B*C = D, usecoeftest.

See Also

|||

Topics

Was this topic helpful?
Statistics and Machine Learning Toolbox Documentation
Other Documentation
金宝app

Try MATLAB, Simulink, and Other Products

Get trial now