groupmeans

Mean response estimates for multivariate analysis of variance (MANOVA)

Since R2023b

Syntax

means = groupmeans(maov)

means = groupmeans(maov,factors)

means = groupmeans(___,Name=Value)

Description

means = groupmeans(maov) returns a table of marginal means, standard errors, and 95% confidence intervals for each value of the factor in a one-way MANOVA. groupmeans calculates each marginal mean by taking the average of the values in the corresponding response vector.

means = groupmeans(maov,factors) returns means with information for each unique combination of values of the factors specified in factors.

means = groupmeans(___,Name=Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in the previous syntaxes. For example, you can specify the confidence level for the confidence intervals, and whether to calculate the marginal means or a mean for each response variable.

Examples

Calculate Marginal Means for One-Way MANOVA

Load the fisheriris data set.

load fisheriris

The column vector species contains iris flowers of three different species: setosa, versicolor, and virginica. The matrix meas contains four types of measurements for the flower: the length and width of sepals and petals in centimeters.

Perform a one-way MANOVA with species as the factor and the measurements in meas as the response variables.

maov = manova(species,meas)

maov = 
1-way manova

Y1,Y2,Y3,Y4 ~ 1 + Factor1

    Source     DF     TestStatistic    Value       F       DFNumerator    DFDenominator      pValue  
    _______    ___    _____________    ______    ______    ___________    _____________    __________

    Factor1      2       pillai        1.1919    53.466          8             290         9.7422e-53
    Error      147                                                                                   
    Total      149                                                                                   


  Properties, Methods

maov is a manova object that contains the results of the one-way MANOVA. The small p-value for species indicates that the flower species has a statistically significant effect on at least one of the flower measurements.

Calculate the marginal means for maov.

means = groupmeans(maov)

means=3×5 table
       Factor1         Mean        SE       Lower     Upper 
    ______________    ______    ________    ______    ______

    {'setosa'    }    2.5355    0.042807    2.4509    2.6201
    {'versicolor'}     3.573    0.042807    3.4884    3.6576
    {'virginica' }     4.285    0.042807    4.2004    4.3696

The 95% confidence intervals in the table output do not overlap, which is consistent with the small p-value for species.

Get Marginal Means for Two-Way MANOVA

Load the patients data set.

load patients

The variables Systolic and Diastolic contain data for patient systolic and diastolic blood pressure. The variables Smoker and SelfAssessedHealthStatus contain data for patient smoking status and self-assessed heath status.

Use the table function to create a table of factor values from the data in Systolic, Diastolic, Smoker, and SelfAssessedHealthStatus.

tbl = table(Systolic,Diastolic,Smoker,SelfAssessedHealthStatus,VariableNames=["Systolic" "Diastolic" "Smoker" "SelfAssessed"]);

Perform a two-way MANOVA to test the null hypothesis that smoking status does not have a statistically significant effect on systolic and diastolic blood pressure, and the null hypothesis that self-assessed health status does not have an effect on systolic and diastolic blood pressure.

maov = manova(tbl,["Systolic" "Diastolic"])

maov = 
2-way manova

Systolic,Diastolic ~ 1 + Smoker + SelfAssessed

       Source       DF    TestStatistic     Value         F       DFNumerator    DFDenominator      pValue  
    ____________    __    _____________    ________    _______    ___________    _____________    __________

    Smoker           1       pillai         0.67917     99.494          2              94         6.2384e-24
    SelfAssessed     3       pillai        0.053808    0.87552          6             190            0.51392
    Error           95                                                                                      
    Total           99                                                                                      


  Properties, Methods

maov is a manova object that contains the results of the two-way MANOVA. The small p-value for the Smoker term in the MANOVA model indicates that enough evidence exists to conclude that mean response vectors are statistically different across the factor values of Smoker. However, the large p-value for the SelfAssessed term indicates that not enough evidence exists to reject the null hypothesis that the mean response vectors are statistically the same across the values for SelfAssessed.

Calculate the marginal means for the values of the factor Smoker.

groupmeans(maov,"Smoker")

ans=2×5 table
    Smoker     Mean       SE       Lower     Upper 
    ______    ______    _______    ______    ______

    false     99.203    0.45685    98.296    100.11
    true      109.45    0.62574    108.21     110.7

The output shows that the marginal mean for non-smokers is lower than the marginal mean for smokers.

Calculate Mean for Each Response Variable

Load the carsmall data set.

load carsmall

The variable Model_Year contains data for the year a car was manufactured, and the variable Cylinders contains data for the number of engine cylinders in the car. The Acceleration and Displacement variables contain data for car acceleration and displacement.

Use the table function to create a table of factor values from the data in Model_Year, Cylinders, Acceleration, and Displacement.

tbl = table(Model_Year,Cylinders,Acceleration,Displacement,VariableNames=["Year" "Cylinders" "Acceleration" "Displacement"]);

Perform a two-way MANOVA using the table variables Year and Cylinders as factors, and the Acceleration and Displacement variables as response variables.

maov = manova(tbl,"Acceleration,Displacement ~ Cylinders + Year")

maov = 
2-way manova

Acceleration,Displacement ~ 1 + Year + Cylinders

     Source      DF    TestStatistic     Value        F       DFNumerator    DFDenominator      pValue  
    _________    __    _____________    ________    ______    ___________    _____________    __________

    Year          2       pillai        0.084893    2.1056          4             190           0.081708
    Cylinders     2       pillai         0.94174     42.27          4             190         2.5049e-25
    Error        95                                                                                     
    Total        99                                                                                     


  Properties, Methods

maov is a manova object that contains the results of the two-way MANOVA. The table output shows that the p-value for the MANOVA model term Year is too large to conclude that Year has a statistically significant effect on Acceleration and Displacement.

Calculate the means, standard errors, and 95% confidence intervals for each response variable, grouped by the factor values in Year.

means = groupmeans(maov,"Year",MarginalMean=false)

means=6×6 table
    Year     ResponseName      Mean       SE       Lower     Upper 
    ____    ______________    ______    _______    ______    ______

     70     "Acceleration"    14.102    0.45499    13.199    15.005
     70     "Displacement"    233.02     6.4983    220.12    245.92
     76     "Acceleration"    15.623    0.41203    14.805    16.441
     76     "Displacement"    218.43     5.8848    206.75    230.12
     82     "Acceleration"    15.083    0.53717    14.016    16.149
     82     "Displacement"    234.09     7.6721    218.86    249.32

The table output shows that the 95% confidence intervals have significant overlap for each response variable, supporting the conclusion that Year does not have a statistically significant effect on Acceleration and Displacement.

Input Arguments

maov — MANOVA results

manova object

MANOVA results, specified as a manova object. The properties of maov contain the factor values and response data used by groupmeans to calculate the means, standard errors, and confidence intervals.

factors — Factors used to group response data

string scalar | character vector | string vector | cell array of character vectors

Factors used to group the response data, specified as a string scalar, a character or string vector, or a cell array of character vectors. The groupmeans function groups the response data by the combinations of values for the factors in factors. The factors argument must be one or more of the names in maov.FactorNames.

Example: ["Factor1","Factor2"]

Data Types: string | cell

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: groupmeans(maov,["Cylinders","Year"],MarginalMean=false,Alpha=0.01) calculates a mean with a 99% confidence interval for each response variable.

Alpha — Significance level

0.05 (default) | scalar value in the range (0,1)

Significance level for the estimates, specified as a scalar value in the range (0,1). The confidence level of the confidence intervals is $$100(1-\alpha )\%$$. The default value for alpha is 0.05, which returns 95% confidence intervals for the estimates.

Example: Alpha=0.01

Data Types: single | double

MarginalMean — Indicator to calculate marginal means

true or 1 (default) | false or 0

Indicator to calculate the marginal means, specified as a numeric or logical 1 (true) or 0 (false). Each marginal mean is the average of the values in the corresponding mean response vector. When MarginalMean is false, groupmeans calculates a separate mean for each response variable.

Example: MarginalMean=false

Data Types: logical

Output Arguments

means — Means, standard errors, and confidence intervals

table

Means, standard errors, and confidence intervals, returned as a table. The table means has one row per unique combination of factor values when MarginalMean is true. Otherwise, means has r rows per unique combination of factor values, where r is the number of response variables.

If maov is a one-way manova object, means contains a column corresponding to the single factor. If maov is a two- or N-way manova object, means contains a column for each factor specified in factors. The table also contains the following columns.

• Mean — Estimate of the marginal or response variable mean corresponding to the factor value. Use the MarginalMean name-value argument to specify the type of mean to calculate.

• SE — Standard error of the mean estimate.

• Lower — 95% lower confidence bound of the mean estimate.

• Upper — 95% upper confidence bound of the mean estimate.

Version History

Introduced in R2023b