manova and sample report

7/24/2019 MANOVA and Sample Report

1/24

MULTIVARIATE ANALYSIS OF VARIANCE(MANOVA)


2/24

MANOVA

Previously, we explored the use ofanalysis of variance to comparegroups on a single dependent

variable. In many research situations, however,

we are interested in comparing groupson a range of dierent characteristics.

This is quite common in clinicalresearch, where the focus is on theevaluation of the impact of an

intervention on a variety of outcomemeasures (e.g. anxiety, depression,


3/24

MANOVA

!ultivariate analysis of variance(!"#$%" is an extension of analysisof variance for use when you havemore than one dependent variable.

These dependent variables should berelated in some way, or there shouldbe some conceptual reason for

considering them together. !"#$%" compares the groups and

tells you whether the meandierences between the groups on the

combination of dependent variables


4/24

MANOVA

!"#$%" creates a new summarydependent variable, which is a linearcombination of each of your originaldependent variables.

It then performs an analysis ofvariance using this new combineddependent variable (composite

dependent variable. !"#$%" will tell you if there is a

signi'cant dierence between yourgroups on this composite dependent

variable


5/24

MANOVA

)hy not *ust conduct a series of"#$%"s separately for eachdependent variable+

y conducting a whole series ofanalyses you run the ris& of an-inated Type / error-.

This means that the more analyses

you run, the more li&ely you are to 'nda signi'cant result, even if in realitythere are no dierences between yourgroups.

The advantage of using !"#$%" is- -


6/24

MANOVA

If separate "#$%"s are conducted oneach dependent variable, then anyrelationship between 0%s is ignored 1we lose information about anycorrelations that might exist between0%s.

y running all 0%s together, !"#$%"

ta&es into account of the relationshipbetween outcome variables. !"#$%" has the power to detect

group dierences within I% along a

combination of dimensions.


7/24

MANOVA

!"#$%" is a much more complex setof procedures, and it has a number ofadditional assumptions that must bemet.

If you have a number of dependentvariables, you can still perform aseries of "#$%"s separately for each

dependent variable. If you choose to do this, you might li&eto reduce the ris& of a Type / error bysetting a more stringent alpha value.

$ne way to control for the Type / error


8/24

MANOVA

To do this, you divide your normalalpha value (typically .23 by thenumber of tests that you intend toperform.

If there are three dependent variables,you would divide .23 by 3 (whichequals .0! after rounding and you

would use this new value as your cut4o. 0ierences between your groups

would need a probability value of less

than .2/5 before you could consider


9/24

MANOVA

To do this, you divide your normalalpha value (typically .23 by thenumber of tests that you intend toperform.

If there are three dependent variables,you would divide .23 by 3 (whichequals .0! after rounding and you

would use this new value as your cut4o. 0ierences between your groups

would need a probability value of less

than ,2/5 before you could consider


10/24

MANOVA

!"#$%" can be used in one4way, two4way and higher4order factorial designs(with multiple independent variablesand when using analysis of covariance(controlling for an additional variable.


11/24

MANOVA (E"a#$le)

In this example, the dierencebetween males and females on anumber of measures of wellbeing isexplored. These include a measure of

negative mood (#egative "ect scale,positive mood (Positive "ect scaleand perceived stress (Total Perceived

6tress scale.


12/24

MANOVA (E"a#$le)

Resea%ch ques&i'7 0o males andfemales dier in terms of overallwellbeing+ "re males better ad*ustedthan females in terms of their positive

and negative mood states and levelsof perceived stress+

)hat you need7 $ne4way !"#$%"

One categorical, independentvariable (e.g. GENDER); and Tw' '% #'%e c'&iu'us

*e$e*e& +a%ia,les (e.g.

negative aect, positive aect,


13/24

MANOVA (E"a#$le)

!"#$%" can also be extended to two4way and higher4order designsinvolving two or more categorical,independent variables.

-ha& i& *'es7 8ompares two or moregroups in terms of their means on a

group of dependent variables. Teststhe null hypothesis that the populationmeans on a set of dependent variablesdo not vary across dierent levels of a

factor or grouping variable.


14/24

MANOVA Assu#$&i' Tes&i/

Sa#$le sie 9ou need to have more cases in each

cell than you have dependentvariables.

:aving a larger sample can also helpyou -get away with- violations of someof the other assumptions (e.g.

normality. The minimum required number ofcases in each cell in this example isthree giving you the minimum total

sample si;e of /


15/24


N'%#ali&1 "lthough the signi'cance tests of

!"#$%" are based on the multivariatenormal distribution, in practice it is

reasonably robust to modest violationsof normality

"ccording to Tabachnic& and =idell

(>225, p. >3/, a sample si;e of atleast >2 in each cell should ensure-robustness-.


16/24


Ou&lie%s !"#$%" is quite sensitive to outliers

(i.e. data points or scores that aredierent from the remainder of the

scores.

9ou need to chec& for univariate

outliers (for each of the dependentvariables separately and multivariateoutliers.


17/24


Liea%i&1 This assumption refers to the presence

of a straight4line relationship betweeneach pair of your dependent variables.

This can be assessed in a number ofways, the most straight forward ofwhich is to generate a matrix ofscatterplots between each pair of yourvariables, separately for each group(male and female separately in this

example


18/24


Mul&ic'lliea%i&1 a* si/ula%i&1 !"#$%" wor&s best when the

dependent variables are onlymoderately correlated.

)ith low correlations, you shouldconsider running separate univariateanalysis of variance for your variousdependent variables.

)hen the dependent variables are

highly correlated, this is referred to as


19/24


Mul&ic'lliea%i&1 a* si/ula%i&1(c'&.) )hile there are quite sophisticated

ways of chec&ing for multicollinearity,

the simplest way is to run 8orrelationand to chec& the strength of thecorrelations among your dependentvariables.

8orrelations up around .< or .9 arereason for concern. If you nd any ofthese, you may need to consider

removing one of the strongly


20/24


2'#'/eei&1 ' +a%iace4c'+a%iace#a&%ices Test of this assumption is generated as

part of !"#$%" output.

The test used to assess this is ox-s !Test of ?quality of 8ovariance!atrices.


21/24

MANOVA

@un !"#$%" using the data provided.


22/24

MANOVA (Sa#$le %e$'%&)

" one4way between4groups multivariate

analysis of variance was performed toinvestigate sex dierences inpsychological wellbeing. Three

dependent variables were used7 positiveaect, negative aect and perceivedstress. The independent variable wasgender. Preliminary assumption testing

was conducted to chec& fornormality, linearity, univariate andmultivariate outliers, homogeneity ofvariance4covariance

matrices, and multicollinearity, with no


23/24

MANOVA (Sa#$le %e$'%&) (c'&.)

There was a statistically signi'cant

dierence between males and femaleson the combined dependent variables, =(A, B>


24/24

manova and sample report

Documents