MANOVA

MANOVA (Multivariate Analysis of Variance) 

(MANOVA) is an extension of analysis of variance (ANOVA) which ANOVA used only single 

dependent variable but with MANOVA more than one dependent variables. 

MANOVA also provide the univariate result which can be shown separately to compare the groups

and also indicate the significance different between mean groups.

It can reduce the chance of getting type 1 error if ANOVA is being used repeatedly to perform the

analysis like MANOVA did.

•To ↓ the type 1 error, alpha value ( usually .05) should be ÷ 3 = .017 .

• This is to put a cut – off value to show that it is statistically significant between the groups value

Assumptions

1.Sample Size 

The sample size need to be larger than the dependent variables. 

2.Normality

It can be divide into two which is multivariate and univariate. 

Usually MANOVA will used the multivariate analysis that represent the Mahalanobis distances. 

For the univariate, usually they will used this analysis when they have lack of sample size on their study. 

In this assumption, it also will help to identify any outliers on the data.

3.Outliers

The outliers actually can be describe as the strange or unusual number combination on the data such as very high or very low between the number

4.Homogeneity of regression

•Only important if you are intending to perform stepdown analysis

•This approach is used when you have some theoretical or conceptual reason for ordering your dependent variables

• Complex procedure

5.Multicollinearity and singularity

•MANOVA works best when DV are moderately correlated

•So you need to check the correlation!

•Need to consider removing one of the strongly correlated pairs of DV

•Strongly correlate when correlations up to 0.8 to 0.9

6.Homogeneity of variance-covariance matrices

•Generated as part of MANOVA output

•Test used is Box’s M Test of Equality of Covariance Matrices

How to write the results 

•There was a statistically significant difference between males and females on the combined dependent variables , F(3, 428)= 3.57, P=.014; Wilks’ Lambda = .98; partial eta squared =.02

•Considering the dependent variables separately , the only difference to observe statistically significance is by using Bonferroni , by adjusting the alpha level of .017 , the result was perceived stress , F ( 1, 430) = 8.34, p=.004 partial eta squared = .02

•Observation of mean score showed that female showed slight higher level s of perceive d stress  ( M= 27.42, SD = 6.08) than males ( M= 25.79, SD =5.41)

BY:

Nurulain Parlan