Conceptual model : An Example
Observation in ANOVA
Conceptual Model: Hypothesis
Conceptual: Model Parameter
Assumptions of MANOVA
- Population covariance are equal.
- Errors are normally distributed.
- Errors are iid.
- Sensitivity of outliers.
Test of Equality of Population Covariance's : Box M Test
What is Spooled variance
Box M text
- Roy’s greatest characteristics root: It is most appropriate when the dependent variables are strongly interrelated. But it is also a measure most likely to be severely affected by violation of the assumption.
- Wilk’s lambda: While Roy is based on first discriminant function, Wilks lambda considers all discriminant function. That is it examines whether the groups are somehow different.
- Pillai criterion and Hoteling's T-square: It is similar to Wilks lambda.
- The effects of several independent variables or treatments rather than using only one single treatment. This capability is primary distinction between MANOVA and discriminant Analysis.
- An analysis with two or more treatments is called factorial design.
Covariate analysis purpose:
- To eliminate systematic error outside the control of researcher that can bias the result.
Over all MANOVA
- # Box M test package biotools
- # Correlation matrix : you want various measurement to be higly correlated it will-
- # give you more power if they are correlated and less if they are not. #However they cannot be perfectly correlated.
- summary(model1,test = "Wilks")
- summary(model1,test = "Roy")
- summary(model1,test = "Hotelling-Lawley")
- #Post hoc
- Different between ANOVA and MANOVA ?
- What are the assumptions of ANOVA?
- What is the test for covariance?
- Name few statistical test in MANCOVA?
- Difference between Roy’s and Wilks test?
- What is box M test?
- What is Factorial Analysis?
- What is Covariate Analysis?