MANOVA in SPSS for Beginner's| Pillai's Trace, Hotelling's T-sq, Roy's Largest Root, Wilk's Lambda

3.MANOVA, or Multivariate Analysis of Variance, is a statistical technique used to analyze the differences between groups in multiple dependent variables simultaneously. It is a more powerful version of ANOVA (Analysis of Variance), which only allows for the analysis of one dependent variable at a time.
Assumptions of MANOVA:
1. Normality: The dependent variables should be normally distributed within each group.
2. Homogeneity of variance-covariance matrices: The variance-covariance matrices of the dependent variables should be equal across all groups.
3. Linearity: There should be a linear relationship between the dependent variables and the independent variables.
4. Independence: The observations should be independent of each other.
Multivariate Statistics:
Pillai's Trace is one of the multivariate statistics used in MANOVA. It is a measure of the overall effect of the independent variable(s) on the dependent variables, and it ranges from 0 to 1. A value of 0 indicates no effect, while a value of 1 indicates a perfect effect. It is a robust statistic and is not affected by violations of the assumption of equal covariance matrices. However, it can be sensitive to violations of normality and can be influenced by sample size.
Other multivariate statistics used in MANOVA include Wilks' Lambda, Hotelling's T-squared, and Roy's Largest Root. Wilks' Lambda is similar to Pillai's Trace, but it is affected by violations of the assumption of equal covariance matrices. Hotelling's T-squared is a measure of the distance between group means in multivariate space. Roy's Largest Root is a measure of the largest difference between group means in any direction.
It is important to interpret the results of MANOVA in conjunction with other statistical tests, such as ANOVA, to understand the effects of the independent variable(s) on each individual dependent variable. Additionally, it is important to check for violations of the assumptions of MANOVA, and if these assumptions are violated, alternative methods such as the Welch test or robust methods may be more appropriate.

[@neerajamenon6213]

Sir can you please create a video on rau's u test

[@theoutlier7395]

Will do Thanks