Correlation and covariance matrices

August 30, 2015

Many statistical procedures such as the ANOVA family, covariates and multivariate tests rely on either covariance and/or correlation matrices. Statistical assumptions such as Levene’s test for homogeneity of variance, the Box’s M test for homogeneity of variance-covariance matrices, and the assumption of sphericity specifically address the properties of the variance-covariance matrix (also referred to as the covariance matrix, or dispersion matrix). The covariance matrix as shown below indicates the variance of the scores on the diagonal, and the covariance on the [READ MORE]

Data Assumption: Homogeneity of variance-covariance matrices (Multivariate Tests)

October 15, 2013

Very brief description: “Homogeneity of variance-covariance matrices” is the multivariate version of the univariate assumption of Homogeneity of variance and the bivariate assumption of Homoscedasticity. Refer to the post “Homogeneity of variance” for a discussion of equality of variances. In short, homogeneity of variance-covariance matrices concerns the variance-covariance matrices of the multiple dependent measures (such as in MANOVA) for each group. For example, if you have five dependent variables, it tests for five correlations and ten covariances for [READ MORE]

Data Assumption: Homoscedasticity (Bivariate Tests)

September 3, 2013

  Very brief description:   Homoscedasticity is the bivariate version of the univariate assumption of Homogeneity of variance, and the multivariate assumption of Homogeneity of variance-covariance matrices.  Refer to the post “Homogeneity of variance” for a discussion of equality of variances. In short, homoscedasticity suggests that the metric dependent variable(s) have equal levels of variability across a range of either continuous or categorical independent variables.  More specifically, in bivariate analysis such as regression, homoscedasticity means that the variance [READ MORE]

Data Assumption: Homogeneity of variance (Univariate Tests)

August 2, 2013

Very brief description: When comparing groups, their dispersion (variances) on the dependent variable should be relatively equal at each level of the independent (factor or grouping) variable (and neither should their sample sizes vary greatly across the groups). In other words, the dependent variable should exhibit equal levels of variance across the range of groups. Homogeneity of variance is the univariate version of bivariate test of homoscedasticity, and the multivariate assumption of homogeneity of variance-covariance matrices.   Who cares Both t-test and ANOVA are sensitive to [READ MORE]

Data Assumption: Homogeneity of regression slopes (test of parallelism)

July 19, 2013

Very brief description: The dependent variable and any covariate(s) such as in ANCOVA and MANCOVA, should have the same slopes (b-coefficient) across all levels of the categorical grouping variable (factors). In other words, the covariate(s) must be linearly related to the dependent variable. On the other hand, covariate(s) and factors should not be significantly correlated.   Who cares ANCOVA MANCOVA Ordinal regression Probit response models   Why is it important The fact is: when groups differ significantly on the covariate (thus an interaction) then placing the covariate into the [READ MORE]