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What does equality of variance mean?
Equal variances (homoscedasticity) is when the variances are approximately the same across the samples. If you are comparing two or more sample means, as in the 2-Sample t-test and ANOVA, a significantly different variance could overshadow the differences between means and lead to incorrect conclusions.
What is equality of variance in t tests?
When running a two-sample equal-variance t-test, the basic assumptions are that the distributions of the two populations are normal, and that the variances of the two distributions are the same.
How to define multivariate variances and covariances?
Let’s talk a little bit about multivariate variances and covariance. So we’re going to define for random vector X the variance of the random Vector X, which says N by one is going to be the expected value of the outer product of X minus mu. With it self so where here mu is equal to the expected value of the, it’s the vector expected value of x.
Which is an example of a multivariate analysis?
For example, three groups (e.g., mood disorders, schizophrenics, and no history of a mental disorder) can be compared on a battery of six personality scales using a MANOVA. Similar to the factorial ANOVA, MANOVA can also be extended to incorporate more than one factor.
Can a variance be equal to a mean?
The variance has nice properties, not unlike the mean. It would be nice if the variance was a linear operator but it’s not. So we cannot say, for example, that variance of x + y is equal to the variance of x + the variance of y. So we cannot say that unless the vectors x and y are mutually independent.
How is MANOVA used in the analysis of variance?
MANOVA can be introduced as the obvious generalization of the analysis of variance (ANOVA) from a single to several outcome variables. In MANOVA, the vectors of outcome variables are assumed to have (possibly distinct) H -variate normal distributions in the categories or groups k = 1,…, K.