Homoscedasticity and homogeneity of effect-sizes assumptions are popular with regression analysis and Anova respectively.These assumptions create lot of confusion at least in my mind. I am not clear about particularly homoscdasticity and how it is different from homogeneity assumption for Anova ?
I disagree with every answer here. Homogeneity of variance means similar variance among grouped scatterplots. Homoscadasticity is a normal distribution occurring for each point on the x-axis (predictor variable) thus there must be a similar kurtosis across every point of the predictor variable which may seem like homogeneity of variance, but it is not the same thing.
(Note: by "homogeneity", I assume you mean "homogeneity of variance".)
They are, in essence, two different names for the same assumption, which might be called in more colloquial English "constant variance of the errors" (of course, in practice we do not have access to the true errors, only the residuals, which are what we actually check). The term "homogeneity of variance" is traditionally used in the ANOVA context, and "homoscedasticity" is used more commonly in the regression context. But they both mean that the variance of the residuals is the same everywhere.
If you are having trouble understanding homo- / heteroscedasticity, I have several posts about the topic that may be helpful for you:
- How to understand what homoscedasticity is, and check for heteroscedasticity: What does having "constant variance" in a linear regression model mean?
- The effect of heteroscedasticity on statistical power: Efficiency of beta estimates with heteroscedasticty
- Possible alternative strategies when you have heteroscedasticity: Alternatives to one-way ANOVA for heteroscedastic data