What are ANOVA, ANCOVA how it differences?

Let’s start with the name that simply tell how it works and differences before we getting into detail

AN — Analysis
O — Of
VA — Variance
COVA — Covariance : refers to the measure of how two random variables will change when they are compared to each other (1).
- positive covariance (1–1)means that asset returns move together
- negative covariance (1–2)means they move inversely.
Limitation is the magnitude is unbounded, and hard to interpret. Thus normalisation [-1,+1] called Correlation(2)

(1) Covariance

(1–1) positive covariance

(1–2) negative covariance

(2) Correlation coef

(M — Multivariate : including more than one observation. It may also mean solving problems where more than one dependent variable is analyzed simultaneously with other variables.)

ANOVA — Analysis of Variance

• tests three or more groups for mean differences based on a continuous interval with reflects with dependent variable
• There are 2 types of ANOVA : only difference is the number of (Factors) independent variables
  1. One way ANOVA — One Factor reflects Response(dependent variable)
  2. Two way ANOVA — Two Factors reflects Response(dependent variable)

ANCOVA — Analysis of Covariance

• “C stands for Covariance”
• analyse the influence of an independent variable on a dependent variable while removing the effect of the covariate factor.