What is analysis of covariance?
Analysis of covariance (ANCOVA) is a method for comparing sets of data that consist of two variables (treatment and effect, with the effect variable being called the “variate”) when a third variable (called the “covariate”) exists. This covariate can be measured but not controlled and has a definite effect on the variable of interest.
What is an interaction with a covariate?
This situation is analogous to an interaction between two or more factors. In ANCOVA, interactions involving the covariate suggest that the nature of the relationship between the response and the covariate differs between the levels of the categorical treatment.
How are covariate ranges adjusted to account for differences in response?
Similar covariate ranges Adjustments made to the response means in an attempt to statistically account for differences in the covariate involve predicting mean response values along displaced linear relationships between the overall response and covariate variables (see Figure d above).
How to calculate covariance from the slope of the regression line?
If the slope of the treatment regression lines is y = 1, analysis of covariance and analysis of variance on Y – X are essentially equivalent. When y = 1, covariance model (22.2) becomes: Yij = fJ.,. Li + Xij +
When to use regression for covariance analysis in unbalanced studies?
For notational simplicity, we consider the case where the treatment sample size is the same for all treatments. However, the regression approach to covariance analysis is general and applies directly when the study is unbalanced, with unequal treatment sample sizes. Covariance Model for Two-Factor Studies
How to state the regression model equivalent to Covariance Model?
State the regression model equivalent to covariance model (22.3) for this case; use 1, -1,0 indicator variables. Also state the reduced regression model for testing for treatmentetfects. c. Fit the full and reduced regression models and test for treatment effects: use a = .OS. State the alternatives, decision mle, and conclusion.