ANCOVA

Question 1

Ancova Overview

Answer 1

ANCOVA investigates interactions between treatment / categorical and continuous explanatory variables

y= u + X (categorical) + A (continuous)

Analyses involves ANOVA and regression

The continuous variable is often considered a co-variante -> statistics used to udnerstand whether co-variant is effecting conclusion reached about the effect of treatments on response variable.

Question 2

Method

Answer 2

ANOVA:
- Anova is used to see if a significant amount of variation is explained by the regression (continuous variable) and factor (cateogrical variable).

Factor SSA r-1 MSA MSE/S^2
**regression **SSR 1 MSR MSR/S^2
Error SSE n-r-1 S^2
**total **SST n-1

Regression
- Calculate the gradient for the 2 slopes and use a T test to see if they are significant different (if there are covariante analyses is inconclusive)
- Fit common slope by carrying out calculations involving sums of squares of product. -> can calc SE
- Calculate the intercept for each treatment -> can calc SE for each intercept -> can carry out T test to see if significantly different using SE of difference

Assess the intercepts -> do they give different relationship between factor and response when considering continuous variable compared to when not considering continuous variable

Question 3

Philosophy of statistical modelling

Answer 3

• fit most complex model and then simplify
• Simplify until get minimum adequate model to describe your data

Two rounds of modelling
i. Interaction between categorical treatment and continuous covariate is tested for significance by testing whether regression slopes were significantly different
ii. If no interaction then interaction term is dropped from model and treatment effect is tested
ii. If there is an interaction, term cannot be dropped and main effects cannot be analysed.

Question 4

Covariant

Answer 4

Numerical confounding variables = covariate

Question 5

Assumptions

Answer 5

• Random and independent sampling.
• Linear relationship between the continuous explanatory and the response.
• Constant variance across the data
• Normal distribution of the response variable within groups