8/9/10: ANOVA & ANCOVA

Question 1

ANOVA + assumptions

Answer 1

Analysis of Variance: compares means based on categorical independent variables and assesses the impact on a continuous dependent variable
Assumptions are:
- independent,
- deviations from the group means follow a normal distribution
- group variances to be equal.

if normality is voilated then -> GLM
Example: comparing the average test scores (continuous dependent variable) of students from different teaching methods (categorical independent variable: method A, B, or C).

Question 2

Factorial ANOVA

Answer 2

method used to examine the effects of two or more independent categorical variables (factors) on a continuous dependent variable (so also two way anova: two independent categorical variables on a continuous dependent variable & multiway anova two or more indepentent catagorical variables)

Example: Diet type (categorical) and exercise intensity (categorical) affect weight loss (continuous), with no need to control for other variables.

Question 3

ANCOVA

Answer 3

Detects differences in means of two or more independent catagorical groups while controlling for one or more continuous covariates, which could influence the continuous dependent variable
ANCOVA is multiple linear regression (assumtion normality and continous data)

Independent Variable: Teaching methods (2 or more groups)
Covariate: Prior knowledge (continuous)
Dependent Variable: Student performance (final exam scores - continuous)

ANCOVA will adjust for differences in pre-test scores (covariate) to better isolate the effect of the teaching methods on the final test scores. This ensures that any differences in final test scores are due to the teaching methods rather than variations in students’ prior knowledge.

Question 4

Before analysing ANOVA/ANCOVA

Answer 4

• check assumptions (independent,normality)
  1. Omnibus test to see if there is any difference at all between the group means (it tests the H0 that all group means are equal)-> if significant then there is a difference somewhere and to clarify which ones…
  2. Post Hoc test to see which groups differ
  Protects against false positives as withholds you looking at induvidual p-values when there is no significant overal difference

If Omnibus is negative then means there is no difference found between groups so why look any further?
The post hoc is often applied with multiple testing correction to adjust Type I errors

Question 5

F-statistic two meanings

Answer 5

1. In regression analysis: A large F-statistic value proves that the regression model is effective in explaining the variance; significant result, then whatever coefficients you included in your model improved the model’s fit -> model significant
2. in ANOVA: The larger the difference in group means the more they vary and the greater the F-value -> supporting evidence against the H0 meaning there is a difference

Regression: models prediction significantly explain the the variance
Anova: indicates there are significant differences between group means

Question 6

Interactions

Answer 6

• Two-Way ANOVA handles interactions between two factors.
• Multi-Way & factorial ANOVA can assess interactions between two or more factors
• ANCOVA: Can assess interactions between covariates

Depending on your data and research question you choose the model.

Question 7

interaction in regression table

Answer 7

if at least one slope differs significantly from another, then not all slopes are equal and there is an interaction. This is the case because slope A differs significantly from b -> look at p value

Question 8

can anova and ancova always be used?

Answer 8

No, only when the data is continous and normaly distributed as poisson and binomial do not posses these assumtions they need an GLM instead

Question 9

Name the data sorts of the groups

Answer 9

1. one way anova: one catagorical indepentent variable + one continuous dependent variable
2. two way/multiway/factorial anova: two or more categorical independent variables + one continous depentent variable
3. ANCOVA: two or more categorical independent variables + one continous dependent variabel + one or more continous covariates