1. ANOVA Demo Part 1: Explanation Psy 320 Cal State Northridge Andrew Ainsworth PhD

2. ANOVA works by: Breaking down participants score into parts – If everyone is from the same population to start with (before any treatment is given to them) then they should all start at the same mean – the grand mean

3. Grand Mean Grand Mean Alone

4. ANOVA works by: Then states that any distance the subject’s score is away from the grand mean is “caused” of the group they belong to (i.e. which treatment they received, etc.)…

5. Grand Mean

6. ANOVA works by: Then states that any difference the subject’s score is away from the grand mean is because of the group they belong to (i.e. which treatment they received) Plus some random subject variation

7. Grand Mean

8. ANOVA works by: If this is done for every person then the Effect (Between Group) Variation and the Random (Within Group) Variation together make up the Total Variability of the participants’ scores around the Grand mean

9. Grand Mean

10. The job of an ANOVA is to Separate the Real Variation “caused” by the different levels of the IV from the random (“fake”) Variation that is also present This is sometimes referred to as trying to see the Signal (the real effect) through the Noise (the random variation) The F-test in an ANOVA is often referred to as a signal-to-noise ratio So let’s illustrate the pieces of ANOVA…

11. Grand Mean

12. Total Variability

13. Grand Mean

14. Between Group Variability

15. Grand Mean Between Group Variability

16. Grand Mean Between Group Variability

17. Grand Mean Between Group Variability

18. Grand Mean Between Group Variability

19. Grand Mean Between Group Variability

20. Grand Mean Between Group Variability

21. Grand Mean Between Group Variability

22. Grand Mean Between Group Variability

23. Grand Mean Between Group Variability + Within Group Variability

24. Grand Mean Total = Between Group Variability + Within Group Variability

25. Within Group Variability

29. Grand Mean Between Group (with WG shown): Random Differences Alone

30. Grand Mean Between Group (with WG shown): Real + Random Differences

31. Summary: ANOVA tries to… Identify the size of the Random (Average Within Groups) variance so that we have an idea of how large the randomness is in our data Identify if the Between Groups variance (“caused” by our IV) is large enough for us to believe that it isn’t really just random Indicate whether our BG variance is significantly large (an not just random) when compared to the Random (WG) variance we identified Assess the size of the BG ratio by calculating the BG and WG variances and forming the F-ratio (see Part 2)