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ANOVA Demo Part 1: Explanation

ANOVA Demo Part 1: Explanation. Psy 320 Cal State Northridge Andrew Ainsworth PhD. ANOVA works by:. Breaking down participants score into parts

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ANOVA Demo Part 1: Explanation

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  1. ANOVA DemoPart 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 Alone Grand Mean

  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 Grand Mean

  13. Grand Mean

  14. Between Group Variability Grand Mean

  15. Between Group Variability Grand Mean

  16. Between Group Variability Grand Mean

  17. Between Group Variability Grand Mean

  18. Between Group Variability Grand Mean

  19. Between Group Variability Grand Mean

  20. Between Group Variability Grand Mean

  21. Between Group Variability Grand Mean

  22. Between Group Variability Grand Mean

  23. Between Group Variability + Within Group Variability Grand Mean

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

  25. Within Group Variability

  26. Within Group Variability

  27. Within Group Variability

  28. Within Group Variability

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

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

  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)

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