ANOVA Demo Part 1: Explanation
description
Transcript of ANOVA Demo Part 1: Explanation
![Page 1: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/1.jpg)
ANOVA DemoPart 1: Explanation
Psy 320Cal State Northridge
Andrew Ainsworth PhD
![Page 2: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/2.jpg)
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
i GMY Y
![Page 3: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/3.jpg)
Grand Mean
Grand Mean Alone
![Page 4: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/4.jpg)
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.)…
i GM IVY Y Effect
![Page 5: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/5.jpg)
Grand Mean
1X 2X 3X
![Page 6: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/6.jpg)
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
i GM IVY Y Effect Random
![Page 7: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/7.jpg)
Grand Mean
1X 2X 3X
![Page 8: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/8.jpg)
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
![Page 9: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/9.jpg)
Grand Mean
1X 2X 3X
![Page 10: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/10.jpg)
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…
![Page 11: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/11.jpg)
Grand Mean
![Page 12: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/12.jpg)
Grand Mean
Total Variability
![Page 13: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/13.jpg)
Grand Mean1X
2X
3X
![Page 14: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/14.jpg)
Grand Mean1X
2X
3X
Between Group Variability
![Page 15: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/15.jpg)
Grand Mean1X
2X
3X
Between Group Variability
![Page 16: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/16.jpg)
Grand Mean1X
2X
3X
Between Group Variability
![Page 17: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/17.jpg)
Grand Mean1X
2X
3X
Between Group Variability
![Page 18: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/18.jpg)
Grand Mean1X
2X
3X
Between Group Variability
![Page 19: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/19.jpg)
Grand Mean1X
2X
3X
Between Group Variability
![Page 20: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/20.jpg)
Grand Mean1X
2X
3X
Between Group Variability
![Page 21: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/21.jpg)
Grand Mean1X
2X
3X
Between Group Variability
![Page 22: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/22.jpg)
Grand Mean1X
2X
3X
Between Group Variability
![Page 23: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/23.jpg)
Grand Mean1X
2X
3X
Between Group Variability + Within Group Variability
![Page 24: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/24.jpg)
Grand Mean1X
2X
3X
Total = Between Group Variability + Within Group Variability
![Page 25: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/25.jpg)
Within Group Variability
![Page 26: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/26.jpg)
Within Group Variability
![Page 27: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/27.jpg)
Within Group Variability
![Page 28: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/28.jpg)
Within Group Variability
![Page 29: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/29.jpg)
Grand Mean
Between Group (with WG shown): Random Differences Alone
![Page 30: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/30.jpg)
Grand Mean
Between Group (with WG shown): Real + Random Differences
![Page 31: ANOVA Demo Part 1: Explanation](https://reader036.fdocuments.net/reader036/viewer/2022062314/56814320550346895daf897e/html5/thumbnails/31.jpg)
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)