WEEK 5 - Multiple Group Designs and ANOVA Flashcards
Why more than 2 groups?
In the real world, independent variables can have any number of categories/levels
There are many situations where more than two groups are needed to give us full information about the relationship between IV and DV.
What is a one-way ANOVA
means one IV (for purpose of this week only discussing one independent variable but multiple categories/groups on independent variable)
Often, we know that a difference exists between groups, or that our IV affects DV (benefit of ANOVA –> multiple levels to IV)
➢ e.g., Several studies have shown that football players have poorer cognitive performance than non-contact athletic controls
➢ But this does not tell us why these differences exist
➢ We could seek to separate football players on the basis of the number of head injuries sustained; zero, one, or two +.
➢ Forming multiple groups can help
➢ refine our understanding of how an IV operates on our DV
➢ evaluate dose-response relationships
What are the common relationships between the IV and DV
linear
curved
Quadratic
What is a linear relationship?
where as the Independent variable increases so does the dependent variable
- eg. effect of alcohol consumption on brain cell death
What is a curved relationship?
plateau function.
where the Independent variable increases so does the dependent variable but then it eventually plateaus without much change
- eg. effect of strength training on endurance performance
What is a quadric relationship?
Something that goes up and then goes down again
* eg. effect of anxiety on exam performance
When designing a ANOVA how do you chose the number of levels of your IV?
- determined by type of relationship expected
- linear - at least three points
- curvilinear – even more
When designing a ANOVA how do you chose how far apart should levels be? (this can vary a lot)
- proportionately across spectrum
- eg. Drug dose: 1mg, 4mg, 7mg, 10mg
- Allows for clear examination of levels of the IV
- Of course this only applies to IVs that are actually based on measurement, rather than categories.
least number of categories but sensitive enough to be able to detect what you are looking for
Philosophy of analysis (why cant we just continue to use T-tests)
Why not just use multiple t-tests to test all the possible
group differences?
* These add up very quickly!
* 3 groups: 3 separate t-tests (1&2, 1&3, 2&3)
* 4 groups: 6 separate t-tests (1&2, 1&3, 1&4, 2&3, 2&4, 3&4)
* 5 groups: 10 different comparisons
* 6 groups: 15 comparisons!
Most importantly, our Type 1 error rate would increase
* In each t-test, we are potentially wrong 5% of the time (if we use the typical 0.05 criterion)
* So with multiple t-tests, our actual error rate will be (much) greater than 0.05 – NOT GOOD
What does an Analysis of Variance (ANOVA) tell you?
*Tells you whether a difference exists somewhere among a set of group means
- If you find a significant difference you can follow up which groups differ specifically. These follow up tests will be explored in a later lecture.
Revision what was the basic objective of the independent groups t-test
to determine whether the difference seen between two group means is large enough for us to be reasonably convinced that it is not due to random error or chance
What is multiple differences
When you have more than two groups, we are not just looking at the difference between 2 things.
We are looking at multiple differences. (example, AB, BC, AD etc)
Multiple differences = variance
What is the foundation of ANOVA which is represented by the F ratio?
In an ANOVA we form a statistical ratio similar to the t-test but representing variance between groups rather than just a single difference
𝑭 = 𝑩𝒆𝒕𝒘𝒆𝒆𝒏 − 𝒈𝒓𝒐𝒖𝒑𝒔 𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆 /
𝑾𝒊𝒕𝒉𝒊𝒏 − 𝒈𝒓𝒐𝒖𝒑𝒔 𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆
What does variance between groups (BG) represent in an ANOVA
representing variance due to the effect of IV i.e. the differences between our means of each condition