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Lecture 13

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Department
Psychology
Course
PSYC 2002
Professor
Steven Carroll
Semester
Winter

Description
Lecture 13ANOVAs continued We were playing with this example last week... Placebo 1/2 Full 3 7 5 1 5 6 2 6 4 M M M 1 . 2 . = 3 . = = 2 6 5 - The grand mean = M... =  X / N = 39 / 9 = 4.33 Source of Variability SS df MS F Between the Treatment 26.19 2 13.1 13.1 Groups Within the 6 6 1 Treatment Groups Total 32.19 8 - F-crit (2,6;  = .05) = 5.14 Some ANOVAphilosophy - MS within groups is a measure of variability attributable to random error and fluctuations - Let’s use  to symbolize “random error” - Since MS between groups was generated from the same people responsible for the random error, some of MS between is also comprised of random error - But some of MS between can also be explained by the effect of our treatment - Let’s use  to symbolize “the effect of treatment” - F = ( + ) /  - What happens if there is no effect of treatment? - In other words, what happens if  = 0? - F = (  + 0) /  •  /  • 1  Theoretically, this is the lowest possible value for an F score Some ANOVAphilosophy - Consider the followingANOVAconducted on a single factor with only two levels, A& B: - A= {1, 2, 3}, B = {4, 5, 6} Source of Variability SS df MS F Between the Treatment 13.5 1 13.5 13.5 Groups Within the 4 4 1 Treatment Groups Total 17.5 5 Some ANOVAphilosophy - What if we did a t-test on these data? A B SS A = 2, dfA = 2 1 4 SS B df B 2 5 = 2, = 2 3 6 2 MA= 2 MB = 5 SP = 1 S( M 1 - M 2 ) = .8165 tobserved = - 3.67 - Just for fun, square the t-observed - t² = 3.67² = 13.5 = F Some ANOVAphilosophy - t² = F - t (∞) = Z - So all of the tests are related to one another: • To fully understandANOVA, you have to understand t • To fully understand t, you have to understand z • To fully understand z, you have to understand variance, SS, and p-values Afew more things: proportions of variance accounted for - This is actually much less complicated than it was for the t-test where r² = t² / (t² + df) - η² = explained variability / total variability - What is our measure of explained variability? - What is our measure of total variability? Afew more things: proportions of variance accounted for - η² = SS between / SS total - calculate η² for our example: Source of Variability SS df MS F Between the Treatment 26.19 2 13.1 13.1 Groups Within the 6 6 1 Treatment Groups Total 32.19 8 - 26.19 / 32.19 = .81 Afew more things: post hoc tests - Asuccessful ANOVAlets you reject H 0 and conclude “at least two of the factor level means differ from one another” - But which ones differ? - If your ANOVAonly has 2 factor levels, you don’t have to worry about this. - Why? Post hoc test: error - Basically, you do a series of t-tests (or
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