PSY248 Lecture Notes - Lecture 5: F-Distribution, Family-Wise Error Rate, Type I And Type Ii Errors
2 Jun 2018
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PSY248 Week 5: One Way ANOVA
ANOVA = analysis of variance
• Experimental and quasi-experimental research designs
• There is manipulation of an independent variable
• A single-factor design
o Factor as an independent variable
• Between-subjects design (different observations) or within subjects design
• Why not use multiple t-tests?
o Some of the t-tests you will determine sufficiently unlikely – may be
different for each t-test results
o Control of the type 1 error rate (alpha) → this is when we reject the
null hypothesis that is actually true
o Doing multiple t-tests will address our RQ, but will make us lose
control of our definition of sufficiently unlikely, which is the
acceptable number of times that we reject the null hypothesis that is
true
• Experiment-wise error rate
• Tha ANOVA model:
o X(ij) = U+T(j) + E(ij)
o X = score
o i = observation
o j = condition
o U = grand population mean (constant)
o T with j = effect parameter (reflects differences between conditions)
o E = error component (differences between scores within conditions)
• Statistical error = difference between observation within different conditions
• From the equation, we can create definitions of an effect
o E.g. T(j) = U(j) – U
o E(ij) = X(ij) – U(j)
Partitioning the variance:
• Given T(j) = U(j) – UandE(ij) = X – u(j)
• THEN
o (X(ij)-U) = (U(j) – U) + (X(ij) – U(j))
• Representation of bracket terms
o (X(ij)-U) → asking any observation in any condition, why is your
value not the same as the population mean (total variance)
o (U(j) – U) → does not involve individual observation, it involves
asking the population mean of a condition, whether it differs from the
grand population mean (between conditions)
o (X(ij) – U(j) → why is your value not equal to the population mean
that you are in (within conditions)
• Is the model calculable?
o No – it assumes we know the value of U and the j’s
o We have estimates from these (our sample)
o Rewrite the model as something that is calculable → (X(ij) – Xbar
(grand)) = (Xbar(j) – Xbar(grand)) + (X(ij) – Xbar(j))
o Xbar = sample mean, Xbargrand = grand population mean
find more resources at oneclass.com
find more resources at oneclass.com
