PSY248 Lecture Notes - Lecture 7: Effect Size, Mean Absolute Difference, Orthogonal Polynomials
2 Jun 2018
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PSY248 Week 7: Trend Analysis and Power
Trend analysis
• Orthogonal polynomials
• IV must vary qualitatively and quantitatively
Example of trend analysis
• IV = blood and alcohol content
• DV = driving performance
o 4 levels of BAC → .00, .03, .06, .09
• Means:
o
o
o
o
• Get the coefficients from orthogonal polynomial tables provided the distances
between the levels of the IV are equal
• = (-3 → 80
• - + (
• = (
• = 11 x 8/20 → 3520
• = 3520/500 → 7.04
• If post-hoc test: = 2.82
o Scheffe: 3 x 2.84 = 8.52
• If planned test:
= 6.24 (if
Decision-wise error rate (DER) – look at ANOVA notes
• Hays procedure/decision rule
• Type 1 error rate not adjusted
• Use only for orthogonal comparisons
Post hoc vs. planned
• EER (post hoc) → overall test conducted first, then use Scheffe tests for
contrasts
• EER (planned) → no overall test conducted, Bonferroni tests for contrasts
• DER (planned) → no overall test conducted, Hays tests for orthogonal
contrasts
• DER (post hoc) → not covering this in the course (but it is called Rodger)
Confidence interval vs. hypothesis testing
• Single mean hypothesis test:
• Single mean confidence interval: +/- t
• Obtaining standard error
o 1. Based on separate variance → =
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