D. Wayne Mitchell, Ph.D.
Kayla N. Jordan – Statistical Analyst
Rstats Institute
Psychology Department
Missouri State University
Review of Statistical Terms
I.
II.
III.
IV.
Type I Error
Type II Error
Power
Effect Size
Four Common Effect Size Indices
I. (r-squared) r2
II. (omega-squared) ω2
III. (eta-squared) η2
IV. Cohen’s d
Size! Small, Medium, Large?
Cohen’s d = .20; r 2 = .01 (small)
Cohen’s d = .50; r 2 = .06 (medium)
Cohen’s d = .80; r 2 = .14 (large)
I.
Given the correlation result:
(r (98) = .40, p < .05); r2 = .16
II.
Given the t-test result:
(t (22) = 4.16, p < .05)
ω2 = (t2-1)/ (t2 + df +1) = .40
r2 or η2 = t2 / (t2 + df ) = .44
Cohen’s d = 2t / = 1.77
One-Way ANOVA Results:
See Pages 4 and 5
I. Omega-Squared
II. Eta-Squared
III. Glasses Delta
To do a Power Analysis
See Suggestions; Page 7
I.
II.
Have to Estimate an Effect Size
Estimate the Smallest Effect
that You Want to Detect
III. Realize the Complexity of the
Design Requires Study to do
Appropriate Power Analysis
Some Rules of Thumb with
Correlation – Regression
I. N > 50 + 8m (m = # IVs)
II. N > 50 + m (for individual
predictions)
III. The effect one might expect…
rxy = est. rxy √ rxx ryy
Some Needed Formulas
f 2 = eta2 / 1 - eta2
d = Mean1 – Mean2
√ s1 2 + s2 2 / 2