WK3: ONE-WAY WITHIN-SUBJECTS ANOVA
SPSS Steps and Output
Terms
Guidelines to Note
Specifically One-way Within Subjects ANOVA
What is One-way Within ANOVA?
Sphericity Assumption (Mauchly's)
Trend Analysis
Partial Eta-squared
Effect Size for Trend Analysis (r alerting)
Key Difference in Between and Within
VS.
Paired Samples T-Test
One-way Within Subjects
More conventional if just 2
Compares only 2 means
Compares 3 or more means
Could handle 2 means, but leave it to t-test
Similar as both share the same within-subject design
Purpose
Solution: Use line graph plotting (bar is for between)
Coefficient of Orthogonal Polynomials (same weightings as contrast coefficient table)
No Cohen's guidelines for Partial Eta-squared (within), unlike Eta-squared (between)
Linear Effect
Quadratic Effect
Trend Analysis
Effect Size (r alerting)
Same group, provide data multiple times
click to edit
Test for significant difference between 3 or more related sample means
Using Multiple Comparisons in Within (limited)
4 Means++: Bonferroni only
One of the options: Sidak
3 Means: Fisher's LSD
Between: Difference in variability
Within: Correlation with time 1 and 2 data = reduce standard error of the differences between 2 means (correlation of area)
Test of Sphericity Assumption
Huynh-Feldt > Greenhouse-Geiser (use if Sphericity is violated)
Epsilon (Unit of measurement for Sphericity .00 - 1.0)
Easily affected by sample size > impacts power > increases chance of violating assumption
If Violated Use
P > .05 is ideal (satisfied)
Often violated (Longer time period > Lesser common / correlation)
Trend Analysis
Advantages
Assumes means follow a particular pattern (e.g. linear / quadratic)
Usefulness
✅ Only one statistical test = more powerful as lesser analysis
❎ Better than running multiple post-hoc tests = increase Type 1 Error
Commonly Tested Patterns
✅ Useful: When time variable have an obvious order to it (e.g. pre-test, post test, no. of exposures)
❎ Not Useful: for randomised order / efficacy of drug A, B and C
Linear Effect (linear increase, can be upward / downward trend)
Quadratic Effect (one bend, can be upward / downward)
Same as Contrast Analysis but for Within-subjects than Between
Effect Size: r alerting (correlation between contrast weightings and observed means)
Huynh-Feldt (recommended)
Greenhouse-Geiser (more conservative)
Lvl 3 Linear (-1, 0, 1)
Lvl 3 Quadratic (1, -2, 1)
Weightings = 0
Related Sample Means
Contains same group of individuals providing data on multiple occasions (repeated-measures).
Each individual in one sample is connected or linked with one specific individual in each other sample (matched design)