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WK3: ONE-WAY WITHIN-SUBJECTS ANOVA (Terms (Trend Analysis (Linear Effect,…
WK3: ONE-WAY WITHIN-SUBJECTS ANOVA
SPSS Steps and Output
Terms
Sphericity Assumption (Mauchly's)
Trend Analysis
Linear Effect
Quadratic Effect
Partial Eta-squared
Effect Size for Trend Analysis (r alerting)
Huynh-Feldt > Greenhouse-Geiser
(use if Sphericity is violated)
Epsilon
(Unit of measurement for Sphericity .00 - 1.0)
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)
Guidelines to Note
Solution:
Use
line graph
plotting (bar is for between)
Coefficient of Orthogonal Polynomials
(same weightings as contrast coefficient table)
Lvl 3 Linear (-1, 0, 1)
Lvl 3 Quadratic (1, -2, 1)
No Cohen's guidelines for Partial Eta-squared (
within), unlike Eta-squared (between)
Weightings
= 0
Specifically One-way Within Subjects ANOVA
Trend Analysis
Effect Size (r alerting)
What is One-way Within ANOVA?
Key Difference in Between and Within
Between:
Difference in variability
Within:
Correlation with time 1 and 2 data =
reduce standard error
of the
differences between 2 means
(correlation of area)
VS.
Paired Samples T-Test
More conventional if just 2
Compares only
2 means
One-way Within Subjects
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
Same group, provide data multiple times
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
Test of Sphericity Assumption
Easily affected by
sample size
> impacts
power
>
increases chance of violating assumption
If Violated Use
Huynh-Feldt (recommended)
Greenhouse-Geiser (more conservative)
P > .05 is ideal (satisfied)
Often violated
(Longer time period > Lesser common / correlation)
Trend Analysis
Advantages
:check: Only
one statistical test
= more powerful as lesser analysis
:green_cross: Better than running
multiple post-hoc tests
=
increase Type 1 Error
Assumes
means follow a particular pattern
(e.g. linear / quadratic)
Usefulness
:check:
Useful:
When time variable have an
obvious order
to it (e.g. pre-test, post test, no. of exposures)
:green_cross:
Not Useful:
for
randomised order
/ efficacy of drug A, B and C
Commonly Tested Patterns
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
)