PSYC3010 comprehensive lecture notes (Psychology Research Methodology III)
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Course
PSYC3010 (PSYC3010)
Institution
University Of Queensland (UQ
)
Comprehensive notes covering all lecture contents for third year psychological statistical research PSYC3010. A summary of lecture notes, tutorials and consultations, including common mistakes, lecturer's remarks and tips from previous exam observations.
Multivariate analysis of variance (MANOVA) ................................................................ 58
Pros and cons of within-participants designs:............................................................... 59
, Week 2 - factorial between-Ps ANOVA I: Omnibus tests
Important concepts:
✓ Three omnibus tests (2 main effects and interactions)
✓ Sources of variances in one-way & two-way ANOVA
✓ how F-ratio is calculated
✓ structural model of one-way & two-way ANOVA
Analysis of Variance (ANOVA)
- it is the partitioning of variables
- it compares 2/more conditions to test an association between variables
- it is an Omnibus test/technique
- Test statistic = F-ratio
Variance:
The dispersion or spread of scores around a point of central tendency (the mean)
—> how spread out are the scores when compared to the mean?
Error variance: Treatment variance:
- Due to random/unmeasured - Systematic differences due to the
influences manipulation of IV
- X be explained - can be explained
- Within-group variance - Between-group variance
One-way ANOVA
Source of variance:
Total variation
Between-group variation Within-group variation
Systematic variance due to membership in Error variance due to random chance /
different groups/treatment X unmeasured influences
n ∑(̅̅̅̅ ̅. )²
𝑋𝑗 + 𝑋 ∑(𝑋𝑖𝑗 + 𝑋̅𝑗 )²
, Hypothesis testing for one-way ANOVA
Hypotheses for 2 means
- Statistical Hypotheses
- 𝐻0 : 𝜇1 = 𝜇2
- 𝐻1 : 𝜇𝑗 ≠ 𝜇.
- Conceptual Hypotheses
- Null hypothesis: no differences between treatment means
- Alternative hypothesis: difference between treatment means
Hypotheses for 3+ means
- Statistical Hypotheses
- 𝐻0 : 𝜇1 = 𝜇2 = 𝜇3 = ⋯ 𝜇𝑗 𝜇𝑗 = mean of
- 𝐻1 : 𝜇𝑗 ≠ 𝜇. group j
- Conceptual Hypotheses 𝜇. = grand mean
- Null hypothesis: no differences between treatment means
- Alternative hypothesis: difference between treatment means
How to Calculate F-ratio?
Sum of Squares (SS):
- A measure of variability
Treatment sum of squares: 𝑆𝑆𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 or 𝑆𝑆𝑚𝑜𝑑𝑒𝑙 or 𝑆𝑆𝑏𝑒𝑡𝑤𝑒𝑒𝑛
- between-groups variability
- How much each group mean varies from the grand mean
Error sum of squares: 𝑆𝑆𝑒𝑟𝑟𝑜𝑟 or 𝑆𝑆𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 or 𝑆𝑆𝑤𝑖𝑡ℎ𝑖𝑛
- within-groups variability
- How much do individual scores in each group vary from that group’s mean
Mean squares (MS):
- An index/measure of variability among sample statistics
- We calculate mean squares to estimate:
- Between-groups variance: 𝑀𝑆𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡
- Within-groups variance: 𝑀𝑆𝑒𝑟𝑟𝑜𝑟
- is roughly equivalent to 𝑠 2 (sample variance) in a t-test
- is a good estimate of 𝜎𝑒2 (population variance)
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