Philosophy and Methodology of Psychology
Philosophy and Methodology of Psychology
Factor Analysis Theory and Statistical PrinciplesIntroduction to Factor Analysis and general statistical principles in the context of psychology. The presentation is made by James Collett from RMIT University.
Learning Objectives
Error Variance: Understand what error variance is and the distinctions between Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA).
Traits and States: Learn the theoretical backgrounds of traits and states, and how they influence factor analysis methods.
Null Hypothesis Testing: Grasp the principles of null-hypothesis significance testing and its implications in psychological research.
Statistical Tests: Distinguish between parametric and non-parametric statistical tests.
Managing Variance
Error Variance
Error variance is the statistical noise that affects measurements.
According to McCall (1939), when we measure constructs, we measure both what we want (the true construct) and factors we do not want, such as time of day, fatigue, and randomness.
These unwanted influences contribute to error variance.
Component Analysis
Alongside EFA, principal component analysis (PCA) is widely used to reduce data dimensions.
PCA’s aim is to simplify multiple variables into manageable composites, but it is theoretically inappropriate for vague psychological constructs, failing to account for error variance.
Misuse in psychology is common; hence it should generally be avoided.
Theoretical Pathways in Factor and Component Analysis
Factor Analysis
Factor analysis involves the relationship between items and an underlying factor, aiming to reveal common sources affecting responses.
Component Analysis
In contrast, all variance is assumed to form composites that aggregate without discernment of underlying factors.
Error Variance
Component Analysis
Component analysis encompasses all variance in the composite, covering the entire spectrum shown in data outputs.
Factor Analysis
EFA recognizes that only the shared variance (within marked areas) highlights common underlying factors.
Factor Analysis Methods
Exploratory Factor Analysis (EFA): Utilized to reveal patterns in the data without prior hypotheses.
Confirmatory Factor Analysis (CFA): Tests hypotheses regarding the influence of known constructs, suited for data already structured by hypotheses.
Note: EFA can validate hypotheses, while CFA may be used to explore data patterns.
Outputs in Factor Analysis
EFA Output Example
Each item shows its correlation with different factors, indicating how strongly each item relates to the underlying constructs measured within the dataset, with specific correlation values assigned to each item against factors.
CFA Output
Instruction specifies that only EFA training will occur in this course.
Ipsatisation
Ipsatisation controls error variance by normalizing individual responses, suggesting that perceptions of response scales could interfere with trait evaluation.
While it may reduce useful variance, retaining the natural perception of scales is vital.
Null Hypothesis Significance Testing
Drawing Inferences in Statistics
Tests whether observed data effects arise from the same sample distribution as data with no effect.
A small p-value (e.g., p < .05) leads to rejecting the null hypothesis, suggesting significant findings.
Challenges with Significance Testing
The influence of sample size (N) can bias results towards lower p-values, hence overstating effects.
Assumptions underpinning significance tests assume normal distributions and equal variances, complicating results when assumptions are violated.
Coping with Assumptions Violations
When faced with messy data, options include:
Proceeding with original tests and qualifying findings in discussions.
Transforming distributions while weighing implications of modifying data.
Identifying alternate tests with suitable assumptions.
Optimal Solutions
Perform analyses in both raw and adjusted formats reflecting assumption violations to observe their effects.
Report adjusted data only when findings substantially differ.
Significance Controversy
There’s a shift away from rigid null-hypothesis significance testing towards confidence intervals and effect size metrics (e.g., Cohen’s d).
Reporting trends in data strength and direction generates debate regarding its utility.
Non-Parametric Tests
Overview
Utilized for small samples or non-metric variables, these tests do not depend on parametric test assumptions.
They may not provide as rich results as parametric tests but are essential when appropriate.
Selection of Non-Parametric Tests
Key tests include:
Chi-square Test: Compares proportions across categorical groups.
Mann-Whitney U Test: Compares two categorical groups based on metric/ordinal variables.
Kruskal-Wallis H Test: Extends the Mann-Whitney for three or more groups, resembling ANOVA but for non-parametric data.
Spearman’s Rank-order Correlation: Used for ordinal or non-normal metric data.
Two-way Contingency Tables: Evaluates relationships among multiple categorical variables.
Thank You and Goodbye
Looking forward to the next session to continue deepening understanding of these concepts.