Podcast
Questions and Answers
What is a key indicator that a retained factor is meaningful in PCA?
What is a key indicator that a retained factor is meaningful in PCA?
In exploratory factor analysis (EFA), a factor should ideally have at least 1 item for reliability.
In exploratory factor analysis (EFA), a factor should ideally have at least 1 item for reliability.
False
How much variance should retained factors ideally explain in PCA?
How much variance should retained factors ideally explain in PCA?
70%
Factors should be conceptually meaningful, and loadings should align well with __________ expectations.
Factors should be conceptually meaningful, and loadings should align well with __________ expectations.
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Match the following indicators with their descriptions:
Match the following indicators with their descriptions:
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What is one of the main goals of Principal Component Analysis (PCA)?
What is one of the main goals of Principal Component Analysis (PCA)?
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Eigenvalues in PCA represent how much variance each principal component captures.
Eigenvalues in PCA represent how much variance each principal component captures.
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PCA can help in reducing dimensionality by transforming __ constructs into three.
PCA can help in reducing dimensionality by transforming __ constructs into three.
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Match the following PCA components with their descriptions:
Match the following PCA components with their descriptions:
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Which criterion is commonly used to decide the number of components to retain in PCA?
Which criterion is commonly used to decide the number of components to retain in PCA?
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In PCA, components need to be correlated with each other to effectively explain variance.
In PCA, components need to be correlated with each other to effectively explain variance.
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What procedure is applied in PCA to calculate a set of linear composites?
What procedure is applied in PCA to calculate a set of linear composites?
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What is the primary purpose of eigenvalues in the context of a data set?
What is the primary purpose of eigenvalues in the context of a data set?
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Eigenvalues allow for the reduction of dimensions without any loss of information.
Eigenvalues allow for the reduction of dimensions without any loss of information.
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What is the Kaison criteria related to eigenvalues?
What is the Kaison criteria related to eigenvalues?
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The sum of the eigenvalues will equal the number of _____ in the data set.
The sum of the eigenvalues will equal the number of _____ in the data set.
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Match the methods for deciding how many components to retain with their descriptions:
Match the methods for deciding how many components to retain with their descriptions:
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Which of the following statements is true regarding eigenvectors?
Which of the following statements is true regarding eigenvectors?
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A component with an eigenvalue less than 1 is considered significant in the context of PCA.
A component with an eigenvalue less than 1 is considered significant in the context of PCA.
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How much of the total variance is captured by all the eigenvalues together?
How much of the total variance is captured by all the eigenvalues together?
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Study Notes
Psychometric Testing
- Focuses on measuring psychological constructs through questionnaires and scales.
- Involves understanding constructs, ensuring reliability and validity of measurements, and managing questionnaire data effectively.
Psychological Constructs
- Abstract concepts like intelligence, stress, or satisfaction.
- Measured indirectly through questions or items.
- Operationalized to become measurable variables (e.g., a questionnaire on stress levels).
- Different operationalisations make consolidating findings difficult.
Jingle and Jangle Fallacies
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Jingle fallacy: Using the same name to denote different things.
- Example: Two narcissism scales, both using similar names but measuring different aspects.
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Jangle fallacy: Using different names to denote the same thing.
- Example: Creating new measures of a construct without considering existing measures.
- This can lead to inconsistent research findings and create unnecessary redundancy.
Connections
- Connects observable phenomena (e.g., item responses) to theoretical attributes (e.g., life satisfaction).
- Psychometricians study the conceptual and statistical foundations of constructs.
- Psychometrics applies across many sciences (e.g., psychology, behavioural genetics, neuroscience, political science, medicine).
- Tests of typical performance measure what participants do regularly (e.g., interests, values, personality, beliefs, as in the "Harry Potter House" quiz.)
- Tests of maximal performance measure performance when participants exert maximum effort (e.g., aptitude tests, exams, cognitive tests).
Types of Psychometric Tests
- Education: Aptitude and ability tests (standard school tests), vocational tests.
- Business: Selection (e.g., personality, skills), development (e.g., interests, leadership), performance (e.g. well-being, engagement).
- Health: Mental health symptoms (e.g., anxiety), clinical diagnoses (e.g., personality disorders).
Criteria for Psychometric Tests
- Validity: The degree to which a test measures what it intends to measure.
- Reliability: The consistency of a measurement over time and various contexts.
- Interpretability: The clarity with which the scores can be understood and used.
- Relevance: The applicability of the test to specific populations or contexts.
Measurement Error
- Random error: Unpredictable and inconsistent values due to factors specific to the measurement.
- Systematic error: Predictable alterations of the observed score due to factors within the measurement.
- Social desirability bias: Tendency to report answers that are socially desirable rather than accurate self-report.
Correlations and Covariance
- Unit of analysis in psychometrics is covariance (relationship between two variables)
- Variance measures how much a variable deviates from the mean.
- Covariance captures how two variables change together.
- Correlation is a standardize version of covariance.
Correlation Coefficient
- Measures the strength and direction of the relationship between two variables.
- Ranges from -1 to 1.
- Indicates a perfect positive correlation = +1 and as one variable increases, the other increases linearly.
Diagrammatical Conventions
- Square: Observed or measured item.
- Circle: Latent or unobserved variable (the concept or construct being measured).
- Two-headed arrow: Covariance (relationship between variables).
- Single-headed arrow: Regression path (indicating the direction of the causal relationship).
Validity
- Content Validity: The extent to which a test adequately measures all important aspects of the construct it's intended to measure.
- Construct Validity: The extent to which a test measures the intended theoretical construct.
- Face Validity: How suitable and relevant the test appears to be for its intended use, in the eyes of the person tasked with taking the test, e.g. using a balloon-blowing task to assess impulsivity.
- Criterion-related Validity: The extent to which a test's results correlate with other measures of the construct (criterion).
Reliability
- Test-retest reliability: Consistency of a test over time.
- Alternate-forms reliability: Consistency between similar tests (or differing versions of a test.)
- Split-half reliability: Consistency between the halves of a single test.
- Internal consistency reliability: How well items within a test measure the same construct (e.g., Cronbach's alpha).
- Inter-rater reliability: Consistency in scoring across different raters or judges when rating the same test subjects.
Scoring in CTT
- Summarising responses to evaluate a psychological construct.
Alternate Forms & Split-Half Reliability
- Correlation between different versions or divided halves of the same test.
Internal Consistency
- How well items on a scale correlate with each other.
Cronbach's Alpha
- Calculates internal consistency reliability of a scale.
Principal Component Analysis (PCA)
- Statistical technique to reduce data dimensionality.
- Transforms many observed variables into fewer uncorrelated principal components.
Factor Analyses (FA)
- Determines underlying latent variables (factors) that contribute to correlations among observed variables.
When to Use PCA or FA
- For dimensionality reduction.
- To understand the structure and relationships between variables.
Structural Validity
- Focuses on understanding the idiosyncratic and expensive process of discovering the factors behind a construct, and then to test whether these factors make sense.
Questionnaire Data Handling
- Data cleaning: Dealing with missing data, coding inconsistencies, and format issues.
- Recoding: Transforming answers to standardise data.
- Reliability: Assessing the consistency of measurement within tests or questionnaires.
- Validity: Ensuring that the instrument measures what it is intended to measure.
- Reverse coding: Adjusting items that are measured inversely.
Psychometric Testing - Steps
- Data importation: Reading data into software.
- Variable renaming: Giving concise names to each variable.
- Recoding responses: Converting data into a usable format (numerical, e.g., Likert scales).
- Reverse coding: Changing the polarity of items when necessary.
- Calculating scale scores: Summing or averaging scores to derive total scores.
- Analysis: Comparing scores to evaluate intervention effectiveness.
Important Considerations
- Item-to-factor relationship: How strongly individual items relate to the factors.
- Factor interpretation: Do the factors derived make sense given the research question?
- Communality: What portion of each variable's variance is explained by the factors.
- Uniqueness: What proportion of variance is not explained.
Evaluating Psychometric Testing
- Validity and reliability: Determining the accuracy and consistency of the test.
- Evaluating factor solutions: Assessing the quality of the factors found, considering item loadings, variance explained, and other concerns.
- Item and factor labels: Determining if labels make sense in the context of the data and research.
Signs of good test design
- Clear, comprehensive measures.
- Clear items and tasks.
- Balanced factors and items.
- Relevant labels for items and factors.
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Description
This quiz delves into the fundamentals of psychometric testing, focusing on measuring psychological constructs through various methodologies, including questionnaires and scales. It highlights crucial concepts like reliability, validity, and the jingle and jangle fallacies that can impact research outcomes.
