Podcast
Questions and Answers
What is the primary goal of factor analysis?
What is the primary goal of factor analysis?
- To visualize the relationship between variables
- To create new variables from existing ones
- To evaluate the performance of a measuring instrument
- To capture as much variance in original variables with as few factors as possible (correct)
Factor analysis assumes that only nominal data is appropriate for its calculations.
Factor analysis assumes that only nominal data is appropriate for its calculations.
False (B)
What does a high correlation between variables in the same group indicate?
What does a high correlation between variables in the same group indicate?
It indicates that the variables are related and share common variance.
Match the following scales with their description:
Match the following scales with their description:
In factor analysis, unique variance for each observed variable is represented by _____.
In factor analysis, unique variance for each observed variable is represented by _____.
What is the role of the correlation matrix in factor analysis?
What is the role of the correlation matrix in factor analysis?
How many factors were illustrated in the example of factor analysis provided?
How many factors were illustrated in the example of factor analysis provided?
Data reduction is one of the goals of factor analysis.
Data reduction is one of the goals of factor analysis.
Factor loadings can only be positive.
Factor loadings can only be positive.
What does a high loading (close to 1 or -1) on a given factor indicate?
What does a high loading (close to 1 or -1) on a given factor indicate?
What procedure is used to calculate the reliability of each factor after a factor analysis?
What procedure is used to calculate the reliability of each factor after a factor analysis?
To increase reliability, one should look at item-total correlations and Cronbach’s alpha if the item is __________.
To increase reliability, one should look at item-total correlations and Cronbach’s alpha if the item is __________.
Which factors showed Cronbach’s alpha values greater than 0.80?
Which factors showed Cronbach’s alpha values greater than 0.80?
Match the type of scale to its characteristic:
Match the type of scale to its characteristic:
Summated scales are created by selecting low loading variables from factor analysis.
Summated scales are created by selecting low loading variables from factor analysis.
What does an eigenvalue greater than 1 indicate in factor analysis?
What does an eigenvalue greater than 1 indicate in factor analysis?
What is the importance of achieving a simple structure in factor analysis?
What is the importance of achieving a simple structure in factor analysis?
Bartlett’s Test of Sphericity tests the hypothesis that all correlations between variables are zero.
Bartlett’s Test of Sphericity tests the hypothesis that all correlations between variables are zero.
The measure of how well the variance is explained by a factor is given by its __________.
The measure of how well the variance is explained by a factor is given by its __________.
What does the rule for selecting factors in factor analysis state?
What does the rule for selecting factors in factor analysis state?
Match the following measurement scales with their descriptions:
Match the following measurement scales with their descriptions:
Study Notes
Variables and Factors
- Variables with high correlation are grouped together
- Variables with low correlation are in different groups
- Factors are calculated using original variables and factor loadings (λ)
Intuitions and Goals
- Assumes interval or ratio scaled data
- Identifies patterns in correlation matrix (finds groups of variables with strong correlations)
- Summarizes groups of variables with high correlations using factors
Explaining Variance
- Factors explain variance in observed variables
- Factors represent latent constructs
- Unique variance (u) cannot be explained by factors
- Each variable has a unique term (u)
Factor Analysis Goals
- Capture maximum variance with minimal factors
- Summarize data
- Detect relationships and dimensions
- Reduce data for simplification and analysis
Interpreting the Rotated Solution
- Rotated Component Matrix shows factor loadings (correlation between factor and original variables )
- Variables with high loadings on a factor help interpret the factor
- Factor loadings can be positive or negative
- Aim for simple structure (each variable loads high on 1 factor and low on others)
- Interpret factors by highlighting the highest factor loadings per row
Cronbach's Alpha
- Calculate Cronbach's alpha post factor analysis for each factor
- Select high loading variables for reliability analysis
- Recode items with negative factor loading
- Calculate Cronbach's alpha for the recoded items
- Analyze item-total correlations and Cronbach's alpha for item deletion
Summated Scales and Factor Scores
- Compute summated scales or factor scores for further analysis
- Each factor represents a summated scale or factor score
- Replace original variables with the new scales for further analysis
Correlation Matrix and Factor Analysis
- Bartlett's Test of Sphericity tests correlation significance (do variables have enough correlation for factor analysis to be appropriate?)
- Ho: all correlations are zero
- Chi-square should be large (p <0.05) to reject Ho
Determining Number of Factors
- Each factor has an eigenvalue
- Eigenvalue represents the amount of variance explained by a factor
- Number of variables = Sum of all eigenvalues
- % variance explained by a factor = eigenvalue/number of variables
- Rule: Eigenvalue > 1 (each factor should explain the variance of at least one variable)
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Description
Explore the fundamentals of factor analysis, including the role of variables, factors, and their relationships. This quiz covers key concepts such as correlation, variance explanation, and interpreting rotated solutions. Understand how to summarize data and capture maximum variance effectively.
