Factor Analysis Overview

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Questions and Answers

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.

False

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:

Likert Scale = Measures attitudes or opinions with a range of options Semantic Differential Scale = Measures meaning of concepts using bipolar adjectives Continuous Rating Scale = Allows for a fluid range of responses Multiple Item Measurement = Uses several questions to assess a single construct Signup and view all the answers

In factor analysis, unique variance for each observed variable is represented by _____.

u Signup and view all the answers

What is the role of the correlation matrix in factor analysis?

To summarize the relationships among variables Signup and view all the answers

How many factors were illustrated in the example of factor analysis provided?

Three factors Signup and view all the answers

Data reduction is one of the goals of factor analysis.

True Signup and view all the answers

Factor loadings can only be positive.

False Signup and view all the answers

What does a high loading (close to 1 or -1) on a given factor indicate?

The item strongly correlates with the factor. Signup and view all the answers

What procedure is used to calculate the reliability of each factor after a factor analysis?

Calculate Cronbach’s alpha. Signup and view all the answers

To increase reliability, one should look at item-total correlations and Cronbach’s alpha if the item is __________.

deleted Signup and view all the answers

Which factors showed Cronbach’s alpha values greater than 0.80?

Planning and participation with staff Signup and view all the answers

Match the type of scale to its characteristic:

Likert Scale = Measures levels of agreement or disagreement Semantic Differential Scale = Measures the meaning of concepts Continuous Rating Scale = Allows for a range of scores Multiple Item Measurement = Utilizes multiple items to assess a concept Signup and view all the answers

Summated scales are created by selecting low loading variables from factor analysis.

False Signup and view all the answers

What does an eigenvalue greater than 1 indicate in factor analysis?

The factor is considered significant in explaining variance Signup and view all the answers

What is the importance of achieving a simple structure in factor analysis?

To ensure each variable loads high on one factor and low on others. Signup and view all the answers

Bartlett’s Test of Sphericity tests the hypothesis that all correlations between variables are zero.

True Signup and view all the answers

The measure of how well the variance is explained by a factor is given by its __________.

eigenvalue Signup and view all the answers

What does the rule for selecting factors in factor analysis state?

Eigenvalue must be greater than 1. Signup and view all the answers

Match the following measurement scales with their descriptions:

Likert Scale = Measures attitudes on a agree-disagree spectrum Semantic Differential Scale = Measures meaning or connotation of concepts Continuous Rating Scale = Allows for precise numeric evaluations Multiple Item Measurement = Combines several items to capture a construct Signup and view all the answers

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.