Factor Analysis: A Comprehensive Guide for Master's Students

Question 1

Which of these is NOT a method used in Factor Analysis?

Accepted Answer

Cluster Analysis

Answer

Principal Component Analysis

Answer

Second-Order Factor Analysis

Question 2

What is the purpose of using scree plots in factor analysis?

Accepted Answer

To determine the number of factors to extract

Answer

To identify potential outliers in the data

Answer

To assess the reliability of the factor loadings

Answer

To visualize the relationships between the factors

Question 3

What is the key difference between exploratory and confirmatory factor analysis?

Accepted Answer

EFA is used to explore data and identify factors, while CFA is used to test hypothesized relationships.

Answer

CFA is used to explore data and identify factors, while EFA is used to test hypothesized relationships.

Answer

EFA is used to test hypothesized relationships, while CFA is used to explore data and identify factors.

Answer

There is no difference between EFA and CFA.

Question 4

What is the role of factor loadings in factor analysis?

Accepted Answer

They indicate the correlation between the original variables and the extracted factors

Answer

They determine the number of factors to extract

Answer

They test the significance of the extracted factors

Answer

They visualize the relationships between the extracted factors

Question 5

What is the purpose of varimax rotation in factor analysis?

Accepted Answer

To make the factor loadings easier to interpret

Answer

To minimize the number of non-zero factor loadings

Answer

To increase the correlation between the factors

Answer

To test the significance of the factors

Question 6

What is the difference between an eigenvector and an eigenvalue in factor analysis?

Accepted Answer

Eigenvectors represent the direction of the factors, while eigenvalues represent their strength.

Answer

Eigenvalues represent the direction of the factors, while eigenvectors represent their strength.

Answer

Eigenvectors and eigenvalues are the same thing.

Answer

Eigenvectors are used to calculate factor loadings, while eigenvalues are used to calculate communalities.

Question 7

The primary purpose of rotation in Factor Analysis is to:

Accepted Answer

Simplify the interpretation of factors

Answer

Remove correlations between factors

Answer

Maximize the variance explained by each factor

Answer

Identify the number of factors to extract

Question 8

The Kaiser-Meyer-Olkin (KMO) measure is used to assess:

Accepted Answer

Sampling adequacy for Factor Analysis

Answer

The number of factors to extract

Answer

The significance of factors

Answer

The reliability of factors

Question 9

Which of the following is a technique used in Factor Analysis, but not a type of Factor Analysis method?

Accepted Answer

Varimax Rotation

Answer

Principal Components Analysis (PCA)

Answer

Common Factor Analysis (CFA)

Answer

Exploratory Factor Analysis (EFA)

Question 10

Which rotation method is most commonly used in Factor Analysis, aiming to minimize the number of variables with high loadings on each factor?

Accepted Answer

Varimax

Answer

Quartimax

Answer

Equimax

Answer

Promax

Question 11

How do exploratory and confirmatory Factor Analysis differ in their primary objectives?

Accepted Answer

Exploratory Factor Analysis aims to identify latent variables, while Confirmatory Factor Analysis tests hypotheses about a predefined factor structure.

Answer

Confirmatory Factor Analysis aims to identify latent variables, while Exploratory Factor Analysis tests hypotheses about a predefined factor structure.

Answer

Exploratory and confirmatory Factor Analysis are the same technique.

Answer

Confirmatory Factor Analysis is more complex than Exploratory Factor Analysis.

Question 12

Which criterion for determining the number of factors to extract in Factor Analysis is NOT widely used?

Accepted Answer

Eigenvalue greater than 1

Answer

Kaiser's criterion

Answer

Scree plot

Answer

Parallel analysis

Question 13

What is the primary purpose of factor scores in Factor Analysis?

Accepted Answer

Estimate the values of latent variables for each observation

Answer

Represent the observed data in a lower-dimensional space

Answer

Rotate the factor loadings

Answer

Calculate the communalities

Question 14

What is the distinction between a common factor and a unique factor in Factor Analysis?

Accepted Answer

Common factors are shared by all variables, while unique factors are specific to individual variables.

Answer

Unique factors are shared by all variables, while common factors are specific to individual variables.

Answer

Both factors are shared by all variables.

Answer

Both factors are specific to individual variables.

Question 15

In Factor Analysis, what is the role of factor loadings?

Accepted Answer

Quantify the strength of relationships between observed variables and latent factors

Answer

Determine the communalities

Answer

Estimate the factor scores

Answer

Rotate the factors

Question 16

Which principle is NOT central to Factor Analysis?

Accepted Answer

Hypothesis testing

Answer

Data reduction

Answer

Identification of latent variables

Answer

Explanation of variance

Question 17

Factor Analysis typically uses which type of correlation matrix?

Accepted Answer

Pearson's correlation matrix

Answer

Spearman's rank correlation matrix

Answer

Partial correlation matrix

Answer

Multiple correlation matrix

Question 18

In Factor Analysis, the component matrix displays:

Accepted Answer

The loadings of variables on the extracted factors

Answer

The correlations between variables and factors

Answer

The variance explained by each factor

Answer

The uniqueness of each variable

Question 19

Which Factor Analysis method aims to maximize the variance of the linear combination of variables?

Accepted Answer

Principal Component Analysis

Answer

Exploratory Factor Analysis

Answer

Confirmatory Factor Analysis

Answer

Partial Least Squares

Question 20

What is the purpose of the Kaiser-Meyer-Olkin (KMO) measure in Factor Analysis?

Accepted Answer

Assessing data adequacy for Factor Analysis

Answer

Determining the optimal number of factors

Answer

Interpreting factor loadings

Answer

Testing factor significance

Question 21

Which of the following is NOT a limitation associated with Factor Analysis?

Accepted Answer

Always identifying the most accurate factor structure

Answer

Assumptions about data distribution and linearity

Answer

Challenges in interpreting extracted factors

Answer

Sensitivity to outliers

Question 22

In Factor Analysis, the primary goal of rotation is to:

Accepted Answer

Enhance the interpretability of factors

Answer

Maximize the variance explained by factors

Answer

Minimize the number of factors

Answer

Identify the definitive structure of the data

Question 23

What is the purpose of the scree plot in Factor Analysis?

Accepted Answer

To determine the number of factors to extract.

Answer

To assess the reliability of the factors.

Answer

To interpret the meaning of the factors.

Answer

To identify the variables that load most heavily on each factor.

Question 24

What is the key difference between an exploratory factor analysis (EFA) and a confirmatory factor analysis (CFA)?

Accepted Answer

EFA generates hypotheses about the factor structure of a set of variables, while CFA tests specific hypotheses about the factor structure.

Answer

CFA generates hypotheses about the factor structure of a set of variables, while EFA tests specific hypotheses about the factor structure.

Answer

EFA and CFA are the same technique.

Answer

CFA has a smaller sample size requirement than EFA.

Question 25

What is the kaiser-meyer-olkin (KMO) measure of sampling adequacy used for?

Accepted Answer

Assessing the sphericity of the data.

Answer

Determining the number of factors to extract.

Answer

Determining the reliability of the factors.

Answer

Interpreting the meaning of the factors.

Question 26

Which of the following is a limitation of Factor Analysis?

Accepted Answer

It can be difficult to interpret the factors.

Answer

It can only be used with small data sets.

Answer

It is not sensitive to outliers.

Answer

It always requires a confirmatory analysis.

Question 27

What is the main purpose of the Bartlett's test of sphericity?

Accepted Answer

To test whether the correlation matrix of the variables is an identity matrix.

Answer

To determine the reliability of the factors.

Answer

To assess the interpretability of the factors.

Answer

To test whether the variables are normally distributed.

Question 28

What is the difference between a factor loading and a factor score?

Accepted Answer

A factor loading is the correlation between a variable and a factor, while a factor score is the value of a factor for a particular observation.

Answer

A factor score is the correlation between a variable and a factor, while a factor loading is the value of a factor for a particular observation.

Answer

Factor loadings and factor scores are the same thing.

Answer

Factor loadings are only used in CFA, while factor scores are only used in EFA.

Question 29

Which step is NOT involved in Factor Analysis?

Accepted Answer

Cluster Analysis

Answer

Data Screening

Answer

Correlation Matrix Calculation

Answer

Eigenvalue Analysis

Question 30

What is the purpose of the scree plot in Factor Analysis?

Accepted Answer

To determine the number of components to retain

Answer

To identify the loadings of variables on each component

Answer

To assess the goodness of fit of the model

Answer

To visualize the distribution of variables in the dataset

Question 31

Which method is commonly used for rotation in Factor Analysis?

Accepted Answer

Varimax

Answer

Principal Axis Factoring

Answer

K-Means Clustering

Answer

Hierarchical Clustering

Question 32

What is the main assumption underlying the use of Factor Analysis?

Accepted Answer

Variables are linearly related

Answer

Variables are normally distributed

Answer

Variables are independent of each other

Answer

Variables are measured on an interval or ratio scale

Question 33

Explain the difference between an Eigenvalue and a Loading in Factor Analysis.

Accepted Answer

Eigenvalues measure the amount of variance explained by a component, while Loadings measure the correlation between a variable and a component.

Answer

Loadings measure the amount of variance explained by a component, while Eigenvalues measure the correlation between a variable and a component.

Answer

Eigenvalues and Loadings are the same thing.

Answer

Loadings are used to determine the number of components to retain, while Eigenvalues are used to interpret the results.

Question 34

What is the purpose of using a Correlation Matrix as the input for Factor Analysis?

Accepted Answer

To eliminate the effects of scale differences between variables

Answer

To make the variables more normally distributed

Answer

To increase the reliability of the analysis

Answer

To reduce the dimensionality of the dataset

Question 35

Describe the relationship between Factor Analysis and Principal Component Analysis (PCA).

Accepted Answer

Factor Analysis is a specialized form of PCA that focuses on identifying latent variables.

Answer

PCA is a specialized form of Factor Analysis that aims to maximize variance.

Answer

Factor Analysis and PCA are unrelated techniques.

Answer

Factor Analysis and PCA are identical techniques.

Question 36

Which of the following is a fundamental assumption of Factor Analysis?

Accepted Answer

The observed variables are linearly related to the latent factors.

Answer

The sample size is large (N > 500).

Answer

The data set is normally distributed.

Question 37

What is the primary purpose of a scree plot in Factor Analysis?

Accepted Answer

To determine the optimal number of factors to extract.

Answer

To identify the variables that have high communality.

Answer

To visualize the relationship between variables and factors.

Question 38

Which rotation method in Factor Analysis is commonly used to maximize the variance of factor loadings?

Accepted Answer

Varimax

Answer

Promax

Answer

Oblimin

Answer

Quartimax

Question 39

What is the interpretation of a factor loading close to -1?

Accepted Answer

The variable is strongly negatively related to the factor.

Answer

The variable has a positive relationship with the factor.

Answer

The variable is weakly related to the factor.

Answer

The variable is uncorrelated with the factor.

Question 40

Which of the following is NOT a potential benefit of using Factor Analysis?

Accepted Answer

It can increase the number of variables in a data set.

Answer

It can improve the interpretability of results.

Answer

It can reduce the dimensionality of data.

Answer

It can identify latent relationships between variables.

Question 41

What is the key difference between exploratory and confirmatory Factor Analysis?

Accepted Answer

Exploratory Factor Analysis is data-driven, while confirmatory Factor Analysis is theory-driven.

Answer

Exploratory Factor Analysis uses large samples, while confirmatory Factor Analysis uses small samples.

Answer

Exploratory Factor Analysis is used for hypothesis testing, while confirmatory Factor Analysis is used for model testing.

Question 42

Which of the following measures is commonly used to assess the reliability of a factor?

Accepted Answer

Cronbach's alpha

Answer

Factor loading

Answer

Pearson's correlation coefficient

Answer

Spearman's rank correlation coefficient

Question 43

What is the purpose of using cross-validation in Factor Analysis?

Accepted Answer

To determine the stability and generalizability of factor structure across different subsets of data.

Answer

To identify outliers in the data.

Question 44

Which of the following is NOT a limitation of Factor Analysis?

Accepted Answer

It can handle non-linear relationships among variables.

Answer

It can be difficult to interpret the factors.

Answer

It assumes multivariate normality.

Answer

It can be sensitive to sample size.

Question 45

In Factor Analysis, what is the distinction between a common factor and a unique factor?

Accepted Answer

A common factor is shared by multiple variables, while a unique factor is specific to a single variable.

Answer

A common factor is extracted first, while a unique factor is extracted later.