Factor Analysis: Uncover Hidden Dimensions in Data

Question 1

What is the primary aim of factor analysis in psychology?

Accepted Answer

To reduce a large number of variables into a more manageable number of factors.

Answer

To identify the correlations between variables.

Answer

To predict the value of one variable based on the values of other variables.

Answer

To test the significance of differences between groups.

Question 2

Which of the following is NOT a commonly used type of factor analysis?

Accepted Answer

Discriminant function analysis

Answer

Principal component analysis

Answer

Exploratory factor analysis

Answer

Confirmatory factor analysis

Question 3

What is the primary purpose of using a scree plot in factor analysis?

Accepted Answer

To determine the appropriate number of factors to extract.

Answer

To identify the variables that contribute most to each factor.

Answer

To assess the significance of the factors.

Answer

To visualize the correlations between variables.

Question 4

What is the main purpose of factor rotation in factor analysis?

Accepted Answer

To make the factors more interpretable.

Answer

To reduce the number of factors.

Answer

To test the significance of the factors.

Answer

To visualize the correlations between variables.

Question 5

Which measure indicates the strength of the relationship between a variable and a factor?

Accepted Answer

Factor loading

Answer

Eigenvalue

Answer

Scree plot

Answer

Correlation coefficient

Question 6

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

Accepted Answer

To assess the suitability of the data for factor analysis.

Answer

To measure the strength of the relationship between variables.

Answer

To determine the number of factors to extract.

Answer

To evaluate the interpretability of the factors.

Question 7

What is the primary objective of principal component analysis (PCA)?

Accepted Answer

To reduce the dimensionality of a dataset by identifying underlying factors.

Answer

To determine the statistical significance of differences between groups.

Answer

To predict the value of one variable based on the values of others.

Answer

To classify individuals into distinct groups.

Question 8

What does the term 'communality' represent in the context of factor analysis?

Accepted Answer

The proportion of variance in a variable that is explained by the common factors.

Answer

The proportion of variance in a variable that is attributable to its unique factor.

Answer

The correlation between two variables.

Answer

The number of factors extracted in a factor analysis.

Question 9

Differentiate between exploratory factor analysis (EFA) and confirmatory factor analysis (CFA).

Accepted Answer

EFA is used to generate hypotheses about the underlying structure of a dataset, while CFA is used to test specific hypotheses.

Answer

CFA is used to generate hypotheses about the underlying structure of a dataset, while EFA is used to test specific hypotheses.

Answer

EFA adopts a bottom-up approach, whereas CFA employs a top-down approach.

Answer

CFA adopts a bottom-up approach, whereas EFA employs a top-down approach.

Question 10

What is the primary reason for rotating factors in factor analysis?

Accepted Answer

To enhance the interpretability of the factors

Answer

To increase the variance explained by the factors

Answer

To reduce the number of factors

Answer

To test the validity of the factors

Question 11

Which type of variables is typically analyzed using factor analysis?

Accepted Answer

Continuous variables

Answer

Categorical variables

Answer

Mixed variables

Answer

Only highly correlated variables

Question 12

What is the purpose of a scree plot in factor analysis?

Accepted Answer

Determining the optimal number of factors to extract

Answer

Evaluating the interpretability of the factors

Answer

Testing the significance of the factors

Answer

Identifying the variables that load most heavily on each factor

Question 13

In exploratory factor analysis, what is the main purpose of the scree plot?

Accepted Answer

To determine the optimal number of factors to extract

Answer

To identify the appropriate rotation method

Answer

To determine the significance of the factor loadings

Answer

To determine the communalities of the variables

Question 14

In exploratory factor analysis, which ethical consideration is paramount in psychological research?

Accepted Answer

Interpreting factors cautiously and transparently

Answer

Ensuring sufficient sample size

Answer

Preventing model overfitting

Question 15

The primary goal of factor analysis is to:

Accepted Answer

Identify underlying factors or dimensions in a set of variables

Answer

Reduce the number of variables in a dataset

Answer

Create a new set of variables that are independent of each other

Answer

Determine the correlation between variables

Question 16

Factor rotation improves the:

Accepted Answer

Interpretability of the factors

Answer

Number of factors

Answer

Orthogonality of the factors

Answer

Normality of the factors

Question 17

Eigenvalues represent:

Accepted Answer

Variance explained by a factor

Answer

Correlation between variables

Answer

Variance unexplained by a factor

Answer

Factor loadings

Question 18

The scree plot aids in:

Accepted Answer

Determining the number of factors to extract

Answer

Identifying the most important factors

Answer

Assessing factor reliability

Answer

Determining variable communality

Question 19

What is the main purpose of the Kaiser-Meyer-Olkin (KMO) measure in factor analysis?

Accepted Answer

To assess the suitability of the data for factor analysis

Answer

To determine the ideal number of factors to extract

Answer

To calculate the correlation between the variables

Answer

To rotate the extracted factors

Question 20

In factor analysis, which assumption is fundamental?

Accepted Answer

Variables have linear relationships.

Answer

Variables are normally distributed.

Answer

Variables exceed observations in number.

Answer

Missing data follows the MAR mechanism.

Question 21

Which of the following is a statistical technique used to identify underlying factors or dimensions in a set of variables?

Accepted Answer

Factor analysis

Answer

Linear regression

Answer

Cluster analysis

Answer

ANOVA

Question 22

What is the primary purpose of exploratory factor analysis?

Accepted Answer

To identify and describe underlying factors that explain the intercorrelations among a set of observed variables

Answer

To predict future events

Answer

To test statistical hypotheses

Question 23

What is the key difference between orthogonal and oblique rotation methods in factor analysis?

Accepted Answer

Orthogonal rotation assumes factors are uncorrelated, while oblique rotation allows for correlated factors.

Answer

Orthogonal rotation is used for exploratory factor analysis, while oblique rotation is used for confirmatory factor analysis.

Question 24

What is the purpose of calculating communalities in factor analysis?

Accepted Answer

To estimate the proportion of variance in each variable that is accounted for by the extracted factors.

Answer

To assess the reliability of the factor solution

Answer

To determine the number of factors to extract

Question 25

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

Accepted Answer

Cronbach's alpha

Answer

Scree plot

Answer

Factor loading

Answer

Eigenvalue

Question 26

What is the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy primarily used for in factor analysis?

Accepted Answer

Assessing the suitability of data for factor analysis

Answer

Determining the number of factors to extract

Answer

Evaluating the reliability of a factor solution

Question 27

**What is a fundamental goal of factor analysis?**

Accepted Answer

To reduce the dimensionality of a dataset

Answer

To enhance the reliability of a dataset

Answer

To predict future outcomes based on observed data

Question 28

In exploratory factor analysis (EFA), the researcher has:

Accepted Answer

No a priori hypotheses about the underlying structure of the data

Answer

Confirmatory hypotheses about the underlying structure of the data

Answer

Partial least squares hypotheses about the underlying structure of the data

Answer

Specific hypotheses about the underlying structure of the data

Question 29

The scree plot in factor analysis is used to determine:

Accepted Answer

The appropriate number of factors to extract

Answer

The variables that load on each factor

Answer

The meaning of the factors

Answer

The reliability of the factors

Question 30

Cronbach's alpha is a measure of the:

Accepted Answer

Reliability of a factor

Answer

Significance of a factor

Answer

Validity of a factor

Answer

Meaning of a factor

Question 31

A factor loading is:

Accepted Answer

The correlation between a variable and a factor

Answer

The proportion of variance in a variable that is accounted for by all the factors

Answer

The sum of all the loadings for a variable

Answer

The difference between a variable and a factor

Question 32

The primary purpose of rotating factors is to:

Accepted Answer

Make the factors easier to interpret

Answer

Increase the reliability of the factors

Answer

Identify variables that load on each factor

Answer

Reduce the dimensionality of the factor solution

Question 33

Varimax is a type of:

Accepted Answer

Factor rotation

Answer

Factor analysis

Answer

Factor extraction

Question 34

The distinction between orthogonal and oblique factor rotation is that:

Accepted Answer

Orthogonal rotation assumes the factors are uncorrelated while oblique rotation allows the factors to be correlated

Answer

Oblique rotation is more interpretable than orthogonal rotation

Answer

Orthogonal rotation is more reliable than oblique rotation

Answer

Oblique rotation assumes the factors are uncorrelated while orthogonal rotation allows the factors to be correlated

Question 35

A common application of factor analysis in psychology is:

Accepted Answer

Identifying the underlying dimensions of personality

Answer

Diagnosing mental disorders

Answer

Predicting job performance

Question 36

**Which of the following best describes the purpose of factor analysis?**

Accepted Answer

To reveal hidden structures or patterns underlying a set of observed variables

Answer

To compare the means of multiple groups

Answer

To determine the validity of a research hypothesis

Question 37

**Which type of factor analysis is typically used for exploratory data analysis?**

Accepted Answer

Exploratory factor analysis (EFA)

Answer

Hierarchical factor analysis (HFA)

Answer

Partial least squares path modeling (PLS-PM)

Answer

Confirmatory factor analysis (CFA)

Question 38

**What is the recommended initial step in conducting factor analysis?**

Accepted Answer

Data screening and preparation

Answer

Factor rotation

Answer

Interpretation of results

Answer

Factor extraction

Question 39

**Which statistical measure is commonly used in PCA to estimate the importance of each factor?**

Accepted Answer

Eigenvalues

Answer

Loadings

Answer

Communalities

Answer

Variances

Question 40

**Which method of factor rotation aims to produce factors that are uncorrelated?**

Accepted Answer

Varimax

Answer

Promax

Answer

Equimax

Answer

Quartimax

Question 41

**What is the primary purpose of using scree tests in PCA?**

Accepted Answer

To determine the optimal number of factors to extract

Answer

To evaluate the reliability of the data

Answer

To identify the most important variables

Question 42

**Which of the following would be an appropriate research question for factor analysis?**

Accepted Answer

What are the underlying dimensions of job satisfaction?

Answer

Is there a significant difference in mean scores between two groups?

Answer

What is the best predictor of academic achievement?

Question 43

**What is a potential limitation of factor analysis?**

Accepted Answer

The results are not unique and can vary depending on the extraction method and rotation criteria used

Answer

It is only applicable to small datasets

Question 44

Which of the following is a common misconception about factor analysis?

Accepted Answer

It is a technique for reducing the number of variables in a dataset.

Answer

It is a method for defining new variables.

Answer

It can be used to explore the relationships between variables.