Deck 18: Exploratory Factor Analysis

Question 1

Varimax rotation should be used when

A) Factors are expected to correlate.
B) Factors are non-orthogonal.
C) Factors are independent.
D) Kaiser's criterion is met.

Answer 1

Factors are independent.

Question 2

Which of the following is not an example of factor analysis methods?

A) Confirmatory factor analysis
B) Principal axis factoring
C) Hypothesis factoring
D) Image factoring

Answer 2

Hypothesis factoring

Question 3

Liu and Shen (2008) conducted a study to investigate and confirm the dimensional structure of the Care Giver Strain Questionnaire measured from subjects used in clinical research. A factor analysis generated a range of data and included the following scree plot. On this plot, where does the point of inflexion occur? Source: http:/ / www2.sas.com/ proceedings/ forum2008/ 383-2008.pdf

A) At eigenvalue 2 on the Y-axis and 2 on the X-axis
B) Between eigenvalues 2 and 3 on the Y-axis and at 2 on the Y-axis
C) Between eigenvalues 3 and 4 on the Y-axis
D) Between eigenvalues 1 and 2 on the Y-axis

Answer 3

Between eigenvalues 3 and 4 on the Y-axis

Question 4

Which statement is not true of exploratory factor analysis (EFA)?

A) EFA identifies the factor structure or model for a set of variables.
B) EFA establishes the number of principal underlying factors in the data.
C) EFA identifies the pattern seen in the correlations of each variable to the factors.
D) EFA confirms the number of constructs identified in previous research.

Question 5

What does the following output from a factor analysis tell us?

A) The sample size is sufficient, but there is multicollinearity in the data.
B) The sample size is inadequate, and there is multicollinearity in the data.
C) The sample size is adequate, and the correlations in the correlation matrix are significantly bigger than zero.
D) The sample size is adequate, but the correlations in the correlation matrix are not big enough.

Question 6

Oblique rotation should be used when

A) Factors are expected to correlate.
B) Factors are orthogonal.
C) Factors are independent.
D) Kaiser's criterion is met.

Question 7

Which of the following must be met for EFA?

A) Presence of relationships determined by the correlation matrix
B) Sphericity determined by a Bartlett test
C) Normal distribution in the variables determined by a Kolmogorov-Smirnov tests
D) Interaction between the variables determined by ANOVA

Question 8

A screen plot in factor analysis is a plot of

A) Each factor against its eigenvalue.
B) The factor loadings of each variable onto each factor.
C) The correlations between variables.
D) The regression coefficient of each variable with each factor.

Question 9

Most researchers use exploratory factor analysis to

A) Confirm the data are real.
B) Determine the number of factors/ constructs underlying a set of variables.
C) Reduce the data to a smaller number of variables.
D) Confirm the number of factors.

Question 10

Based on this screen plot, how many factors should be extracted?

A) 2.
B) 3.
C) 4.
D) 5.

Question 11

Cronbach's alpha identified the following values for each of the three factors Factor 1 0.943
Factor 2 0.876
Factor 3 0.877
What process in SPSS provided this information?

A) Extraction
B) Rotation
C) Communalities
D) None of the above

Question 12

Kaiser's criterion for retaining factors is

A) Retain any factor with an eigenvalue greater than 0.7.
B) Retain any factor with an eigenvalue greater than 1.
C) Retain factors before the point of inflexion on a scree plot.
D) Retain factors with communalities greater than 0.7.

Question 13

Which of these is a form of oblique rotation?

A) Varimax
B) Quartimax
C) Equamax
D) Promax

Question 14

Based on the following output, which item on this questionnaire would most improve the reliability of the questionnaire if it were removed?

A) Q12.
B) Q16.
C) Q21.
D) Q4.

Question 15

Rotation means

A) Turning the matrix on one side.
B) Simplifying the loadings.
C) Interpretation of the factors.
D) Interpretation of the graph.

Question 16

Which procedure would you not use to determine the number of factors to be included in your interpolation of an EFA?

A) Select the number of factors with eigenvalues of 1.00 or higher.
B) Examine a scree plot of eigenvalues plotted against the factor numbers.
C) Disregard any communalities.
D) Analyse increasing numbers of factors; stop when all non-trivial variance is accounted for.

Question 17

In SPSS what criterion is used to extract factors?

A) Varimax
B) Kaiser's
C) Promax
D) None of the above

Question 18

Factor loadings are

A) The weights of each factor.
B) The weights of each variable.
C) Correlations between each variable and each factor.
D) Correlations between all the variables.

Question 19

A screen plot is a graphical representation of which of the following?

A) Eigenvalues plotted against associated factors
B) Eigenvalues plotted against relevant variables
C) Eigenvalues plotted against eigenvectors
D) None of the above

Question 20

Principal component analysis is

A) Used to summarize data whilst retaining maximum variance.
B) Used to summarize data whilst retaining minimum variance.
C) Derive as few factors as possible.
D) Derive as many solutions as possible.

Question 21

Principal component analysis is

A) Used to summarize data whilst retaining maximum variance.
B) Used to summarize data whilst retaining minimum variance.
C) Derive as few factors as possible.
D) Derive as many solutions as possible.

Question 22

Based on this scree plot, how many factors should be extracted?

A) 2.
B) 3.
C) 4.
D) 5.

Question 23

Which statement is not true of exploratory factor analysis (EFA)?

A) EFA identifies the factor structure or model for a set of variables.
B) EFA establishes the number of principal underlying factors in the data.
C) EFA identifies the pattern seen in the correlations of each variable to the factors.
D) EFA confirms the number of constructs identified in previous research.

Question 24

Which of the following is not an assumption of factor analysis?

A) Large sample size (> 150)
B) Small sample size (< 50)
C) Linearity
D) Factorability of correlation matrix

Question 25

Which of the following is not an example of factor analysis methods?

A) Confirmatory factor analysis
B) Principal axis factoring
C) Hypothesis factoring
D) Image factoring

Question 26

Which of these is a form of oblique rotation?

A) Varimax
B) Quartimax
C) Equamax
D) Promax

Question 27

Oblique rotation should be used when

A) Factors are expected to correlate.
B) Factors are orthogonal.
C) Factors are independent.
D) Kaiser's criterion is met.

Question 28

What does Cronbach's alpha test for?

A) Significance of factors
B) Functionality
C) Reliability
D) Significance of variables

Question 29

Factor loadings are

A) The weights of each factor.
B) The weights of each variable.
C) Correlations between each variable and each factor.
D) Correlations between all the variables.

Question 30

A screen plot is a graphical representation of which of the following?

A) Eigenvalues plotted against associated factors
B) Eigenvalues plotted against relevant variables
C) Eigenvalues plotted against eigenvectors
D) None of the above

Question 31

Based on the following output, which item on this questionnaire would most improve the reliability of the questionnaire if it were removed?

A) Q12.
B) Q16.
C) Q21.
D) Q4.

Question 32

Which procedure would you not use to determine the number of factors to be included in your interpolation of an EFA?

A) Select the number of factors with eigenvalues of 1.00 or higher.
B) Examine a scree plot of eigenvalues plotted against the factor numbers.
C) Disregard any communalities.
D) Analyse increasing numbers of factors; stop when all non-trivial variance is accounted for.

Question 33

Kaiser's criterion for retaining factors is

A) Retain any factor with an eigenvalue greater than 0.7.
B) Retain any factor with an eigenvalue greater than 1.
C) Retain factors before the point of inflexion on a scree plot.
D) Retain factors with communalities greater than 0.7.

Question 34

Which of the following must be met for EFA?

A) Presence of relationships determined by the correlation matrix
B) Sphericity determined by a Bartlett test
C) Normal distribution in the variables determined by a Kolmogorov-Smirnov tests
D) Interaction between the variables determined by ANOVA

Question 35

Varimax rotation should be used when

A) Factors are expected to correlate.
B) Factors are non-orthogonal.
C) Factors are independent.
D) Kaiser's criterion is met.

Question 36

What does the following output from a factor analysis tell us?

A) The sample size is sufficient, but there is multicollinearity in the data.
B) The sample size is inadequate, and there is multicollinearity in the data.
C) The sample size is adequate, and the correlations in the correlation matrix are significantly bigger than zero.
D) The sample size is adequate, but the correlations in the correlation matrix are not big enough.

Question 37

A screen plot in factor analysis is a plot of

A) Each factor against its eigenvalue.
B) The factor loadings of each variable onto each factor.
C) The correlations between variables.
D) The regression coefficient of each variable with each factor.

Question 38

Most researchers use exploratory factor analysis to

A) Confirm the data are real.
B) Determine the number of factors/ constructs underlying a set of variables.
C) Reduce the data to a smaller number of variables.
D) Confirm the number of factors.

Question 39

Liu and Shen (2008) conducted a study to investigate and confirm the dimensional structure of the Care Giver Strain Questionnaire measured from subjects used in clinical research. A factor analysis generated a range of data and included the following scree plot. On this plot, where does the point of inflexion occur? Source: http:/ / www2.sas.com/ proceedings/ forum2008/ 383-2008.pdf

A) At eigenvalue 2 on the Y-axis and 2 on the X-axis
B) Between eigenvalues 2 and 3 on the Y-axis and at 2 on the Y-axis
C) Between eigenvalues 3 and 4 on the Y-axis
D) Between eigenvalues 1 and 2 on the Y-axis

Question 40

Rotation means

A) Turning the matrix on one side.
B) Simplifying the loadings.
C) Interpretation of the factors.
D) Interpretation of the graph.

Question 41

In SPSS what criterion is used to extract factors?

A) Varimax
B) Kaiser's
C) Promax
D) None of the above

Question 42

Reverse-scoring items prior to running a reliability analysis allows for which of the following?

A) Bartlett's test of sphericity
B) Rotation techniques
C) Identification of outliers
D) None of the above

Question 43

Cronbach's alpha identified the following values for each of the three factors Factor 1 0.943
Factor 2 0.876
Factor 3 0.877
What process in SPSS provided this information?

A) Extraction
B) Rotation
C) Communalities
D) None of the above

Question 44

What does Cronbach's alpha test for?

A) Significance of factors
B) Functionality
C) Reliability
D) Significance of variables