Deck 18: Exploratory Factor Analysis

Question 1

A colleague has asked you to explain which of the following statements 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.

Answer 1

EFA confirms the number of constructs identified in previous research.

Question 2

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

Answer 2

Correlations between each variable and each factor

Question 3

Similarly, oblique 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 3

Factors are expected to correlate.

Question 4

When interpreting Cronbach's alpha in business research, a value above ____ generally indicates a reliable scale?

A) 0.7
B) 0.5
C) 0.1
D) 0.01

Question 5

Which of these is a form of oblique rotation?

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

Question 6

Which of the following must a business researcher ensure is met before interpreting factors?

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 7

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

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

Question 8

Nine items from a scale of grocery store service quality were assessed by exploratory factor analysis. Based on this scree plot, how many factors should be extracted?

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

Question 9

An accountancy firm would like to establish groups of similar taxation policies based on a database they have populated. They are faced with Kaiser's criterion for retaining factors. What rule should they follow for retaining factors?

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 10

Which of the following would you not do or use when deciding how many factors to retain from an exploratory factor analysis?

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 high communalities.
D) Analyse increasing numbers of factors, and stop when all non-trivial variance is accounted for.

Question 11

A consultant has asked you to distinguish between factor analysis and principal component analysis. What is the latter most commonly used for?

A) To summarize data whilst retaining maximum variance.
B) To summarize data whilst retaining minimum variance.
C) To derive as few factors as possible.
D) To derive as many solutions as possible.

Question 12

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 13

Some debate over rotation methods has caused confusion amongst analysts working for the grocery retailer. You have been asked to explain that 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 14

Rotation means?

A) Turning the matrix on one side
B) Simplifying the loadings
C) Simplifying the interpretation of factors
D) Provision of a graph

Question 15

A sports manufacturer performs a customer satisfaction survey, and would like to reduce the scale items into a smaller number of factors. What does the following output suggest?

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 16

The scree plot, such as the one used in Q1, represents 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.