Deck 18: Exploratory Factor Analysis

Question 1

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

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

Answer 1

B

Question 2

A variable that shares none of its variance with any other variable would have a communality of:

A)0.01
B)0
C)1
D)0.1

Answer 2

B

Question 3

A variable that has no unique variance (or random variance) would have a communality of:

A)1
B)0
C)0.1
D)0.01

Answer 3

A

Question 4

An examiner of trainee chefs wanted to look at the underlying constructs of their 12 core culinary skills assessments. They ran a factor analysis with varimax rotation on the scores of the 12 assessments. Looking at the rotated factor matrix from their output below, which factor is the most likely to be labelled 'preparation of fruit and vegetables'?

A)Factor 1
B)Factor 2
C)Factor 3
D)None of them

Question 5

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

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

Question 6

An examiner of trainee chefs wanted to look at the underlying constructs of their 12 core culinary skills assessments. They ran a factor analysis with varimax rotation on the scores of the 12 assessments. Looking at the rotated factor matrix from their output below, which factor is the most likely to be labelled 'creativity'?

A)Factor 2
B)Factor 3
C)Factor 1
D)None of them

Question 7

Oblique rotation should be used when:

A)You believe that the underlying factors will be correlated.
B)You believe that the underlying factors are orthogonal.
C)You believe that the underlying factors are independent.
D)Kaiser's criterion is met.

Question 8

Marvin Zuckerman's work on dimensions of sensation seeking reveals four dimensions to this trait: (1) thrill and adventure seeking susceptibility to boredom (e.g., being easily bored by predictable experiences and people). These dimensions are theoretically independent. Using the SPSS output below, do you think that the factor structure of the questionnaire supports Zuckerman's theory?

A)It isn't clear whether the factor structure supports Zuckerman's theory.
B)There is evidence for susceptibility to boredom, experience seeking, thrill and adventure seeking but there is no evidence for disinhibition.
C)Zuckerman's theory is not at all supported by the factor structure of the questionnaire.
D)The four factors clearly represent susceptibility to boredom, experience seeking, thrill and adventure seeking and disinhibition.

Question 9

An examiner of trainee chefs wanted to look at the underlying constructs of their 12 core culinary skills assessments. They ran a factor analysis with varimax rotation on the scores of the 12 assessments. Looking at the rotated factor matrix from their output below, which factor is the most likely to be labelled 'hygiene'? Rotated Factor Matrix

A)Factor 3
B)Factor 1
C)Factor 2
D)None of them

Question 10

Which of the following is true of factor scores?

A)Factor scores can be used to assess how each variable correlates to each factor.
B)Factor scores quantify the correlation between factors.
C)Factor scores can be used to overcome collinearity problems.
D)Factor scores can be used to overcome sphericity.

Question 11

Which of the following regarding the determinant of the R-matrix, denoted |R|, is false?

A)The determinant is related to eigenvalues and eigenvectors, but instead of describing the height and width of the data it describes the overall area.
B)The determinant tells us whether the correlation matrix is singular, or if all variables are completely unrelated, or somewhere in between.
C)The determinant of the R-matrix should be less than .00001.
D)The determinant can be used to detect multicollinearity in a data set.

Question 12

A scree plot in factor analysis is a plot of:

A)The factor loadings of each variable (Y-axis) onto each factor (X-axis).
B)The correlations between variables.
C)The regression coefficient of each variable (X-axis) with each factor (Y-axis).
D)Each eigenvalue (Y-axis) against the factor with which it is associated (X-axis).

Question 13

An examiner of trainee chefs wanted to look at the underlying constructs of their 12 core culinary skills assessments. They ran a factor analysis with varimax rotation on the scores of the 12 assessments. Looking at the rotated factor matrix from their output below, what would be a good label for factor 2?

A)Slicing and seeding
B)Cleanliness
C)Culinary skills
D)Creativity

Question 14

Marvin Zuckerman's work on dimensions of sensation seeking reveals four dimensions to this trait: (1) thrill and adventure seeking susceptibility to boredom (e.g., being easily bored by predictable experiences and people). These dimensions are theoretically independent. A researcher was interested in designing a new questionnaire to measure sensation seeking. A 16-item questionnaire using a 5-point Likert scale (1 = strongly disagree, 2 = disagree, 3 = neither, 4 = agree, 5 = strongly agree) was devised and given to 750 people. Based on the SPSS output below, what could you conclude?
Based on the SPSS Output below, that relates to the analysis of the sensation-seeking questionnaire, what could you conclude?

A)The analysis has been conducted on an adequately sized sample.
B)The analysis has not been conducted on an adequately sized sample.
C)It's unclear whether the sample size is adequate but there is significant multicollinearity in the data.
D)There is singularity in the data.

Question 15

Which of the following sentences regarding the similarities of factor analysis and PCA is false?

A)Both factor analysis and PCA are linear models in which loadings are used as weights.
B)Unlike PCA, factor analysis contains an error term.
C)Both PCA and exploratory factor analysis take advantage of 'rotation'.
D)In both PCA and factor analysis we predict components from measured variables.

Question 16

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

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

Question 17

An examiner of trainee chefs wanted to look at the underlying constructs of their 12 core culinary skills assessments. They ran a factor analysis with varimax rotation on the scores of the 12 assessments. Looking at the rotated factor matrix from their output below, how many variables load onto factor 1?

A)6
B)11
C)5
D)1

Question 18

A reliability analysis was run on items from a questionnaire and gave rise to a Cronbach's alpha of α = -.8. What is the most likely explanation?

A)There are too few items on the questionnaire.
B)The questionnaire has 'inverse reliability'.
C)There were reverse-phrased items on the questionnaire that were not reverse-scored before the analysis was done.
D)The questionnaire is unreliable.

Question 19

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

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