Deck 18: Exploratory Factor Analysis

Question 1

Factors are retained in the model based on the size of which value?

A) Eigenvalue
B) Discriminant value
C) Locus value
D) Entry value

Answer 1

A

Question 2

Calculate the factor scores for aerobic (factor 1) and strength (factor 2) when using the following equation Aerobic = .78AeroCap + .88PEF + .81Hae + .01DynS - .12Endur + .09IsoS
Strength = .02AeroCap + .11PEF + .009Hae + .72DynoS + .79Endur + .88IsoS
Aerobic = 61; PEF = 480; Hae = 45; DynS = 150; Endur = 60; IsoS = 200

A) Aerobic = 518.7; Strength = 385.8
B) Aerobic = 441.9; Strength = 783.8
C) Aerobic = 631.7; Strength = 112.4
D) Aerobic = 1005.1; Strength = 917.3

Answer 2

A

Question 3

Which of the following adjustments are required when the regression technique is used to determine factor scores? (You may select more than one option.)

A) Bartlett method
B) Anderson-Rubin method
C) Hans-Blix method
D) Ebden Meyerhoff method

Answer 3

A AND B

Question 4

To visually inspect the factor values and assist you in deciding which to retain, what type of plot can be used?

A) Scree plot
B) Screw plot
C) Screen plot
D) Scream plot

Question 5

The fundamental calculations that underpin principal component analysis (correlation matrices) are similar to which other statistical functions?

A) MANOVA and discriminant analysis
B) ANOVA and chi-square
C) ANOVA and logistic regression
D) MANOVA and multilevel analysis

Question 6

Which of the following are dimension reduction methods? (You may select more than one option.)

A) Principal component analysis
B) Factor analysis
C) Cluster analysis
D) Association analysis

Question 7

In principal component analysis and factor analysis, how do the equations used to calculate factors differ from a conventional linear model (i.e. Y = b₀ + bx + E)? (You may select more than one option.)

A) No intercept (b₀)
B) No gradient (b)
C) No error (E)
D) The equations are exactly the same.

Question 8

What are the purposes of using dimension reduction methods? (You may select more than one option.)

A) To understand the structure of a set of variables (e.g. latent variables).
B) Questionnaire development.
C) Reducing a data set by identifying the most relevant variables.
D) Identifying where significant differences exist in different variables.

Question 9

The fundamental aim of principal component analysis and factor analysis is to reduce the factors so that the model is simplified, but what is the process called?

A) Extraction
B) Interaction
C) Separation
D) Integration

Question 10

What is meant by the term 'latent variable'?

A) A variable that cannot be measured directly
B) A variable that acts as a 'master' predictor variable
C) A variable that is used to predict multiple outcome (i.e. dependent) variables
D) A variable that is not correlated with any other variables of interest

Question 11

Suppose you wished to determine physical health and you measure the following variables - isoinertial muscular strength, aerobic capacity, peak expiratory flow, static muscular strength, muscular endurance and haematocrit. Before conducting a principal component analysis or a factor analysis, what would you look to do first?

A) Run paired samples t-tests between each variable.
B) Run a one-way repeated-measures ANOVA' between the variables.
C) Run a series of correlations (correlation matrix) between each variable.
D) Run a Kolmogorov-Smirnov test between each variable.

Question 12

Prior to beginning your factor analysis, which of the following would be appropriate initial checks to perform on your data? (You may select more than one option.)

A) Sample size calculation
B) Correlations between variables
C) Factor rotation
D) Reliability check

Question 13

Assume the six variables tended to cluster into two dimensions (i.e. two factors). The first dimension (aerobic) involved aerobic capacity, peak expiratory flow and haematocrit, whilst the second dimension (strength) involved static muscular strength, muscular endurance and isoinertial muscular strength. Ideally, how would we expect to see the relationships between the variables and the factors (coordinates) presented graphically on x- and y-axes?

A) High on one axis (e.g. aerobic), low on the other axis (e.g. strength)
B) High on one axis (e.g. aerobic), high on the other axis (e.g. strength)
C) Low on one axis (e.g. aerobic), low on the other axis (e.g. strength)
D) Moderate on one axis (e.g. aerobic), low on the other axis (e.g. strength)

Question 14

Which academic discipline within sports science tends to use methods of dimension reduction the most to measure intangible phenomena?

A) Psychology
B) Physiology
C) Biomechanics
D) Nutrition

Question 15

Rotation is used to discriminate between factors. Which of the following are methods of rotation? (You may select more than one option.)

A) Orthogonal rotation
B) Oblique rotation
C) Octagon rotation
D) Ornithological rotation

Question 16

Based on the earlier example of physical health, what is the minimum number of participants that should be recruited for this study when there are six variables?

A) 60-90
B) 90-120
C) 120-150
D) 150-180

Question 17

Whilst visually inspecting the data is important, Kaiser (1960) developed a criterion to strengthen the researcher's decision. Which of the following criteria is correct?

A) Eigenvalues greater than 0.7
B) Eigenvalues less than 1.5
C) Eigenvalues greater than 10
D) Eigenvalues between 10 and 20

Question 18

Based on your answer to Q14, which factors will be retained?

A) Factors with the largest values
B) Factors with the smallest values
C) Factors with intermediate values
D) The factor value is irrelevant

Question 19

How would you differentiate between principal component analysis (PCA) and factor analysis (FA)?

A) PCA is concerned with explaining the maximum amount of total variance, whilst FA is concerned with covariance.
B) FA is concerned with explaining the maximum amount of total variance, whilst PCA is concerned with covariance.
C) PCA and FA are essentially the same thing, but PCA relates to psychology, whereas FA relates specifically to motor control.
D) PCA and FA are essentially the same thing, but FA relates to psychology, whereas PCA relates specifically to motor control.

Question 20

Which of the following could be deemed to be a latent variable? (You may select more than one option.)

A) Mood state
B) Physical health
C) Aerobic capacity (VO₂ max)
D) Ground reaction force

Question 21

What is the purpose of measuring a questionnaire's reliability?

A) To examine the consistency of a measure.
B) To determine whether a test measures what it should be measuring.
C) To generalize the findings to a wider population.
D) To decide whether the test or questionnaire is robust enough to be applied to different populations.

Question 22

Likert scales are commonly used by psychologists to measure specific phenomena, but how would you classify this data scale? (You may select more than one option.)

A) Nominal
B) Ordinal
C) Interval
D) Ratio

Question 23

What is the most common measure of scale reliability?

A) Cronbach's alpha
B) Pearson correlation
C) Spearman's beta
D) Kendall's sigma

Question 24

What is generally regarded as an acceptable score for reliability?

A) .7 to .8
B) .6 to .7
C) .5 to .6
D) .4 to .5

Question 25

To proceed with the factor analysis, what is the minimum value required for the KMO statistic?

A) .1
B) .2
C) .5
D) .9