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

Accepted Answer

Eigenvalue is used as a measure of the amount of variance in the data that is accounted for by each factor or component in factor analysis. Factors with eigenvalues greater than 1 are generally considered significant and retained in the model. Discriminant value, locus value, and entry value are not commonly used terms in factor analysis.

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

Accepted Answer

Using the given equation and plugging in the values: 
Aerobic = (.78*61) + (.88*480) + (.81*45) + (.01*150) - (.12*60) + (.09*200) = 518.7 
Strength = (.02*61) + (.11*480) + (.009*45) + (.72*150) + (.79*60) + (.88*200) = 385.8

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

Accepted Answer

The Bartlett method and the Anderson-Rubin method are both adjustments that are required when the regression technique is used to determine factor scores. The Bartlett method is used to adjust for the effects of multicollinearity, while the Anderson-Rubin method is used to adjust for the effects of measurement error.

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

Accepted Answer

A Scree plot is the best choice for visually inspecting factor values and deciding which to retain. It shows the eigenvalues for each factor and helps determine the point at which there is a significant drop in eigenvalues, indicating the number of factors that should be retained.

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

Accepted Answer

The correlation matrices used in principal component analysis are also used in MANOVA and discriminant analysis. ANOVA and chi-square use different calculations, and ANOVA and logistic regression use similar but not identical calculations. MANOVA and multilevel analysis use different calculations altogether.

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

Accepted Answer

B AND C

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.

Accepted Answer

In principal component analysis and factor analysis, the equations do not include an intercept (b₀) or an error term (E), as they focus on transforming data into a new coordinate system or explaining variance, rather than fitting a predictive model.

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.

Accepted Answer

B AND C

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

Accepted Answer

The process of reducing the factors in principal component analysis and factor analysis is called extraction. This involves identifying the underlying variables or dimensions that are responsible for the observed variability in the data and representing them in a simplified form. The aim is to identify the key factors that explain most of the variance in the data while minimizing the number of variables needed.

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

Accepted Answer

A latent variable is a variable that cannot be directly observed or measured but is inferred from other variables that can be measured. It is often used in statistical models to explain the relationship between observable variables.

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.

Accepted Answer

Before conducting a principal component analysis or a factor analysis, it is important to run a correlation matrix between each variable to determine the strength of the relationship between them. This will help determine if variables can be combined into factors or components. Running paired samples t-tests or a one-way repeated-measures ANOVA will not provide information about the relationships between the variables. A Kolmogorov-Smirnov test is used to determine if two samples come from the same distribution and is not relevant in this case.

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

Accepted Answer

The answer of Prior to beginning your factor analysis, which...

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)

Accepted Answer

The variables related to aerobic capacity would be high on the aerobic axis and low on the strength axis, and vice versa for strength-related variables, indicating distinct clustering into two dimensions.

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

Accepted Answer

Psychology tends to use methods of dimension reduction such as factor analysis and principal component analysis to measure intangible phenomena such as motivation, team cohesion, and mental toughness.

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

Accepted Answer

Orthogonal rotation and oblique rotation are the two main methods of rotation used in factor analysis. Octagon rotation and ornithological rotation are not valid methods of 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

Accepted Answer

The answer of Based on the earlier example of physical...

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

Accepted Answer

Kaiser's criterion states that only factors with eigenvalues greater than 1 should be retained. However, many researchers have revised this criterion to set a higher minimum threshold of 0.7 or even 0.5. Therefore, eigenvalues greater than 0.7 or 0.5 can be a better choice. Options B, C, and D are incorrect because they set the threshold too high and would result in retaining fewer factors than necessary.

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

Accepted Answer

Factors with the largest values are typically retained because they explain the most variance in the data, which is often the goal in factor analysis or similar statistical methods.

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.

Accepted Answer

PCA is used to identify the underlying structure in a data set by reducing the number of variables while retaining the most amount of information, i.e., variance. The goal of PCA is to maximize the total variance, and it's concerned with the covariance between variables. On the other hand, factor analysis is used to identify the latent variables that underlie observable variables, i.e., factors, that are responsible for the correlations between observed variables. The goal of FA is to explain the maximum amount of total variance, and it's concerned with the inter-correlation between variables.

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 (VO₂max) D) Ground reaction force

Accepted Answer

Mood state and physical health are both latent variables because they are not directly observable and must be inferred from other variables.

Quiz 18: Exploratory Factor Analysis

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

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

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

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

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

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.)

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

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?

What is meant by the term 'latent variable'?

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.)

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

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

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?

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?

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

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

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