Question 1

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 the most to measure intangible phenomena such as motivation, personality traits, and emotions.

Question 2

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 measured directly. It is inferred from other observed variables or indicators, which are used to assess or measure the latent variable.

Question 3

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

Aerobic = (.78 x 61) + (.88 x 480) + (.81 x 45) + (.01 x 150) - (.12 x 60) + (.09 x 200) = 518.7
Strength = (.02 x 61) + (.11 x 480) + (.009 x 45) + (.72 x 150) + (.79 x 60) + (.88 x 200) = 385.8

Question 4

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 factors through principal component analysis and factor analysis is called extraction. This involves identifying the underlying patterns in the data and representing them with a smaller set of variables, known as components or factors.

Question 5

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 6

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.

Accepted Answer

The purpose of measuring a questionnaire's reliability is to examine its consistency. This means determining whether the results obtained from the questionnaire are consistent over time or across different groups of people. This is important in ensuring that the questionnaire is a reliable measure of the construct it is intended to measure.

Question 7

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 will be retained because they have the greatest influence on the dependent variable, thus are the most important predictors.

Question 8

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

Principal component analysis, MANOVA and discriminant analysis all involve the use of linear algebraic techniques and correlation matrices. ANOVA, chi-square and logistic regression involve different statistical approaches. Multilevel analysis involves modeling hierarchies and does not necessarily rely on correlation matrices or linear algebraic techniques.

Question 9

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 answer of Assume the six variables tended to cluster...

Question 10

What is the most common measure of scale reliability?
A) Cronbach's alpha
B) Pearson correlation
C) Spearman's beta
D) Kendall's sigma

Accepted Answer

Cronbach's alpha is the most common measure of scale reliability because it assesses the internal consistency of a scale by measuring how strongly items in the scale are related to each other. A higher Cronbach's alpha value indicates higher reliability and consistency of the scale. Pearson correlation, Spearman's beta, and Kendall's sigma are measures of correlation between two variables and do not assess the reliability of a scale.

Question 11

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 suggests retaining factors with eigenvalues greater than 1. However, some researchers have suggested a slightly higher cutoff of 0.7. This is because factors with eigenvalues below 0.7 may not explain enough variance in the data to be meaningful or reliable. Factors with eigenvalues greater than 0.7 (or 1 in some cases) are considered to be potentially meaningful and can be included in the final factor solution. Therefore, the correct criterion is Eigenvalues greater than 0.7.

Question 12

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

Factors are typically retained based on their eigenvalues, as these values indicate how much variance they explain in the data. Factors with higher eigenvalues are considered more important and are retained in the model, while those with lower eigenvalues may be dropped. Discriminant value, locus value, and entry value are not typically used as criteria for deciding which factors to retain.

Question 13

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 concerned with finding the principal components that explain the maximum amount of variance in the data, whereas FA is concerned with finding underlying factors that explain the covariance among the variables. Therefore, A is the best choice as it correctly describes the main differences between the two methods. B, C, and D are incorrect as they conflate or misrepresent the key features of PCA and FA.

Question 14

To proceed with the factor analysis, what is the minimum value required for the KMO statistic?
A) .1
B) .2
C) .5
D) .9

Accepted Answer

The answer of To proceed with the factor analysis, what...

Question 15

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 first run a correlation matrix to determine the strength and direction of the relationships between each variable. This step is necessary to determine if the variables are suitable for use in a factor analysis. Pairwise comparisons or ANOVA would not be appropriate in this case, as they do not assess the relationships between variables. A Kolmogorov-Smirnov test is also not appropriate, as it is used to determine if a sample differs significantly from a normal distribution.

Question 16

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 commonly used for visually inspecting the factor values and deciding which to retain. It plots the eigenvalues of each factor on the y-axis against the number of factors on the x-axis. The plot typically shows a steep drop-off in eigenvalues, indicating the number of factors that should be retained.

Question 17

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

Accepted Answer

Generally, a reliability score of .7 to .8 is considered acceptable in research. This means that the measures used in the study are consistent and produce similar results when tested multiple times. However, the acceptable score may vary depending on the type of research and the context in which it is being used.

Quiz 18: Exploratory Factor Analysis

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

What is meant by the term 'latent variable'?

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?

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?

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

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

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

What is the most common measure of scale reliability?

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?

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

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

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

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

What is generally regarded as an acceptable score for reliability?