Question 1

________ is an approach to factor analysis that estimates the factors based only on the common variance.
A)Principal components analysis
B)Common factor analysis
C)Omega method
D)Unweighted least squares

Accepted Answer

Common factor analysis is the approach to factor analysis that estimates the factors based only on the common variance. Principal components analysis, on the other hand, estimates the factors based on both common and unique variance. The Omega method is a reliability analysis approach, not a factor analysis approach. Unweighted least squares is a regression analysis technique, not a factor analysis technique.

Question 2

m represents ________ in the factor model,X_i= A_i1 F₁+ A_i2 F₂+A_i3 F₃+ ...+ A_im F_m+V_iU_i,. A)the number of variables B)the number of common factors C)the mth standardized variable D)the common factors

Accepted Answer

In the factor model, "m" typically represents the number of common factors influencing the variables being analyzed.

Question 3

A ________ is a lower triangle matrix showing the simple correlations,r,between all possible pairs of variables included in the analysis.
A)factor matrix
B)classification matrix
C)correlation matrix
D)total correlation matrix

Accepted Answer

A correlation matrix shows the simple correlations between all possible pairs of variables included in the analysis.

Question 4

________ is an approach to factor analysis that considers the total variance in the data.
A)Principal components analysis
B)Common factor analysis
C)Omega method
D)Unweighted least squares

Accepted Answer

Principal components analysis considers the total variance in the data and tries to identify the most important patterns in the data by finding linear combinations of the original variables that explain the maximum amount of variance. Common factor analysis, on the other hand, assumes that the observed variables are influenced by a smaller number of underlying latent factors and tries to identify these factors by estimating the correlations among the observed variables. Omega method is a reliability analysis method, and unweighted least squares is a regression method. Therefore, the correct choice is A.

Question 5

Which of the following is a way to interpret factors?
A)based on the variables that load high on a factor
B)by plotting the variables using the factor loadings as coordinates
C)both A and B
D)none of the above

Accepted Answer

Interpreting factors can be done by looking at the variables that load high on a factor, as well as by plotting those variables using the factor loadings as coordinates. These two methods of interpretation complement each other and provide a more complete understanding of the factor.

Question 6

A principal components analysis was run and the following eigenvalue results were obtained: 2.731,2.218,.442,.341,.183,and .085.How many factors would you retain using the eigenvalues to determine the number of factors?
A)one
B)two
C)four
D)six

Accepted Answer

The rule of thumb for determining the number of factors to retain is to only retain factors with eigenvalues greater than 1. In this case, there are two factors with eigenvalues greater than 1 (2.731 and 2.218), so we would retain two factors (Choice B). The other factors with eigenvalues less than 1 would not contribute significantly to explaining the variance in our data.

Question 7

________ should be used when factors in the population are likely to be strongly correlated.
A)Orthogonal rotation
B)The varimax procedure
C)Oblique rotation
D)None of the above

Accepted Answer

Oblique rotation allows for the factors to be correlated, which may reflect the true underlying structure of the population. Orthogonal rotation (such as varimax) assumes that the factors are uncorrelated, which may not be true in many cases. Therefore, oblique rotation is the best choice when factors in the population are likely to be strongly correlated.

Question 8

________ are simple correlations between the variables and the factors.
A)Factor scores
B)Factor loadings
C)Correlation loadings
D)Both A and B are correct

Accepted Answer

Factor loadings represent the strength and direction of the relationship between each variable and factor. They are correlation coefficients that measure how much of the variation in the variable is explained by the factor. Factor scores, on the other hand, are the values obtained by multiplying each variable by its corresponding factor loading and summing the products.

Question 9

Which is not a method of factor analysis?
A)principal components analysis
B)common factor analysis
C)omega method
D)unweighted least squares

Accepted Answer

Principal components analysis, common factor analysis, and unweighted least squares are all legitimate methods of factor analysis. The omega method, however, is not a recognized approach to factor analysis.

Question 10

Which statement is not true about principal components analysis (PCA)?
A)The factors are estimated based only on the common variance.
B)The total variance in the data is considered.
C)PCA is recommended when the primary concern is to determine the minimum number of factors that will account for maximum variance in the data for use in subsequent multivariate analysis.
D)The diagonal of the correlation matrix consist of unities.

Accepted Answer

PCA considers both common and unique variances of the variables, not just the common variance. The other statements accurately describe aspects of PCA.

Question 11

Factor analysis may not be appropriate in all of the following situations except ________.
A)a small value for Bartlett's test of sphericity is found
B)small values of the KMO statistic are found
C)the variables are not correlated
D)the variables are correlated

Accepted Answer

Factor analysis is appropriate when the variables under study are correlated, as it aims to identify underlying factors that explain the patterns of correlations among variables.

Question 12

The ________ represents the total variance explained by each factor.
A)eigenvalue
B)percentage of variance
C)residual
D)communality

Accepted Answer

The eigenvalue in factor analysis represents the total variance explained by each factor. It indicates the amount of the overall variance in the observed variables that can be attributed to that factor.

Question 13

Which of the following statements is not true about factor rotation?
A)Through rotation,the factor matrix is transformed into a simpler one that is easier to interpret.
B)Rotation affects the communalities and the percentage of total variance explained.
C)Preferably,each factor should have a nonzero,or significant,loadings or coefficients for only some of the variables.
D)Different methods of rotation may result in the identification of different factors.

Accepted Answer

Factor rotation affects the factor loadings or coefficients, but it does not affect the communalities or the total percentage of variance explained.

Question 14

Communality is ________.
A)the amount of variance a variable shares with all the other variables being considered
B)the percentage of the total variance attributed to each factor
C)the proportion of variance explained by the common factors
D)both A and C are correct

Accepted Answer

Communality refers to the amount of variance a variable shares with all the other variables being considered (option A) and the proportion of variance explained by the common factors (option C). Therefore, both options A and C are correct, making option D the best choice. Option B refers to the percentage of total variance attributed to each factor, which is not the same as communality.

Question 15

Sometimes,because of prior knowledge,the researcher knows how many factors to expect and thus can specify the number of factors to be extracted beforehand.This is referred to as ________.
A)a priori determination
B)determination based on split-half reliability
C)determination based on significance tests
D)determination based on scree plot

Accepted Answer

A priori determination refers to the process of deciding the number of factors to be extracted based on prior knowledge or theory. This approach is different from other methods such as split-half reliability, significance tests and scree plot, which rely on statistical procedures to determine the number of factors to be extracted. A priori determination is useful when the researcher has theoretical or empirical reasons to believe that a certain number of factors is appropriate for the analysis.

Question 16

It is recommended that the factors extracted should account for at least ________ of the variance.
A)50 %
B)60%
C)65%
D)70%

Accepted Answer

It is commonly recommended that the factors extracted in factor analysis should account for at least 60% of the variance to ensure that a significant portion of the data's variability is captured by the model.

Question 17

As a rough guideline,there should be at least ________ times as many observations (sample size)as there are variables.
A)two or three
B)three or four
C)four or five
D)five or six

Accepted Answer

This guideline is known as the "rule of thumb" for determining the appropriate sample size for statistical analysis. It suggests that there should be at least four or five times as many observations as there are variables to ensure that the analysis is robust and valid. A smaller sample size may lead to inaccurate or unreliable results.

Question 18

________ is an index that compares the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficient.
A)Mahalanobis ratio
B)KMO measure of sampling adequacy
C)Bartlett's test of sphericity
D)Wilks' lambda

Accepted Answer

The KMO (Kaiser-Meyer-Olkin) measure of sampling adequacy compares the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficients. It helps in determining the adequacy of the sample for conducting a factor analysis.

Question 19

A ________ is a plot of the original variables using the factor loadings as coordinates.
A)scree plot
B)territorial map
C)factor loading plot
D)scattergram

Accepted Answer

A factor loading plot is a graphical representation of the factor analysis results, displaying the factor loadings of each variable as points on a graph. The axes of the graph represent the extracted factors, while the variables are represented by points. The factor loading plot is useful for understanding the relationship between variables and factors, as well as identifying patterns and outliers in the data.

Question 20

The first step in conducting factor analysis is ________.
A)construct the correlation matrix
B)determine the method of factor analysis
C)formulate the problem
D)determine the number of factors

Accepted Answer

Formulating the problem is the first step in conducting factor analysis, as it involves defining what you are trying to investigate or analyze before proceeding with any statistical methods or decisions on how many factors to consider.

Quiz 19: Factor Analysis

________ is an approach to factor analysis that estimates the factors based only on the common variance.

m represents ________ in the factor model,X_i= A_i1 F₁+ A_i2 F₂+A_i3 F₃+ ...+ A_im F_m+V_iU_i,.

A ________ is a lower triangle matrix showing the simple correlations,r,between all possible pairs of variables included in the analysis.

________ is an approach to factor analysis that considers the total variance in the data.

Which of the following is a way to interpret factors?

A principal components analysis was run and the following eigenvalue results were obtained: 2.731,2.218,.442,.341,.183,and .085.How many factors would you retain using the eigenvalues to determine the number of factors?

________ should be used when factors in the population are likely to be strongly correlated.

________ are simple correlations between the variables and the factors.

Which is not a method of factor analysis?

Which statement is not true about principal components analysis (PCA) ?

Factor analysis may not be appropriate in all of the following situations except ________.

The ________ represents the total variance explained by each factor.

Which of the following statements is not true about factor rotation?

Communality is ________.

Sometimes,because of prior knowledge,the researcher knows how many factors to expect and thus can specify the number of factors to be extracted beforehand.This is referred to as ________.

It is recommended that the factors extracted should account for at least ________ of the variance.

As a rough guideline,there should be at least ________ times as many observations (sample size) as there are variables.

________ is an index that compares the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficient.

A ________ is a plot of the original variables using the factor loadings as coordinates.

The first step in conducting factor analysis is ________.