Question 1

A nonhierarchical clustering program is one in which objects are allowed to leave one cluster to join another as clusters are being formed if the clustering criterion will be improved by doing so.

Accepted Answer

Nonhierarchical clustering programs, also known as Partitioning algorithms, allow objects to move between clusters as the algorithm progresses in order to improve the clustering criteria.

Question 2

Common factor analysis focuses on shared variance, hence communalities are used in the diagonal of the matrix

Accepted Answer

Communalities represent the proportion of variance in each variable that is accounted for by the common factors, and are used in the diagonal of the correlation matrix in common factor analysis.

Question 3

The first factor accounts for more of the variation in the data than the second factor.

Accepted Answer

This means that the first factor is more important in explaining the variability in the data than the second factor.

Question 4

An attractive feature of principal components analysis is the easy interpretability of the factors.

Accepted Answer

Principal Components Analysis (PCA) often results in components that are linear combinations of the original variables, making the interpretation of these components less straightforward compared to the original variables.

Question 5

An attractive feature of varimax rotation is that it may retain the variance explained, while reducing the number of factors in the solution as compared to principal components analysis).

Accepted Answer

Varimax rotation, a method of orthogonal rotation, does not reduce the number of factors in the solution; it aims to make the loadings within each factor more interpretable by maximizing the variance of the squared loadings of a factor on all the variables. The number of factors is determined before applying the rotation, and the total variance explained remains the same before and after rotation.

Question 6

In the hierarchical approach, the commonly used methods are single linkage, complete linkage, average linkage, Ward's method, and the centroid method.

Accepted Answer

The hierarchical approach commonly uses single linkage, complete linkage, average linkage, Ward's method, and the centroid method.

Question 7

In both principal components analysis and varimax rotation, the factors are constrained to be uncorrelated or geometrically perpendicular.

Accepted Answer

Both principal components analysis and varimax rotation aim to create uncorrelated or geometrically perpendicular factors, which can simplify the interpretation of the data and reduce multicollinearity.

Question 8

Rotation of factors changes the interpretation of the factors while retaining the principal component patterns of loadings.

Accepted Answer

Rotation of factors changes the interpretation of the factors by altering the loadings to achieve a simpler, more interpretable structure, but it does not retain the original principal component patterns of loadings.

Question 9

After performing a principal components analysis, a researcher finds that the cumulative variance explained by the solution is 0.56.He can increase the explained variance by performing a varimax rotation.

Accepted Answer

Varimax rotation, a method of orthogonal rotation, simplifies the interpretation of the principal components by redistributing the variance but does not increase the total explained variance.

Question 10

Communality is the percent of a variable's variance which contributes to the correlation with other variables or is common to other variables.

Accepted Answer

Communality represents the proportion of variance in a variable that can be explained by other variables in the dataset. It ranges from 0 to 1, with higher values indicating stronger shared variance.

Question 11

Simple Euclidean distance is a common measurement of similarity on a perceptual map.

Accepted Answer

Euclidean distance is a commonly used metric for calculating similarity on a perceptual map. It measures the distance between two points in a multi-dimensional space, which can be visualized as the distance between two points on a map.

Question 12

The percent of variance explained is a summary measurement indicating how much of the total original variance of all the respondents is represented by the factor.

Accepted Answer

The statement accurately describes the concept of percent of variance explained.

Question 13

The basic task in cluster analysis is to uncover competing explanations for a causal phenomenon.

Accepted Answer

The basic task in cluster analysis is to group together similar observations based on their characteristics, not to uncover explanations for causality.

Question 14

If a clustering procedure starts with one cluster and subdivides until all objects are in their own single-object cluster, the procedure is termed top-down hierarchical clustering.

Accepted Answer

This is an accurate definition of top-down hierarchical clustering.

Question 15

The ABC Company is involved in trying to segment its market so that it can better design specific marketing programs directed at each segment.One method of segmenting that it might use is cluster analysis.

Accepted Answer

Cluster analysis is a method of market segmentation where data is analyzed to identify groups of customers with similar characteristics and needs. This helps the company tailor its marketing programs to specific segments and improve its overall effectiveness.

Question 16

A major advantage of cluster analysis is the availability of standard statistical tests to ensure that the output does not represent pure randomness.

Accepted Answer

Cluster analysis does not typically offer standard statistical tests to validate the absence of randomness in its results; it is more exploratory in nature, focusing on finding patterns or groupings without providing statistical proofs of non-randomness.

Question 17

While analyzing and interpreting consumer perception data using factor analysis, a researcher found the factor loading on Factor 1 to be high.However, he could not interpret the factor meaningfully.A probable cause for this situation is computation error or shortsightedness in his interpretation, since a high loading ensures meaningfulness.

Accepted Answer

A high loading does not always ensure meaningfulness. It is possible for a high loading to be an artifact or coincidence, and further analysis and interpretation may be necessary to understand the underlying factor.

Question 18

All factor analysis methods constrain the factors to be uncorrelated.

Accepted Answer

Factor analysis methods can be divided into two main types: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). In EFA, factors can be either correlated or uncorrelated, depending on the rotation method used (orthogonal rotations assume uncorrelated factors, while oblique rotations allow for correlated factors). CFA, on the other hand, can explicitly model factors to be correlated if specified by the researcher.

Question 19

The variation in variable 3 is shown to be completely explained by the two-factor solution.

Accepted Answer

The statement does not provide enough information to conclude that the variation in variable 3 is completely explained by the two-factor solution without additional statistical evidence or analysis details.

Question 20

Factor loadings and correlations are identical if each variable has its mean subtracted and is divided by its standard deviation.

Accepted Answer

When each variable is standardized by subtracting its mean and dividing by its standard deviation, the resulting correlation matrix is identical to the matrix of factor loadings.

Quiz 20: Discriminant, Factor and Cluster Analysis