Question 1

The following questions focus on Multidimensional Scaling:
-Kruskal's stress

Accepted Answer

A)  is an index of variation. 
B)  is a measure of central tendency. 
C)  is a lack of fit index. 
D)  is an index of reproducibility. 
E)  is an index of dispersion. 
A)  is an index of variation. 
B)  is a measure of central tendency. 
C)  is a lack of fit index. 
D)  is an index of reproducibility. 
E)  is an index of dispersion.

Question 2

-What proportion of the variability in the data is accounted for by the two factor solution?

Accepted Answer

A)  51% 
B)  100% 
C)  78% 
D)  27% 
E)  more information is needed 
A)  51% 
B)  100% 
C)  78% 
D)  27% 
E)  more information is needed

Question 3

To determine the "hit rate" in a matrix of actual vs. predicted classifications, the analyst should focus most of his/her attention on the

Accepted Answer

A)  individual column totals. 
B)  individual row totals. 
C)  both the individual column and row totals. 
D)  total number of subjects in the diagonal of the matrix. 
E)  average of the column totals. 
A)  individual column totals. 
B)  individual row totals. 
C)  both the individual column and row totals. 
D)  total number of subjects in the diagonal of the matrix. 
E)  average of the column totals.

Question 4

The following questions focus on Multidimensional Scaling:
-Which of the following are not methods for naming underlying dimensions in multidimensional scaling?

Accepted Answer

A)  After subjects have evaluated objects in terms of defined attributes, the researcher can correlate the attribute scale scores for each object with the coordinates for each object in the perceptual map. 
B)  Managers may use their experience to interpret the dimensions. 
C)  Researchers may attempt to relate the dimensions to actual attributes of the objects under study. 
D)  Researchers may name the resulting dimensions based on a priori hypotheses. 
E)  All of the above are methods for naming dimensions in MDS. 
A)  After subjects have evaluated objects in terms of defined attributes, the researcher can correlate the attribute scale scores for each object with the coordinates for each object in the perceptual map. 
B)  Managers may use their experience to interpret the dimensions. 
C)  Researchers may attempt to relate the dimensions to actual attributes of the objects under study. 
D)  Researchers may name the resulting dimensions based on a priori hypotheses. 
E)  All of the above are methods for naming dimensions in MDS.

Question 5

The cutting score in a discriminant analysis is the score that

Accepted Answer

A)  divides the mean discriminant scores. 
B)  determines which discriminant functions are statistically significant. 
C)  determines which discriminant coefficients are statistically significant. 
D)  is used as a guide to classify subjects. 
E)  is a and d above. 
A)  divides the mean discriminant scores. 
B)  determines which discriminant functions are statistically significant. 
C)  determines which discriminant coefficients are statistically significant. 
D)  is used as a guide to classify subjects. 
E)  is a and d above.

Question 6

Once the discriminant function has been produced, the researcher's next step is to:

Accepted Answer

A)  begin interpretation of the function by examining the discriminant coefficients 
B)  check the statistical significance of the function 
C)  standardize the discriminant coefficients 
D)  classify individuals using the discriminant function 
E)  none of the above 
A)  begin interpretation of the function by examining the discriminant coefficients 
B)  check the statistical significance of the function 
C)  standardize the discriminant coefficients 
D)  classify individuals using the discriminant function 
E)  none of the above

Question 7

When making a decision as to how many factors to retain in the final factor analysis solution, the researcher should

Accepted Answer

A)  examine the size of the latent roots. 
B)  plot the size of the latent roots against the number of factors. 
C)  examine the amount of covariability recovery. 
D)  examine the amount of variability recovery. 
E)  all of the above. 
A)  examine the size of the latent roots. 
B)  plot the size of the latent roots against the number of factors. 
C)  examine the amount of covariability recovery. 
D)  examine the amount of variability recovery. 
E)  all of the above.

Question 8

-For which pair of variables is the estimated original correlation the highest?

Accepted Answer

A)  inactivity and aggressiveness 
B)  inactivity and ambition 
C)  aggressiveness and stress 
D)  aggressiveness and ambition 
E)  stress and ambition 
A)  inactivity and aggressiveness 
B)  inactivity and ambition 
C)  aggressiveness and stress 
D)  aggressiveness and ambition 
E)  stress and ambition

Question 9

To test whether the cluster results offer a reasonable summary of the similarity, correlation, or distance matrix, that is, are the individual clusters sufficiently homogeneous and is the system as a whole consistent with the input similarities, the following procedure(s) can be performed:

Accepted Answer

A)  the variables used to determine the clusters can be tested to determine if the clusters have statistically different values across the groups. 
B)  the reliability of the estimates can be assessed by splitting the data into multiple subsets and assessing whether the same clusters are produced when the subsets are analyzed. 
C)  significance tests can be performed that compare the clusters on variables not used to generate the solution. 
D)  All of the above procedures are correct. 
E)  Both b and c are correct. 
A)  the variables used to determine the clusters can be tested to determine if the clusters have statistically different values across the groups. 
B)  the reliability of the estimates can be assessed by splitting the data into multiple subsets and assessing whether the same clusters are produced when the subsets are analyzed. 
C)  significance tests can be performed that compare the clusters on variables not used to generate the solution. 
D)  All of the above procedures are correct. 
E)  Both b and c are correct.

Question 10

A factor loading is typically assumed to be significant if its value is in the neighborhood of

Accepted Answer

A)  .20 to .25. 
B)  .25 to .30. 
C)  .30 to .35. 
D)  .35 to .40. 
E)  .40 to .45. 
A)  .20 to .25. 
B)  .25 to .30. 
C)  .30 to .35. 
D)  .35 to .40. 
E)  .40 to .45.

Question 11

Which of the following statements is NOT true regarding cluster analysis?

Accepted Answer

A)  Different methods of cluster analysis can produce different results. 
B)  There is consensus on which method of cluster analysis is best under all circumstances. 
C)  Nodal methods of factor analysis involve the selection of an object or objects to serve as focal points for the clusters. 
D)  The average linkage method works better than the other hierarchical method of cluster analysis. 
E)  Cluster analysis seeks to identify natural groupings of objects given the multivariate nature of the data. 
A)  Different methods of cluster analysis can produce different results. 
B)  There is consensus on which method of cluster analysis is best under all circumstances. 
C)  Nodal methods of factor analysis involve the selection of an object or objects to serve as focal points for the clusters. 
D)  The average linkage method works better than the other hierarchical method of cluster analysis. 
E)  Cluster analysis seeks to identify natural groupings of objects given the multivariate nature of the data.

Question 12

-Use the traditional eigenvalue test to determine the number of factors that should be retained in the factor analysis. How many factors should be retained?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5 
A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 13

Which of the following is NOT one of the quantities used to assess the relative importance of variables in discriminating between groups in discriminant analysis?

Accepted Answer

A)  the mean differences of the groups on each variable 
B)  the discriminant coefficients 
C)  the pairwise correlations between the variable and the discriminant score 
D)  the standardized coefficients 
E)  Both b and c are not quantities used to assess the relative importance of variables in discriminating between groups. 
A)  the mean differences of the groups on each variable 
B)  the discriminant coefficients 
C)  the pairwise correlations between the variable and the discriminant score 
D)  the standardized coefficients 
E)  Both b and c are not quantities used to assess the relative importance of variables in discriminating between groups.

Question 14

(Use the information below to answer the next three questions.)
In a five variable two group discriminant analysis, the following weights were derived: VS1U1B11S1U1B0 = .561, VS1U1B12S1U1B0 = .030, VS1U1B13S1U1B0 = .049, VS1U1B14S1U1B0 = .701, VS1U1B15S1U1B0 = -.021. The corresponding pooled standard deviations are SS1U1B11S1U1B0 = 4.60, SS1U1B12S1U1B0 = 1.23, SS1U1B13S1U1B0 = 10.40, SS1U1B14S1U1B0 = 13.23, and SS1U1B15S1U1B0 = 8.30. For individual 1, the values for the four variables were XS1U1B11S1U1B0 = 10, XS1U1B12S1U1B0 = 3, XS1U1B13S1U1B0 = 25, XS1U1B14S1U1B0 = 36, and XS1U1B15S1U1B0 = 42.
-Individual 1's standardized discriminant score is

Accepted Answer

A)  363.08. 
B)  365.21. 
C)  372.53. 
D)  380.47. 
E)  392.03. 
A)  363.08. 
B)  365.21. 
C)  372.53. 
D)  380.47. 
E)  392.03.

Question 15

Which of the following is NOT a key decision that needs to be made when factor analyzing data?

Accepted Answer

A)  What is the dependent variable? 
B)  Should factor analysis be applied to the data? 
C)  Which factor model should be used? 
D)  Should the initial solution be rotated? 
E)  All of the above are key decisions that need to be made when factor analyzing data. 
A)  What is the dependent variable? 
B)  Should factor analysis be applied to the data? 
C)  Which factor model should be used? 
D)  Should the initial solution be rotated? 
E)  All of the above are key decisions that need to be made when factor analyzing data.

Question 16

Principal components factor analysis seeks to

Accepted Answer

A)  transform a set of interrelated variables into a set of unrelated linear combinations of these variables. 
B)  choose the set of linear combinations so that each factor accounts for an increasing proportion of the variance in the original variables. 
C)  choose the set of linear combinations so that the factors are uncorrelated with each other. 
D)  a and b. 
E)  a and c. 
A)  transform a set of interrelated variables into a set of unrelated linear combinations of these variables. 
B)  choose the set of linear combinations so that each factor accounts for an increasing proportion of the variance in the original variables. 
C)  choose the set of linear combinations so that the factors are uncorrelated with each other. 
D)  a and b. 
E)  a and c.

Question 17

The square of a factor loading indicates

Accepted Answer

A)  the proportion of variation accounted for by the factor. 
B)  the proportion of variation in the variable accounted for by the complete set of possible factors. 
C)  the proportion of variation shared by one pair of variables. 
D)  the proportion of variation in the variable shared by all variables in the analysis. 
E)  none of the above. 
A)  the proportion of variation accounted for by the factor. 
B)  the proportion of variation in the variable accounted for by the complete set of possible factors. 
C)  the proportion of variation shared by one pair of variables. 
D)  the proportion of variation in the variable shared by all variables in the analysis. 
E)  none of the above.

Question 18

(Use the information below to answer the next three questions.)
In a five variable two group discriminant analysis, the following weights were derived: VS1U1B11S1U1B0 = .561, VS1U1B12S1U1B0 = .030, VS1U1B13S1U1B0 = .049, VS1U1B14S1U1B0 = .701, VS1U1B15S1U1B0 = -.021. The corresponding pooled standard deviations are SS1U1B11S1U1B0 = 4.60, SS1U1B12S1U1B0 = 1.23, SS1U1B13S1U1B0 = 10.40, SS1U1B14S1U1B0 = 13.23, and SS1U1B15S1U1B0 = 8.30. For individual 1, the values for the four variables were XS1U1B11S1U1B0 = 10, XS1U1B12S1U1B0 = 3, XS1U1B13S1U1B0 = 25, XS1U1B14S1U1B0 = 36, and XS1U1B15S1U1B0 = 42.
-Which variable is least important in discriminating between the two groups?

Accepted Answer

A)  X1 
B)  X2 
C)  X3 
D)  X4 
E)  X5 
A)  X1 
B)  X2 
C)  X3 
D)  X4 
E)  X5

Question 19

Rotation of the original factor analysis solution typically results in

Accepted Answer

A)  an improved substantive interpretation of the solution. 
B)  a change in the achieved communality estimate for any one variable. 
C)  a change in the proportion of variance accounted for by any one factor. 
D)  a and b above. 
E)  a and c above. 
A)  an improved substantive interpretation of the solution. 
B)  a change in the achieved communality estimate for any one variable. 
C)  a change in the proportion of variance accounted for by any one factor. 
D)  a and b above. 
E)  a and c above.

Question 20

Varimax rotation of a factor solution attempts to

Accepted Answer

A)  maintain the right angles between the factors. 
B)  enhance the substantive interpretation of the unrotated factor solution. 
C)  force the entries in the columns of the factor loading matrix to be near 0 or 1. 
D)  all of the above. 
E)  a and b above. 
A)  maintain the right angles between the factors. 
B)  enhance the substantive interpretation of the unrotated factor solution. 
C)  force the entries in the columns of the factor loading matrix to be near 0 or 1. 
D)  all of the above. 
E)  a and b above.

Exam 18: Multivairate Data Analysis: Discriminant Analysis, Factor Analysis, Cluster Analysis, and Multidimensional Scaling

The following questions focus on Multidimensional Scaling: -Kruskal's stress

-What proportion of the variability in the data is accounted for by the two factor solution?

To determine the "hit rate" in a matrix of actual vs. predicted classifications, the analyst should focus most of his/her attention on the

The following questions focus on Multidimensional Scaling: -Which of the following are not methods for naming underlying dimensions in multidimensional scaling?

The cutting score in a discriminant analysis is the score that

Once the discriminant function has been produced, the researcher's next step is to:

When making a decision as to how many factors to retain in the final factor analysis solution, the researcher should

-For which pair of variables is the estimated original correlation the highest?

To test whether the cluster results offer a reasonable summary of the similarity, correlation, or distance matrix, that is, are the individual clusters sufficiently homogeneous and is the system as a whole consistent with the input similarities, the following procedure(s) can be performed:

A factor loading is typically assumed to be significant if its value is in the neighborhood of

Which of the following statements is NOT true regarding cluster analysis?

-Use the traditional eigenvalue test to determine the number of factors that should be retained in the factor analysis. How many factors should be retained?

Which of the following is NOT one of the quantities used to assess the relative importance of variables in discriminating between groups in discriminant analysis?

Which of the following is NOT a key decision that needs to be made when factor analyzing data?

Principal components factor analysis seeks to

The square of a factor loading indicates

Rotation of the original factor analysis solution typically results in

Varimax rotation of a factor solution attempts to

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Research Design, Exploratory Research, and Qualitative Data

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Data Collection: Secondary Data

Data Collection: Primary Data

Questionnaires and Data Collection Forms

Attitude Measurement

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Sampling Procedures

Sample Size

Collecting the Data: Field Procedures and Nonsampling Error

Data Analysis: Preliminary Steps

Appendix 14: Chi-Square Tests

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Data Analysis: Examination of Differences

Appendix 16 A: Analysis of Variance

Data Analysis: Investigation of Association

Appendix: More Multivariate Statistical Techniques

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