Discriminant, Factor and Cluster | Test Bank + Answers Ch.20

Test Bank

CHAPTER 20 Discriminant, Factor and Cluster Analysis

True-False

1. Discriminant analysis techniques are used to classify into one of

two or more alternate groups based on a set of measurements.

2. Discriminant analysis can only be used for description and not for

prediction purposes.

3. The statistical explanation for discriminant analysis is that of

maximizing the between-group variance relative to the within-group variance.

4. The group mean, in a discriminant analysis, is known as the centroid.

5. The underlying assumption in a discriminant analysis is that the

independent variables are assumed to be normally distributed.

6. The objective of a discriminant analysis is to predict the value of

the dependent variable based on the values of the fixed independent variables.

7. Larger values of Wilks lambda indicate that the group means appear

to be different.

8. In discriminant analysis, predictors with a large coefficient

contribute more to the discriminating power of the function.

9. In discriminant analysis, with 'm' groups and 'p' predictor

variables, min (p,m-1) gives the number of discriminant functions.

10. Discriminant analysis involves the maximization of the between-group variance

relative to the within-group variance

11. Regression and Discriminant analyses are computationally similar

12. Factor analysis is usefully employed when there is a need to

determine the direction of causality between two or three variables.

1. Factor analysis is usefully employed when it is desirable to combine

several questions, thereby creating a new variable.

14. The cutoff score is the criterion (score) against which each individual’s discriminant

score is judged to determine into which group the individual should be classified

15. A factor is a variable or construct that is not directly observable

but needs to be inferred from the input variables.

16. One function of factor analysis is to identify underlying constructs in the data.

17. A factor score is a measurement of how closely related each input

variable is to a derived factor.

18. Each respondent has a factor score on each factor in addition to the

respondent's rating on the original variables.

19. Factor loadings are a measurement of the correlations between the

factors and the original variables.

20. One rule of thumb in deciding on the number of factors to retain is

to include all factors that explain at least 50 percent of the variance.

21. Communality is the percent of a variable's variance which

contributes to the correlation with other variables or is common to other variables.

22. 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.

23. Rotation of factors changes the interpretation of the factors while

retaining the principal component patterns of loadings.

24. In both principal components analysis and varimax rotation, the

factors are constrained to be uncorrelated or geometrically perpendicular.

25. Varimax searches for a set of factor loadings such that each factor

has some loadings close to 0 and some loadings close to -1 or +1.

Factor Loadings

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

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

28. An attractive feature of principal components analysis is the easy

interpretability of the factors.

29. 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.

30. All factor analysis methods constrain the factors to be uncorrelated.

31. Common factor analysis focuses on shared variance, hence communalities are used

in the diagonal of the matrix

32. 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).

33. 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.

34. Factor loadings and correlations are identical if each variable has

its mean subtracted and is divided by its standard deviation.

35. 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.

36. The basic task in cluster analysis is to uncover competing

explanations for a causal phenomenon.

37. In the hierarchical approach, the commonly used methods are single

linkage, complete linkage, average linkage, Ward’s method, and the centroid method.

38. Consider the following data:

The following is an accurate graphical representation of the data shown above:

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

40. 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.

41. 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.

42. A major advantage of cluster analysis is the availability of standard statistical tests

to ensure that the output does not represent pure randomness.

43. Given multivariate data, cluster analysis techniques seek to

identify natural groupings of objects.

44. Nonhierarchical clustering will produce tighter clusters due to the fact that an object

will be admitted into a cluster only if it improves the clustering criterion.

45. Factor is observable that is why it is a variable.

Multiple Choice

1. Which of the following statements is not true of Wilks’ Lamba?
2. it is the ratio of within-group variance to total variance
3. it takes values between 0 and 1
4. larger values indicate that group means do not appear to be different
5. none of the above
6. The simple correlation between the independent variable and the discriminant function is

represented by

1. discriminant loading
2. structure correlation
3. total correlation matrix
4. centroid
5. For discrimination to be based on all predictors the most appropriate function

estimation method is

1. sequential
2. direct
3. pooled
4. stepwise

4. The analysis technique used to identify variables that contribute to

differences in the a prior defined groups is

a. regression.

b. discriminant analysis.

c. conjoint analysis.

d. factor analysis.

5. Which one of the following is not an objective of discriminant analysis?

a. Determining linear combinations of the predictor variables to separate groups

b. Developing procedures for assigning new objects

c. Determining the variables that explain the intergroup differences

d. Predicting the level of the dependent variable when the independent variable is changed.

6. In discriminant analysis, with M groups and p predictor variables,

the number of discriminant functions is given by

a. (m-1, p-1)

b. (m-1, p)

c. (m, p-1)

d. (m, p)

7. If the primary purpose is data reduction one would use

1. cluster analysis
2. factor analysis
3. discriminant analysis
4. conjoint analysis

8. The amount of variance a variable shares with other variables is called

1. communality
2. factor loading
3. factor score
4. none of the above

9. A plot of eigenvalues against the number of factors is called

1. factor loading
2. scree
3. factor score
4. communality

10. Which of the following methods of clustering uses the “nearest neighbor” approach?

1. complete linkage
2. single linkage
3. Ward’s method
4. average linkage

11. In factor analysis each subsequent factor accounts for

1. increasing amount of variance in data
2. decreasing amount of variance in data
3. same amount of variance in data
4. none of the above

12. Initial starting points in nonhierarchical clustering is represented by

1. cluster membership
2. cluster seeds
3. cluster centurions
4. none of the above

13. All of the following are true about factor analysis except

a. it is a technique that serves to combine questions, thereby creating new variables.

b. it is an analysis of interdependence technique that analyzes the

interdependence between questions, variables, or objects.

c. it can help the analyst determine which questions, variables, or

objects are redundant and what they are measuring.

d. all of these are true

14. Which of the following is not true about cluster analysis?

a. it is a technique for grouping individuals or objects into unknown groups.

b. there are two approaches to clustering- hierarchical and nonhierarchical.

c. the centroid – the average value of the objects in a cluster on each of the variables making up each object’s profile - is used to describe the clusters.

d. there is a single approach to determining the appropriate number of clusters

15. Consider the following:

Which of the following statements is true?

a. Factor 1 is composed of variables 1 and 2.

b. Factor 1 is composed of variables 1, 2, and 4.

c. Factor 1 is composed of variables 3 and 5.

d. Factor 2 is composed of variables 1, 2, and 4.

16. The basic assumption of cluster analysis is that

1. It is always possible to group data into well-defined homogeneous groups.

2. The basic measurement of similarity is a valid

measurement of proximity between objects.

3. There is theoretical justification for structuring the objects into clusters.

a. 1

b. 2

c. 1 and 2

d. 2 and 3

17. Which of the following is a valid approach to clustering?

1. "Top-down" hierarchical clustering
2. "Top-down" nonhierarchical clustering
3. Piecewise linear clustering
4. "Bottom-up" nonhierarchical clustering

18. Which of the following statements are true of the hierarchical approach?

1. The approach is relatively easy to read and interpret.
2. The output has the logical structure that should theoretically always exist.
3. The subsequent analysis is constrained by the first combination or separation of objects.
4. It tends to be more reliable.
5. Split-sample results will tend to look more similar.

a. I and II.

b. I, II, III, and V.

c. I, IV, and V.

d. I, II and III.

19. The coefficients that link the factors to the variables are called

• 1. factor loadings
  2. screes
  3. factor scores
  4. eigenvalues

20. The amount of variance in the original variables that is associated with a factor

is represented by

1. factor loading
2. scree
3. factor score
4. eigenvalue