Correlation Techniques

Question 1

____ ____ are used to describe the degree of association between two or more variables (or, put another way, the degree to which two or more variables co-vary) and are often used to ____ ____ about ____ ____ or ____ of ____ based on ____ or ____ on ____ ____ or ____ of ____.

Answer 1

Correlational Techniques; Make Predictions; One Variable or Set of Variables; Status or Performance; Another Variable or Set of Variables

Question 2

The psychologist in Study #3, for example, could calculate a correlation coefficient for product knowledge test scores and yearly sales and then, if the coefficient is sufficiently large, use a regression equation to predict the future sales of job applicants from their scores on the product knowledge test. When correlational techniques are used for the purpose of ____, the X (independent) variable is often referred to as the ____, while the Y (dependent) variable is called the ____. Correlational techniques are divided into two basic types — ____ and ____.

Answer 2

Prediction; Predictor; Criterion; Bivariate and Multivariate

Question 3

____ ____ techniques are used to describe or summarize the degree of association between two variables and include ____ and ____ ____.

Answer 3

Bivariate Correlation; Scattergrams and Correlation Coefficients

Question 4

____: The degree of association for two variables can be depicted in a ____, which is also known as a scatter diagram or scatterplot. In a scattergram, the X (predictor) variable is placed on the ____ ____, while the Y (criterion) variable is located on the ____ ____. In Study #3, if product knowledge is measured with a 10-item test and sales success is measured in terms of dollar amount of sales, the product knowledge and sales success of 35 salespeople could be presented.

Answer 4

Scattergrams; Scattergram; Horizontal Axis; Vertical Axis

Question 5

Each data point in the scattergram corresponds to the two scores obtained by a single person. When data points are widely scattered, this means that the variables have a ____ ____. Conversely, when there is a narrow scatter of data points, this indicates a ____ ____.

Answer 5

Weak Relationship; Strong Relationship

Question 6

A ____ ____ summarizes the degree of association between variables with a single number. As indicated in Table 5, there are several correlation coefficients, and the selection of a coefficient is based on the ____ of ____ of the ____ being ____.

Answer 6

Correlation Coefficient; Scale of Measurement; Variables; Correlated

Question 7

Correlation Coefficients

Answer 7

Pearson r; Spearman rho; Point Biserial; Biserial; Eta

Question 8

The Pearson r and correlation coefficients derived from it range in value from __ to __. The magnitude of the coefficient indicates the ____ ____. The closer the coefficient is to __ or __, the ____ the ____. The sign of the correlation coefficient (+ or -) indicates the ____ ____. When there is a positive (direct) correlation between X and Y, the value of Y ____ as the value of X ____. Conversely, when there is a negative (inverse) correlation, the value of Y ____ as the value of X ____.

Answer 8

-1.0 to +1.0; Relationship’s Strength; -1.0 or +1.0; Stronger the Relationship; Relationship’s Direction; Increases; Increases; Decreases; Increases

Question 9

____: Use of the Pearson r and most other correlation coefficients require that ____ ____ be met. Violation of one or more of these assumptions can produce an ____ or ____ ____ ____.

Answer 9

Assumptions; Three Assumptions; Inaccurate or Misleading Correlation Coefficient

Question 10

____: The first assumption is that there is a ____ ____ ____ the ____. In other words, in a scattergram, the relationship between X and Y can be summarized by a ____ ____. If the relationship is nonlinear, the Pearson r will ____ the ____ of ____.

Answer 10

Linearity; Linear Relationship Between the Variables; Straight Line; Underestimate the Degree of Association

Question 11

____ ____: The second assumption is that there is an ____ ____ of ____ on ____ ____. This means that the data have been collected from people who are ____ regarding the ____ ____ by _ and _. If there is a restriction in range (if the people are homogeneous), the Pearson r is likely to be an ____.

Answer 11

Unrestricted Range; Unrestricted Range of Scores on Both Variables; Heterogeneous; Characteristics Measured by X and Y; Underestimate

Question 12

____: The third assumption is that the range of Y scores is about the same for ____ ____ of _ — i.e., that there is ____. For example, if the range of Y scores is 10 at low values of X, the range should also be about 10 at moderate and high values of X. The difference between homoscedasticity and heteroscedasticity is illustrated in Figure. Violation of the assumption of homoscedasticity does not necessarily result in a coefficient that is too low or too high but produces a coefficient that does not represent the ____ ____ of ____.

Answer 12

Homoscedasticity; All Values of X; Homoscedasticity; Full Range of Scores

Question 13

You might encounter a question that asks what it means when “the range of Y scores at every value of X is equal to the total range of Y scores. “ This statement [s similar to the first sentence in the above description of homoscedasticity, but it is not identical to that sentence. Both describe homoscedasticity, but this statement refers to a particular kind of homoscedasticity that occurs when there Is either a very wide scatter of data points in the scatterplot or when all of the data points fall on a horizontal line. The answer to this question is that it means that there is a _ (or ____ _) ____ ____.

Answer 13

0 (or Near 0) Correlation Coefficient

Question 14

____ of a ____ ____: A correlation coefficient can be interpreted in several ways.

Answer 14

Interpretation of a Correlation Coefficient

Question 15

____ of ____: A correlation coefficient can be interpreted directly in terms of ____ of ____. The closer the coefficient is to either -1.0 or + 1.0, the ____ the ____ ____ ____; the closer it is to 0, the ____ the ____.

Answer 15

Degree of Association; Degree of Association; Stronger the Association Between Variables; Weaker the Association

Question 16

Note that the correlation coefficient is sometimes erroneously interpreted in terms of causality. However, it is the ____ ____ that permits causal inferences, not the way in which the data are analyzed or described. When a ____ ____ ____ has been conducted, a researcher can infer a cause-effect relationship when the correlation coefficient is sufficiently large. However, a large coefficient alone does not mean that variability in one variable ____ variability in the other variable.

Answer 16

Research Method; True Experimental Study; Causes

Question 17

____ of ____: Whenever a correlation coefficient represents the degree of association between two different variables, it can be squared to obtain a ____ of ____, which provides a measure of ____ ____. Put another way, the squared correlation coefficient indicates the proportion of variability in Y that is ____ ____, or ____ ____ ____, variability in X. For example, if the correlation coefficient for sales success and product knowledge is .60, then 36% (.60 squared = .36) of variability in sales success is accounted for by product knowledge. The remaining 64% is ____ ____, which might be due to such factors as attitude toward the company, work-related motivation, previous sales experience, and sales territory.

Answer 17

Coefficient of Determination; Coefficient of Determination; Shared Variability; Explained by; Accounted For By; Unexplained Variability

Question 18

Keep in mind that a bivariate correlation coefficient should be ____ to obtain a measure of shared variability only when it indicates the ____ of ____ ____ ____ ____ ____. As noted in the Test Construction chapter, when a correlation coefficient is a ____ ____, which is the correlation of a measure with itself, the coefficient is ____ ____. Instead, it is interpreted directly as a measure of “____ ____ ____.” The ____ of a correlation coefficient indicates whether it is a coefficient for two different variables or a single variable: If the subscript contains two different letters or numbers (e.g., “xy”), it represents the correlation between ____ ____ ____. When the subscript contains the same letters or numbers (e.g., “xx”), it is a ____ ____.

Answer 18

Squared; Degree of Association Between Two Different Variables; Reliability Coefficient; Never Squared; True Score Variability; Subscript; Two Different Variables; Reliability Coefficient

Question 19

____ ____: Correlation coefficients can be evaluated to determine if they are statistically significant by comparing the ____ ____ to the ____ ____ ____. The magnitude of the critical value is determined by ____ (the level of significance) and the ____ ____. The smaller the sample, the ____ the ____ ____ must be to be ____ ____. For example, when the level of significance is .05 and the number of observations is 10, the correlation coefficient must be at least .63 to be statistically significant. In contrast, when the number of observations is 50, a correlation of only .28 is significant.

Answer 19

Hypothesis Testing; Obtained Coefficient; Appropriate Critical Value; Alpha; Sample Size; Larger the Correlation Coefficient; Statistically Significant

Question 20

____ ____: Investigators are often interested in correlation because their goal is to use a ____ to ____ or ____ ____ on a ____. ____ ____ is the technique that allows such predictions to be made when there is one predictor (X) and one criterion (Y). An assumption underlying regression analysis is that there is a ____ ____ ____ _ and _, and, therefore, that the relationship can be described by a ____ ____. The scattergram for product knowledge test scores and dollar amount of sales (Figure 13) reveals that there is a linear relationship between these variables, and, Consequently, their relationship can be described by a ____ ____ (“line of best fit”).

Answer 20

Regression Analysis; Predictor to Predict or Estimate Performance on a Criterion; Regression Analysis; Linear Relationship Between X and Y; Straight Line; Regression Line

Question 21

The technique used to locate the regression line in a scatterplot is referred to as the ____ ____ ____, which locates the line so that the amount of error in prediction is minimized. The regression line or its formula (the regression equation) is then used to make ____ ____ _ ____ on ____ on _.

Answer 21

Least Squares Criterion; Predictions About Y Based on Information on Y

Question 22

Example: The psychologist in Study #3 assesses the degree of association between product knowledge and yearly sales by administering the product knowledge test to a sample of 35 current salespeople and determining each salesperson’s sales for the previous year from employment records. The correlation coefficient for test scores and sales is statistically significant, so the psychologist decides to use regression analysis to facilitate hiring decisions in the future. She does this by using the ____ ____ to predict the yearly sales of job applicants from their product knowledge test score.

Answer 22

Regression Equation

Question 23

The degree of predictive accuracy when using a regression equation is directly related to the ____ of the ____ ____. Unless the coefficient is equal to + 1.0 or —1.0, there will be some ____ in ____. Consequently, the standard error of estimate is used to construct a ____ ____ around a predicted _ ____ so that the score is not “____.” (The standard error of estimate and confidence intervals are described in the Test Construction chapter.)

Answer 23

Magnitude of the Correlation Coefficient; Error in Prediction; Confidence Interval; Y Score; Overinterpreted

Question 24

Correlational techniques are used to determine the degree of (1) ____ between two or more variables and to make predictions about status or score(s) on one or more criteria based on status or score(s) on one or more (2) ____. A scattergram illustrates the relationship between two variables. The wider the scatter of data points in the scattergram, the (3) ____ the correlation between the variables.

Answer 24

(1) association; (2) predictors; (3) lower

Question 25

A correlator coefficient is a number that indicates the average degree of association between variables. The choice of a coefficient is based primarily on the scale of measurement of the variables being correlated. For example, the Pearson r is used when both variables are measured on a(n) (4) ____ scale, while (5) ____ is used when both variables are ranks. The (6) ____ correlation coefficient is appropriate when one variable is a true dichotomy and the other is measured on an interval or ratio scale, and the (7) ____ correlation coefficient is appropriate when one variable is an artificial dichotomy and the other is measured on an interval or ratio scale.

Answer 25

(4) interval or ratio; (5) Spearman rho; (6) point biserial; (7) biserial

Question 26

The Pearson r and coefficients derived from it range in value from (8) ____. The magnitude of the coefficient indicates the (9) ____ of the relationship, while the sign indicates its (10) ____. Use of the Pearson r is based on three assumptions: First, there must be a (11) ____ relationship between variables; second, there must be an (12) ____ range of scores on both variables; and, third, there must be (13) or the same range of Y scores at every value of X.

Answer 26

(8) —1.0 to + 1.0; (9) strength; (10) direction; (11) linear; (12) unrestricted; (13) homoscedasticity

Question 27

A large correlation coefficient for two variables alone cannot be interpreted as evidence of a(n) (14) ____ relationship between X and Y but can be interpreted in terms of shared variability. This is done by (15) ____ the correlation coefficient. For example, if the correlation coefficient for X and Y is.30, this means that (16) ____% of variability in Y is explained by variability in X.

Answer 27

(14) casual; (15) squaring; (16) 9

Question 28

Regression analysis is the technique that makes it possible to use a predictor (X) score to predict or estimate a (17) ____ (Y) score. An assumption underlying the use of regression analysis is that the relationship between X and Y can be described by a (18) ____. The position of the regression line in a scattergram is identified using the (19) ____ criterion, which locates the regression line so that error in prediction is minimized.

Answer 28

(17) criterion; (18) straight line; (19) least squares

Question 29

The term “____ ____” is applied to a variety of techniques that are used to investigate the relationships among three or more variables. One approach to categorizing these techniques distinguishes between ____ and ____ ____: ____ ____ are used when a distinction is made between independent and dependent variables (predictors and criteria) and the former will be used to predict or estimate status on the latter. This category includes techniques for ____ ____ and for ____ ____ ____ or ____. ____ ____ are used when a distinction is not made between independent and dependent variables and include several ____ ____ ____.

Answer 29

Multivariate Technique; Dependence and Interdependence Techniques; Dependence Methods; Making Predictions; Testing Causal Methods or Theories; Interdependence Methods; Data Reduction Techniques

Question 30

Techniques for testing causal models and theories are described in Section C, and data reduction techniques are described in Section D. In this section, multivariate techniques for making predictions are addressed. The primary considerations when choosing a technique for this purpose are the ____ of ____ of the ____ and ____ ____ and the ____ of ____ ____.

Answer 30

Scale of Measurement of the Predictor and Criterion Variables and the Number of Criterion Variables

Question 31

____ ____ is the appropriate multivariate technique when two or more continuous or discrete predictors will be used to predict status on a single continuous criterion. The use of multiple regression is based on the assumption that the relationships between variables is ____ (although adaptations of multiple regression for nonlinear relationships are available).

Answer 31

Multiple Regression; Linear

Question 32

The output of a multiple analysis is a ____ ____ ____ and a ____ ____ ____. The multiple correlation coefficient (R) indicates the ____ of ____ between the ____ and a ____ ____ of the ____; and, like the correlation coefficient for two variables, R can be squared to obtain a measure of ____ ____. The multiple regression equation is an extension of the regression equation and permits prediction of a person’s score on the criterion based on a ____ ____ of their ____ on ____ or ____ ____.

Answer 32

Multiple Correlation Coefficient; Multiple Regression Equation; Degree of Association; Criterion and a Linear Combination; Predictors; Shared Variability; Linear Combination; Scores on Two or More Predictors

Question 33

The sigi (+ or -) of the regression coefficient (b) for each predictor indicates whether the relationship between the ____ and ____ is ____ or ____, and the magnitude of each predictor’s coefficient is determined by a combination of two factors — the ____ of the ____ between the ____ and the ____ and the ____ of the ____ between the ____ and ____ ____ ____. The optimal situation (and the situation that yields the largest and most easily interpretable regression coefficients) is for each predictor to have a ____ ____ with the ____ and ____ ____ with the ____ ____.

Answer 33

Predictor and Criterion is Positive or Negative; Magnitude of Correlation; Predictor; Criterion; Magnitude; Correlation; Predictor and Every Other Predictor; High Correlation; Criterion and Low Correlations; Other predictors

Question 34

A high correlation between two or more predictors is referred to as multicollinearity and is undesirable for at least two reasons: First, the presence of ____ means that the predictors are providing ____ ____. Second, when predictors are highly correlated, the magnitude of a regression coefficient is not ____ to the ____ between the ____ and ____, which makes it difficult to interpret the ____ ____.

Answer 34

Multicollinearity; Redundant Information; Proportional; Correlation; Predictor and Criterion; Interpret the Regression Coefficients

Question 35

Example: The psychologist in Study #3 administers measures of product knowledge, attitude toward the company, and interpersonal assertiveness to 50 current salespeople and determines each salesperson’s sales for the previous year from employment records. She finds that there is a strong correlation between each predictor and the criterion and that the correlations between the predictors are low and, therefore, decides to use the ____ ____ ____ to facilitate hiring decisions in the future. She does this by using the equation to predict the yearly sales of job applicants from their scores on the measures of product knowledge, attitude toward the company, and interpersonal assertiveness.

Answer 35

Multiple Regression Equation

Question 36

____ of ____ ____: The most basic form of multiple regression is called ____ (____) ____ and entails analyzing the effects of all of the predictors on the criterion at once. Another form is ____ ____, which can be either “forward” or “backward.” In ____ (____-____) ____, one predictor is added in each subsequent analysis; in ____ (____-____) ____, the analysis begins with all predictors and one predictor is eliminated in each subsequent analysis. The goal of stepwise regression is to explain the ____ ____ of ____ in the ____ using the ____ ____ of ____. When using this method, the decision to add or subtract a predictor is based on the resulting change in the ____ of _-____.

Answer 36

Types of Multiple Regression; Simultaneous (Simple) Regression; Stepwise Regression; Forward (Step-Up) Regression; Backward (Step-Down) Regression; Greatest Amount of Variability; Criterion; Fewest Number of Predictors; Size of R-Squared

Question 37

____ ____ ____ ____ of ____: Multiple regression is often used instead of the analysis of variance, and it is particularly useful when groups are ____ in ____ since this condition can reduce both the ____ and ____ of the ___. Multiple regression is also useful when the IVs are measured on a ____ ____ because the ANOVA requires continuous data to be converted to ____, which also reduces ____. Another advantage of multiple regression over the ANOVA is that it permits a researcher to ____ or ____ ____ ____ (predictors) to the ____ to determine which subset of variables best explains ____ in the ____ ____ (criterion).

Answer 37

Multiple Regression Versus Analysis of Variance; Unequal in Size; Power and Robustness of the ANOVA; Continuous Scale; Categories; Power; Add or Subtract Independent Variables; Analysis; Variability in the Dependent Variable

Question 38

____-____: Whenever a multiple correlation coefficient and multiple regression equation are ____-____ (tried out) on another sample, the size of the correlation coefficient tends to “shrink” and the predictive accuracy of the regression equation decreases ____ occurs because the regression weights, which are used in the calculation of R as well as in the regression equation, were derived from the original sample and do not “fit” the new sample as well since the same chance factors operating in the original sample are not present in subsequent samples. Shrinkage is greatest when the original sample was ____ and the number of ____ is ____.

Answer 38

Cross-Validation; Cross-Validation; Shrinkage; Small; Predictors is Large

Question 39

____ ____ is an extension of multiple regression that is used when two or more continuous predictors are to be used to predict status on two or more continuous criteria. It would be the appropriate technique if the psychologist in Study #3 wants to use measures of interpersonal assertiveness, attitude toward the company, and previous experience to predict status on several different measures Of job performance such as yearly sales, number of new customers, and level of customer satisfaction. Canonical correlation can also be used to identify the number and nature of the underlying dimensions that account for the ____ ____ ____ ____ of ____.

Answer 39

Canonical Correlation; Correlation Between Two Sets of Variables

Question 40

____ ____ ____ is also known as discriminant analysis and is the appropriate technique when two or more continuous predictors will be used to predict or estimate a person’s status on a single discrete (nominal) criterion. It could be employed in Study #3 if several measures are to be used to predict whether a sales applicant will belong to the “successful salesperson” or “unsuccessful salesperson” group after he or she is hired. The accuracy of a discriminant function analysis is often assessed by determining the ____ ____, which is the proportion of cases that are correctly classified.

Answer 40

Discriminant Function Analysis; Hit Rate

Question 41

____ ____ is similar to discriminant function analysis and is used to predict status on a single discrete criterion using two or more continuous or discrete predictors. In contrast to discriminant function analysis, which requires the relationships between variables to be linear, logistic regression assumes that the relationships are ____. Logistic regression would be appropriate in Study #3 if interpersonal assertiveness has a ____ relationship with sales success — i.e., if moderate levels of assertiveness are characteristic of successful salespeople, while low and high levels are characteristic of unsuccessful salespeople.

Answer 41

Logistic Regression; Nonlinear; Curvilinear

Question 42

A number of ____ ____ have been developed to test a predefined causal model or theory. Like other correlational techniques, these techniques cannot ____ ____ but, in contrast to those techniques, they can provide investigators with some evidence that their ____ ____ or ____ is ____ or ____. These techniques are called ____ ____ (____) ____ ____ and include path analysis and LISREL.

Answer 42

Multivariate Techniques; Prove Causality; Causal Model or Theory is Correct or Incorrect; Structural Equation (Causal) Modeling Techniques

Question 43

____ ____ can be considered an extension of multiple regression. It involves translating a theory about the causal relationships among a set of variables into a path diagram, collecting data on the variables, and using the data to derive path coefficients (regression coefficients) that indicate the direction and strength of the relationship between pairs of variables. If the pattern of coefficients is consistent with what is predicted by the theory, the analysis provides ____ for the ____. One restriction when using path analysis is that all paths between variables must be ____; that is, they must involve only a one-way causal flow.

Answer 43

Path Analysis; Support for the Theory; Recursive

Question 44

___ (linear structural relations analysis) is more ____ than path analysis and can be used when a causal model includes recursive (one-way) and non-recursive (two-way) paths. Like path analysis, LISREL examines the relationship between observed (measured) variables, but it also takes into account the ____ ____ those variables are believed to measure and the effects of ____ ____.

Answer 44

LISREL; Complex; Latent Traits; Measurement Error

Question 45

Several multivariate techniques are used for the purpose of ____ ____ — i.e., for or classifying a large group of variables into smaller subgroups. These techniques include ____ ____ and ____ ____.

Answer 45

Data Reduction; Factor Analysis and Cluster Analysis

Question 46

____ ____ involves simplifying a set of data by reducing a larger number of variables (e.g., tests or test items) to a smaller number of factors that explain the intercorrelations between those variables. It is used for several purposes including ____ ____ for ____. To illustrate, assume that the psychologist in Study #3 develops a new measure of interpersonal assertiveness by observing salespeople while they work and using the information she obtains to write 50 items that correspond to specific behaviors she believes represent interpersonal assertiveness. She then administers the 50 items to a sample of salespeople and uses factor analysis to develop subscales for the measure that each consist of items that correlate with each other. (Additional information about factor analysis is provided in the Test Construction chapter.)

Answer 46

Factor Analysis; Developing Subscales for Tests

Question 47

____ ____ is used to group people or objects into a smaller number of mutually exclusive and exhaustive subgroups (clusters) based on their similarities i.e., to Coup people or objects so that the identified subgroups have within-group homogeneity and between-group heterogeneity. In contrast to discriminant function analysis and logistic regression which are used to place people into predefined groups, cluster analysis is used to ____, ____, or ____ the ____ and ____ of ____.

Answer 47

Cluster Analysis; Identify, Define, or Confirm the Nature and number of Subgroups

Question 48

If the psychologist in Study #1 is interested in determining if children with different patterns of symptoms respond differently to the self-control procedure, his first step would be to administer measures of cognitive and behavioral symptoms to a sample of 50 children who have received a diagnosis of ADHD and use ____ ____ to identify subgroups of children, with those in each subgroup displaying a unique pattern of symptoms. If the cluster analysis confirms that there are, in fact, subgroups of children with unique symptom patterns, he could then conduct a study to determine if the self-control procedure has different effects on the academic achievement test scores of children belonging to those subgroups.

Answer 48

Cluster Analysis

Question 49

Multivariate techniques are used to assess the degree of association among three or more variables. Multiple regression analysis yields a (1) ____ coefficient (R) and a (2) ____ equation and is used when two or more (3) or discrete predictors will be used to predict status on a single (4) ____ criterion. To be most useful, the predictors included in the multiple regression equation should have (5) ____ correlations with each other and a (6) ____ correlation with the criterion.

Answer 49

(1) multiple correlation; (2) multiple regression; (3) continuous; (4) continuous; (5) low; (6) high

Question 50

When predictors have high correlations with each other, this condition is referred to as (7) ____. One type of multiple regression, stepwise regression, involves adding or subtracting predictors one at a time, with the decision to add or subtract a predictor being based on the size of (8) ____. When a multiple regression equation is cross-validated, the multiple correlation coefficient tends to (9) ____.

Answer 50

(7) multicollinearity; (8) R-squared; (9) shrink

Question 51

When an investigator’s goal is to use several predictors to classify an individual into a predefined category or group and the relationships between variables are linear, the appropriate multivariate technique is (10) ____. If any of the relationships are nonlinear, (11) ____ can be used. Finally, (12) ____ is the appropriate technique when a set of continuous predictors will be used to predict status on a set of continuous criteria. path analysis and LISREL are multivariate techniques that are used to test a (13) ____ model or theory about the relationships among a set of variables.

Answer 51

(10) discriminant function analysis; (11) logistic regression; (12) canonical correlation; (13) causal

Question 52

In contrast to path analysis, LISREL provides information on the relationships between both observed variables and the (14) ____ those variables are believed to measure. Finally, some multivariate techniques are used for the purpose of data reduction. For example, (15) ____ is used to group people or objects into mutually exclusive and exhaustive subgroups based on their similarities.

Answer 52

(14) latent traits; (15) cluster analysis