The positive sign shows the direction, and indicates a relatively strong relationship.
Incorrect! Try again.
13What does multiple correlation examine?
multiple correlation
Easy
A.One variable and one score
B.One criterion and several predictors
C.Two group averages
D.One rank and one frequency
Correct Answer: One criterion and several predictors
Explanation:
Multiple correlation examines the relationship between one criterion variable and two or more predictor variables.
Incorrect! Try again.
14What symbol commonly represents the multiple correlation coefficient?
multiple correlation
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The uppercase letter is commonly used for the multiple correlation coefficient.
Incorrect! Try again.
15How many predictor variables are required for multiple correlation?
multiple correlation
Easy
A.Exactly ten
B.No variables
C.At least two
D.Exactly one
Correct Answer: At least two
Explanation:
Multiple correlation uses two or more predictor variables to relate to one criterion variable.
Incorrect! Try again.
16What is the usual range of the multiple correlation coefficient ?
multiple correlation
Easy
A. to
B. to
C. to
D. to
Correct Answer: to
Explanation:
The multiple correlation coefficient is nonnegative and ranges from to .
Incorrect! Try again.
17A multiple correlation of indicates what?
multiple correlation
Easy
A.Perfect prediction
B.A negative prediction
C.A rank difference
D.No linear prediction
Correct Answer: No linear prediction
Explanation:
An value of indicates no linear relationship between the criterion and the set of predictors.
Incorrect! Try again.
18What type of data is especially suitable for Spearman's rank-order correlation?
Spearman's rank-order correlation
Easy
A.Unordered names
B.Ranked data
C.Raw text only
D.Nominal labels
Correct Answer: Ranked data
Explanation:
Spearman's correlation is designed for ranked or ordinal data.
Incorrect! Try again.
19What symbol commonly represents Spearman's rank-order correlation?
Spearman's rank-order correlation
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
Spearman's rank-order correlation is commonly represented by the Greek letter .
Incorrect! Try again.
20Spearman's rank-order correlation is based mainly on what?
Spearman's rank-order correlation
Easy
A.Ranks of observations
B.Population variances
C.Raw group means
D.Sample frequencies
Correct Answer: Ranks of observations
Explanation:
Spearman's method calculates the relationship using the ranks of observations rather than only their raw scores.
Incorrect! Try again.
21A researcher finds that as daily stress increases, sleep quality tends to decrease in a fairly consistent pattern. What type of correlation is most appropriate?
types of correlation
Medium
A.Zero correlation
B.Perfect curvilinear correlation
C.Negative correlation
D.Positive correlation
Correct Answer: Negative correlation
Explanation:
A negative correlation occurs when higher values of one variable are associated with lower values of the other.
Incorrect! Try again.
22The relationship between arousal and performance is low at very low and very high arousal but highest at moderate arousal. Which type of relationship does this illustrate?
types of correlation
Medium
A.Positive linear correlation
B.Zero-order correlation
C.Negative linear correlation
D.Curvilinear correlation
Correct Answer: Curvilinear correlation
Explanation:
A curvilinear relationship changes direction or follows a curved pattern rather than a straight-line pattern.
Incorrect! Try again.
23If two psychological variables have a correlation of , which conclusion is most justified?
types of correlation
Medium
A.The variables have no linear relationship
B.The variables have no relationship of any kind
C.The variables are measured with perfect reliability
D.The variables have an exact inverse relationship
Correct Answer: The variables have no linear relationship
Explanation:
A correlation of zero indicates no linear association, but a nonlinear relationship may still exist.
Incorrect! Try again.
24A scatterplot shows points closely following a downward-sloping straight line. Which description best fits the relationship?
types of correlation
Medium
A.Strong negative linear correlation
B.Weak positive linear correlation
C.Weak negative curvilinear correlation
D.Strong positive linear correlation
Correct Answer: Strong negative linear correlation
Explanation:
A close downward pattern indicates that the variables have a strong negative linear association.
Incorrect! Try again.
25A study reports a correlation between study time and examination scores. Which statement is the most appropriate interpretation?
types of correlation
Medium
A.Higher scores necessarily cause more study time
B.Higher study time is associated with higher scores
C.Study time definitely causes higher scores
D.The variables must have identical measurement scales
Correct Answer: Higher study time is associated with higher scores
Explanation:
Correlation describes association and does not by itself establish a causal direction.
Incorrect! Try again.
26What does Pearson's correlation coefficient primarily measure?
Pearson's correlation coefficient correlation
Medium
A.The difference between two sample means
B.The percentage of participants in each category
C.The strength and direction of a linear relationship
D.The statistical significance of a single mean
Correct Answer: The strength and direction of a linear relationship
Explanation:
Pearson's summarizes both the direction and strength of a linear association between two quantitative variables.
Incorrect! Try again.
27A sample produces between social anxiety and number of social interactions. Which interpretation is best?
Pearson's correlation coefficient correlation
Medium
A.Exactly of interactions are caused by anxiety
B.A moderate-to-strong negative linear relationship exists
C.There is no relationship because the value is negative
D.A strong positive linear relationship exists
Correct Answer: A moderate-to-strong negative linear relationship exists
Explanation:
The negative sign indicates direction, while the magnitude of indicates a fairly strong linear association.
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28If , what proportion of variance is explained by the linear relationship?
Pearson's correlation coefficient correlation
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The coefficient of determination is , or .
Incorrect! Try again.
29Which value indicates the strongest linear relationship between two variables?
Pearson's correlation coefficient correlation
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Strength is determined by the absolute value of . Since is largest, it represents the strongest relationship.
Incorrect! Try again.
30Which situation is most likely to make Pearson's correlation misleading?
Pearson's correlation coefficient correlation
Medium
A.The sample includes independent observations
B.The scatterplot contains a major outlier
C.Both variables are quantitative
D.The relationship appears approximately linear
Correct Answer: The scatterplot contains a major outlier
Explanation:
Pearson's is sensitive to extreme observations, which can substantially change the value and interpretation of the coefficient.
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31If every participant's score on one variable is converted from minutes to seconds, what happens to Pearson's ?
Pearson's correlation coefficient correlation
Medium
A.Its value remains unchanged
B.It becomes half as large
C.Its sign changes from positive to negative
D.It becomes exactly twice as large
Correct Answer: Its value remains unchanged
Explanation:
Pearson's correlation is unaffected by positive changes in measurement units, such as converting minutes to seconds.
Incorrect! Try again.
32A researcher obtains from a sample of 20 participants. Which statement is most accurate?
Pearson's correlation coefficient correlation
Medium
A.The relationship is necessarily statistically significant in every population
B.The relationship explains exactly of the outcome variance
C.The relationship is positive and moderate in the sample
D.The relationship proves that one variable causes the other
Correct Answer: The relationship is positive and moderate in the sample
Explanation:
The coefficient indicates a moderate positive sample association. It does not prove causation or guarantee statistical significance.
Incorrect! Try again.
33What does a multiple correlation coefficient, usually denoted by , describe?
multiple correlation
Medium
A.The reliability of one psychological test score
B.The difference between several independent group means
C.The association between one criterion and several predictors together
D.The association between two ranks after removing ties
Correct Answer: The association between one criterion and several predictors together
Explanation:
Multiple correlation assesses how well a set of predictors jointly relates to or predicts one criterion variable.
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34A regression model predicts academic performance from conscientiousness, prior achievement, and study hours. What does represent?
multiple correlation
Medium
A.The proportion of criterion variance explained jointly by the predictors
B.The mean prediction error in the model
C.The correlation between the two strongest predictors
D.The number of predictors included in the model
Correct Answer: The proportion of criterion variance explained jointly by the predictors
Explanation:
indicates the proportion of variance in the criterion that is accounted for by the predictors considered together.
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35A multiple correlation coefficient is reported as . What is the corresponding coefficient of determination?
multiple correlation
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The coefficient of determination is , meaning of criterion variance is explained jointly.
Incorrect! Try again.
36Which statement about the multiple correlation coefficient is correct?
multiple correlation
Medium
A. can range from to
B. must equal the largest predictor-criterion correlation
C. is unaffected by adding any new predictor
D. can range from to
Correct Answer: can range from to
Explanation:
Multiple represents the magnitude of the relationship between the criterion and the combined predictors, so it ranges from to $1.
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37When a second predictor is added to a multiple regression model, the ordinary will generally:
multiple correlation
Medium
A.Become equal to zero
B.Change its sign
C.Always decrease
D.Stay the same or increase
Correct Answer: Stay the same or increase
Explanation:
Adding predictors cannot reduce the ordinary sample , although the increase may be very small or due partly to chance.
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38Spearman's rank-order correlation is most appropriate when the variables are:
Spearman's rank-order correlation
Medium
A.Nominal categories with no ordering
B.Repeated measurements from one person only
C.Means from unrelated experimental groups
D.Ordinal ranks or nonnormally distributed scores
Correct Answer: Ordinal ranks or nonnormally distributed scores
Explanation:
Spearman's correlation evaluates the monotonic association between ranked or ordinal variables and is less dependent on normality.
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39Six students receive the same ordering of ranks for motivation and attendance. What is Spearman's rank correlation likely to be?
Spearman's rank-order correlation
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Identical rank ordering represents a perfect positive monotonic association, so Spearman's coefficient is .
Incorrect! Try again.
40For six cases, the differences between paired ranks have squared values that sum to . Using , what is ?
Spearman's rank-order correlation
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
With , .
Incorrect! Try again.
41A researcher observes that stress rises with workload up to a moderate level, but among employees with extremely high workload, stress scores plateau because of emotional disengagement. Which type of association is most appropriate for describing the overall relationship?
types of correlation
Hard
A.A negative linear correlation
B.A zero-order correlation
C.A positive linear correlation
D.A nonlinear correlation
Correct Answer: A nonlinear correlation
Explanation:
The direction or rate of change is not constant across the range of workload, so a linear coefficient may fail to represent the relationship adequately.
Incorrect! Try again.
42Variable increases as variable increases, but the increases become progressively smaller. Which statement is most accurate?
types of correlation
Hard
A.The variables have a positive partial association
B.The variables have a positive nonlinear association
C.The variables have a perfect negative association
D.The variables have no correlation
Correct Answer: The variables have a positive nonlinear association
Explanation:
Both variables move in the same direction, but the changing rate of increase indicates a nonlinear rather than strictly linear relationship.
Incorrect! Try again.
43In a sample, anxiety and performance show a strong positive correlation within low-anxiety participants and a strong negative correlation within high-anxiety participants. The aggregate correlation is close to zero. What is the best interpretation?
Correct Answer: The aggregate coefficient masks subgroup-specific relationships
Explanation:
Opposite relationships in subgroups can cancel in the aggregate, making the overall coefficient misleading.
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44If every score on is transformed to while is unchanged, what happens to Pearson's correlation?
Pearson's correlation coefficient correlation
Hard
A.Its sign reverses but magnitude is unchanged
B.Its sign and magnitude both change
C.Its magnitude triples
D.It becomes zero unless is standardized
Correct Answer: Its sign reverses but magnitude is unchanged
Explanation:
Adding a constant and multiplying by a positive value do not alter correlation; multiplication by a negative value reverses its sign.
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45A dataset has Pearson correlation . One observation is deleted, and the new correlation is . Which conclusion is justified?
Pearson's correlation coefficient correlation
Hard
A.The original correlation was necessarily computed incorrectly
B.The deleted observation was influential for the correlation
C.The new correlation must be statistically significant
D.The variables changed from interval to nominal measurement
Correct Answer: The deleted observation was influential for the correlation
Explanation:
A large change after deleting one case indicates that the observation had substantial influence, often because it was an outlier or had high leverage.
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46Suppose , , and . What is the least-squares regression slope for predicting from ?
Pearson's correlation coefficient correlation
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The slope is .
Incorrect! Try again.
47A study reports between therapy attendance and symptom improvement. Which statement is most defensible?
Pearson's correlation coefficient correlation
Hard
A.Attendance causes of all symptom variation
B.Approximately of participants improved because of attendance
C.The linear association accounts for approximately of variance
D.The association is necessarily free from third-variable influence
Correct Answer: The linear association accounts for approximately of variance
Explanation:
The coefficient of determination is , or about , but this does not establish causation.
Incorrect! Try again.
48A scatterplot shows a strong U-shaped relationship between study time and exam performance. Pearson's is approximately zero. What does this result primarily indicate?
Pearson's correlation coefficient correlation
Hard
A.The variables have no systematic relationship
B.There is little or no linear association
C.The variables are statistically independent
D.The sample must contain identical scores
Correct Answer: There is little or no linear association
Explanation:
Pearson's correlation measures linear association and can be near zero when a strong curvilinear relationship exists.
Incorrect! Try again.
49For a bivariate normal population, a researcher tests with and obtains . Using , which conclusion is closest?
Pearson's correlation coefficient correlation
Hard
A., significant at the .01 level
B., significant at the .05 level
C., significant at the .05 level
D., not significant at the .05 level
Correct Answer: , significant at the .05 level
Explanation:
with degrees of freedom, which exceeds the two-tailed .05 critical value of about .
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50If the reliability of is .64 and the reliability of is .81, and the observed correlation is .36, what is the estimated disattenuated correlation?
Pearson's correlation coefficient correlation
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The corrected correlation is .
Incorrect! Try again.
51A criterion correlates with predictors and at and , while . What is the squared multiple correlation?
multiple correlation
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
For two predictors, .
Incorrect! Try again.
52A predictor correlates with a criterion at . After adding a second predictor, the multiple correlation is . What does the second predictor contribute?
multiple correlation
Hard
A.It contributes no incremental linear prediction
B.It proves the predictors are perfectly correlated
C.It increases explained variance by
D.It reverses the first predictor's regression weight
Correct Answer: It contributes no incremental linear prediction
Explanation:
The first predictor alone has , and the full model also has , so the second predictor adds no incremental explained variance.
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53A model with three predictors has . The zero-order correlations between the criterion and the predictors are all positive. Which conclusion is still possible?
multiple correlation
Hard
A.At least one standardized regression coefficient may be negative
B.Every standardized regression coefficient must be positive
C.The criterion must be measured on a nominal scale
D.The predictors must be mutually uncorrelated
Correct Answer: At least one standardized regression coefficient may be negative
Explanation:
With correlated predictors, suppression or multicollinearity can produce a negative unique regression weight even when all zero-order correlations are positive.
Incorrect! Try again.
54Two predictors correlate at , and each correlates with at approximately . What is the primary statistical concern?
multiple correlation
Hard
A.The multiple correlation must equal zero
B.The predictors are likely affected by multicollinearity
C.The regression model has no intercept
D.The criterion cannot be predicted linearly
Correct Answer: The predictors are likely affected by multicollinearity
Explanation:
Very high intercorrelation among predictors makes unique regression coefficients unstable and difficult to interpret.
Incorrect! Try again.
55A regression model's rises from .36 to .49 when two predictors are added. Which statement is correct?
multiple correlation
Hard
A.The model's residual variance increases by
B.The correlation between added predictors is necessarily zero
C.The added predictors provide a percentage-point increment in explained variance
Correct Answer: The added predictors provide a percentage-point increment in explained variance
Explanation:
The incremental contribution is , although the two predictors may share explanatory variance.
Incorrect! Try again.
56For six participants with no tied ranks, the squared rank differences sum to . What is Spearman's rank-order correlation?
Spearman's rank-order correlation
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
.
Incorrect! Try again.
57A researcher ranks five observations on two variables. The rank pairs are . What is ?
Spearman's rank-order correlation
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The squared rank differences are , so .
Incorrect! Try again.
58When tied ranks occur, which procedure is generally most appropriate for computing Spearman's correlation?
Spearman's rank-order correlation
Hard
A.Assign average ranks and correlate the rank variables
B.Assign arbitrary distinct ranks to tied observations
C.Use raw scores without any ranking
D.Delete all observations involved in ties
Correct Answer: Assign average ranks and correlate the rank variables
Explanation:
Average ranks preserve the tied ordering and allow Spearman's coefficient to be computed as the Pearson correlation between the rank-transformed variables.
Incorrect! Try again.
59Which pattern can produce a high Spearman correlation but a much smaller Pearson correlation?
Spearman's rank-order correlation
Hard
A.A random permutation of identical rank pairs
B.A monotonic but strongly curved relationship
C.Two independent variables with equal variances
D.A perfectly linear relationship with no outliers
Correct Answer: A monotonic but strongly curved relationship
Explanation:
Spearman's coefficient captures monotonic ordering, whereas Pearson's coefficient can be reduced when the monotonic relationship is substantially nonlinear.
Incorrect! Try again.
60If every rank on one variable is transformed from to , while the other variable remains unchanged, what happens to Spearman's correlation?
Spearman's rank-order correlation
Hard
A.Its sign reverses but magnitude is unchanged
B.Its magnitude doubles
C.It becomes zero for every dataset
D.It changes only when ties are present
Correct Answer: Its sign reverses but magnitude is unchanged
Explanation:
Reversing ranks is a negative linear transformation of the rank variable, so the correlation changes sign while retaining its absolute value.
Incorrect! Try again.
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