Question 1

If a relationship between two variables is spurious, we conclude that it is
A) nearly always a cause and effect relationship.
B) partially regressed.
C) accounted for by another extraneous variable
D) not a statistically significant relationship.

Accepted Answer

A spurious relationship occurs when there appears to be a relationship between two variables, but in reality, it is only because of another extraneous variable that affects both. Therefore, the correct choice is C, which states that the relationship is accounted for by another extraneous variable.

Question 2

The following graph resulted when a researcher plotted the paired scores from two sets of data: 
Which of the following conclusions is justified from an examination of the graph?
A) The coefficient of correlation is close to .50.
B) The correlation between X and Y is negative and low.
C) The correlation between X and Y is positive and high.
D) A Spearman rho coefficient of correlation is appropriate for these data.
E) A Pearson's coefficient of correlation is not appropriate for these data.

Accepted Answer

The answer of The following graph resulted when a researcher...

Question 3

Research shows that aptitude scores are better predictors of achievement in the lower grades than in college.This finding can best be interpreted to mean that
A) college students are not as predictable as elementary school pupils.
B) aptitude tests should not be used with college students.
C) there is less variability in aptitude and achievement among elementary school students than among college students.
D) there is greater variability in aptitude and achievement among elementary school students than among college students.
E) college teachers tend to be more objective in grading than elementary school teachers.

Accepted Answer

There is greater variability in aptitude and achievement among elementary school students than among college students.

Question 4

The most useful correlational technique to use when one wants to test a causal hypothesis is
A) factor analysis.
B) path analysis.
C) discriminant analysis.
D) regression analysis.

Accepted Answer

Although correlation does not prove causation, path analysis is a technique that allows researchers to test causal hypotheses by incorporating both correlational and causal relationships among variables. Path analysis is used to identify the direct and indirect effects of one or more independent variables on a dependent variable while controlling for other variables. Therefore, it is an appropriate technique to test causal hypotheses. The other options, factor analysis, discriminant analysis, and regression analysis are not typically used to test causal hypotheses. Factor analysis is used to identify underlying factors in a set of variables, discriminant analysis is used to classify individuals into groups based on their scores on a set of predictor variables, and regression analysis is used to predict scores on a dependent variable based on one or more predictor variables.

Question 5

Research has shown that high school students' scores on the SAT correlate .40 with college freshman grades.Assuming that only half of the students who took the SAT were admitted to a given college, what would you estimate the correlation to be between their SAT scores and freshman grades?
A) Negative and lower than .40
B) Negative and higher than .40
C) Positive and higher than .40
D) Positive and lower than .40

Accepted Answer

Restricting the sample to only those admitted (half of the students) typically reduces variability, which can lower the correlation, making it positive and lower than .40.

Question 6

Exhibit 13-5.Choose the type of correlational statistic that would be used for each of the purposes listed.
-Refer to Exhibit 13-5.Used to determine whether a set of variables can be reduced to a smaller number of measures
A) Product-moment correlation
B) Partial correlation
C) Factor analysis
D) Canonical correlation
E) Multiple regression

Accepted Answer

Factor analysis is a statistical technique used to identify patterns among variables and reduce them into a smaller set of underlying factors.

Question 7

Before calculating a correlation coefficient, a researcher wants to determine whether the relationship between the two variables is linear.Which of the following would be most appropriate to use?
A) Histogram
B) Frequency polygon
C) Data matrix
D) Scatterplot

Accepted Answer

A scatterplot is the most appropriate tool to determine whether the relationship between two variables is linear. It graphically displays the relationship between the two variables, and allows the researcher to visually identify whether the relationship appears to be linear or not. Histograms and frequency polygons are used to show the distribution of a single variable, and a data matrix is simply a table of values without any graphical representation.

Question 8

The Pearson's product-moment correlation coefficient is used to measure the
A) magnitude of the curvilinear relationship between two variables.
B) linearity of the relationship between two variables.
C) direction of the curvilinear relationship between two variables.
D) magnitude and direction of the linear relationship between two variables.

Accepted Answer

The Pearson's product-moment correlation coefficient is used to measure the strength (magnitude) and direction of the linear relationship between two variables. It is not used to measure curvilinear relationship or the linearity of the relationship alone. Therefore, the best choice is (D) magnitude and direction of the linear relationship between two variables.

Question 9

A correlational design often achieves control through the use of
A)counterbalancing.
B)random selection.
C)partial correlation.
D)matching.

Accepted Answer

Partial correlation is used in correlational designs to control for the influence of one or more extraneous variables, allowing researchers to examine the relationship between the primary variables of interest more accurately.

Question 10

If X is positively correlated with Y, one can conclude that
A) X probably causes changes in Y.
B) Y probably causes changes in X.
C) changes in X and Y are both probably caused by Z.
D) None of these is true.

Accepted Answer

Correlation does not imply causation. A positive correlation between X and Y only indicates that as X increases, Y tends to increase as well (or vice versa), but it does not establish a cause-and-effect relationship between the two variables.

Question 11

A researcher wishes to predict those college students who will be persistent in their education, that is, those who will stay in college and graduate within five years as opposed to those who will not complete a degree within five years.Which of the following methods would the researcher use?
A) Factor analysis
B) Partial correlation
C) Path analysis
D) Multiple regression
E) Discriminant analysis

Accepted Answer

Discriminant analysis is the best choice in this scenario as it is a statistical method used to classify individuals into groups based on a set of predictor variables. In this case, the researcher wants to predict whether a student will be persistent in their education or not, which requires classifying them into one of two groups. Discriminant analysis allows the researcher to determine which predictor variables are most important in making this distinction and can be used to develop a predictive model to classify future students based on these variables.

Question 12

Which of the following statistics is most important in the calculation of test validity and reliability?
A) Standard error of estimate
B) Coefficient of correlation
C) Median
D) Percentile
E) Standard deviation

Accepted Answer

The coefficient of correlation is the most important statistic for calculating test validity and reliability. It measures the strength and direction of the relationship between two variables, such as test scores and actual performance. A high coefficient of correlation indicates that the test is measuring what it is supposed to measure, and that the scores are reliable over time. Other statistics, such as standard deviation and percentile rank, may be useful for interpreting test scores, but they do not directly measure validity or reliability.

Question 13

Under which of the following conditions would one expect multiple correlation coefficients to show relatively large shrinkage?
A) When the original sample is small
B) When the original sample is large

Accepted Answer

Multiple correlation coefficients tend to be less stable and more susceptible to shrinkage when the original sample size is small. This is because small samples are more likely to be affected by random sampling error, which can inflate or deflate the estimated correlations. Shrinkage occurs when the estimated correlation coefficients are adjusted to account for this variability, resulting in coefficients that are closer to zero (i.e., less extreme) than the original estimates. As sample size increases, the estimated coefficients become more stable and closer to the true population coefficients, resulting in less shrinkage.

Question 14

The purpose of cross-validation is to
A) validate the test for different criteria.
B) try out the test with the same sample after a period of time.
C) confirm the correlation in a different sample.

Accepted Answer

Cross-validation is a technique used to confirm that a statistical model is robust and not overfitting the data. It involves splitting the dataset into multiple subsets and training the model on one subset while testing it on the other subsets. This helps to ensure that the model can generalize well to unseen data and is not just memorizing the training data. Therefore, choice C, confirming the correlation in a different sample, best describes the purpose of cross-validation.

Question 15

Consider the correlation matrix below with independent variables A, B, and C and dependent variable Y $\begin{array}{lccc}
&A& B &C& Y \
A&--&.60&.60&.70 \
B&--&--&.00&.80 \
C&--&--&--&.70 \
\end{array}$

Which of the variables A, B, or C will enter first in a stepwise multiple regression equation?
A) A
B) B
C) C
D) cannot tell from the data given

Accepted Answer

Variable B will enter first in a stepwise multiple regression equation because it has the highest correlation (.80) with the dependent variable Y, indicating the strongest linear relationship among the independent variables.

Question 16

If one fails to reject the null hypothesis in a multiple regression analysis, then one concludes
A) there is no evidence for a relation between the combination of independent variables and the dependent variable.
B) the observed relationship between the independent variables in combination and the dependent variable is greater than would be expected by chance.
C) the population correlation between X and Y is not zero.
D) the population correlation between X and Y is less than zero.

Accepted Answer

Failing to reject the null hypothesis in a multiple regression analysis means that there is no significant evidence for a relationship between the combination of independent variables and the dependent variable. It does not provide evidence for or against any specific population correlation or relationship between the variables.

Question 17

Assume you are using GRE scores and undergraduate grades to predict graduate GPA.If the correlation of GRE scores and undergraduate grades were .18 rather than .56, then GRE scores would be ____ for predicting graduate GPA.
A) more useful
B) equally useful
C) less useful

Accepted Answer

The answer of Assume you are using GRE scores and...

Question 18

Exhibit 13-5.Choose the type of correlational statistic that would be used for each of the purposes listed.
-Refer to Exhibit 13-5.Used to describe the extent of relationship between two variables, X and Y, after the influence of a third variable, Z, has been removed.
A) Product-moment correlation
B) Partial correlation
C) Factor analysis
D) Canonical correlation
E) Multiple regression

Accepted Answer

Partial correlation is used to describe the extent of relationship between two variables, X and Y, after the influence of a third variable, Z, has been removed.

Question 19

A high negative correlation was found between days absent from school and grade achievement for middle school students.This finding means that
A) absence from school causes low achievement.
B) students who miss school more often tend to make lower grades than students who attend regularly.
C) low achievement causes high absence from school.
D) measures on the two variables do not tend to covary.

Accepted Answer

A high negative correlation means that as one variable (days absent from school) increases, the other variable (grade achievement) decreases. Therefore, option B is the correct answer as it suggests that students who miss school more often tend to make lower grades than students who attend regularly. Option A implies a causal relationship, which cannot be determined from the correlation alone. Option C suggests that low achievement leads to high absence, which is not supported by the given correlation. Option D contradicts the initial statement that a negative correlation was found.

Question 20

The correlation between the Graduate Record Examination (GRE) and undergraduate GPA for all people taking the GRE is .56.If the correlation is recomputed for only those students admitted to graduate school, the value of the correlation will most likely
A) increase.
B) decrease.
C) stay the same.

Accepted Answer

The correlation is likely to decrease because the range of GRE scores and GPAs will be more restricted among those admitted to graduate school (restriction of range effect), leading to a lower correlation compared to the broader, more variable population of all GRE takers.

Quiz 13: Correlation Research

If a relationship between two variables is spurious, we conclude that it is

The following graph resulted when a researcher plotted the paired scores from two sets of data: Which of the following conclusions is justified from an examination of the graph?

Research shows that aptitude scores are better predictors of achievement in the lower grades than in college.This finding can best be interpreted to mean that

The most useful correlational technique to use when one wants to test a causal hypothesis is

Research has shown that high school students' scores on the SAT correlate .40 with college freshman grades.Assuming that only half of the students who took the SAT were admitted to a given college, what would you estimate the correlation to be between their SAT scores and freshman grades?

Exhibit 13-5.Choose the type of correlational statistic that would be used for each of the purposes listed. -Refer to Exhibit 13-5.Used to determine whether a set of variables can be reduced to a smaller number of measures

Before calculating a correlation coefficient, a researcher wants to determine whether the relationship between the two variables is linear.Which of the following would be most appropriate to use?

The Pearson's product-moment correlation coefficient is used to measure the

A correlational design often achieves control through the use of

If X is positively correlated with Y, one can conclude that

A researcher wishes to predict those college students who will be persistent in their education, that is, those who will stay in college and graduate within five years as opposed to those who will not complete a degree within five years.Which of the following methods would the researcher use?

Which of the following statistics is most important in the calculation of test validity and reliability?

Under which of the following conditions would one expect multiple correlation coefficients to show relatively large shrinkage?

The purpose of cross-validation is to

Consider the correlation matrix below with independent variables A, B, and C and dependent variable Y $\begin{array}{lccc}&A& B &C& Y \\A&--&.60&.60&.70 \\B&--&--&.00&.80 \\C&--&--&--&.70 \\\end{array}$ Which of the variables A, B, or C will enter first in a stepwise multiple regression equation?

If one fails to reject the null hypothesis in a multiple regression analysis, then one concludes

Assume you are using GRE scores and undergraduate grades to predict graduate GPA.If the correlation of GRE scores and undergraduate grades were .18 rather than .56, then GRE scores would be ____ for predicting graduate GPA.

Exhibit 13-5.Choose the type of correlational statistic that would be used for each of the purposes listed. -Refer to Exhibit 13-5.Used to describe the extent of relationship between two variables, X and Y, after the influence of a third variable, Z, has been removed.

A high negative correlation was found between days absent from school and grade achievement for middle school students.This finding means that

The correlation between the Graduate Record Examination (GRE) and undergraduate GPA for all people taking the GRE is .56.If the correlation is recomputed for only those students admitted to graduate school, the value of the correlation will most likely