Chapter 15: Cousins or Just Good Friends? Testing Relationships Using the Correlation Coefficient Test Bank MULTIPLE CHOICE The correlation coefficient is a measure of _ a Mean differences b Causation c Prediction d Association ANS: D PTS: DIF: Easy REF: Introduction to Testing the Significance of the Correlation Coefficient OBJ: How to interpret the correlation coefficient COG: Knowledge While you can use the correlation coefficient as its own test statistic, what is the other appropriate test statistic often used to examine the significance of a correlation? a F-test b Cohen’s d c t-test d  ANS: C PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Knowledge This chapter illustrates that you can also incorporate _ into the correlation coefficient a Statistical significance b Substantial significance c Descriptive statistics d Generalizability ANS: REF: OBJ: COG: A PTS: DIF: Easy Introduction to Testing the Significance of the Correlation Coefficient How to test the significance of the correlation coefficient Knowledge Correlation coefficients examine a Differences between two groups b Differences between two or more groups c The relationship between variables d How variables can be arranged into higher-order factors ANS: C PTS: DIF: Easy REF: Introduction to Testing the Significance of the Correlation Coefficient OBJ: How to interpret the correlation coefficient COG: Knowledge Correlation coefficients can test _ variable(s) at a time a Only one b Only two c One or more d Two or more ANS: B PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge The appropriate test statistic to use is the _ a t-test for the correlation coefficient b p-test for the correlation coefficient c r-test for the correlation coefficient d t-test for statistical significance ANS: A PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Knowledge Correlations can be _ a Directional or nondirectional b Only directional c Only nondirectional d Neither directional nor nondirectional ANS: A PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge Significant correlations are not able to indicate _ a The probability level b The size of the effect c Causality d The strength of the effect ANS: C PTS: REF: Causes and Associations (Again!) COG: Knowledge DIF: Medium OBJ: How to interpret the correlation coefficient What is another term for a positive correlation? a Indirect b Nondirectional c Direct d Unidirectional ANS: C PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge 10 What is another term for a negative correlation? a Indirect b Nondirectional c Direct d Unidirectional ANS: A PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge 11 What is the most important characteristic of a correlation coefficient? a Number of variables included b Absolute value c One tailed d Two tailed ANS: B PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge 12 Which of the following is an example of a null hypothesis for testing a correlation coefficient? a H1: xy = b H1: xy > c H0: xy = d H0: xy > ANS: C PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge 13 If you posit that a relationship between two variables will be either positive or negative, what type of test should you use? a Two tailed b ANOVA c One tailed d Cohen’s d ANS: C PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Comprehension 14 If you not predict that a relationship between two variables will be either positive or negative, what type of test should you use? a Two tailed b ANOVA c One tailed d Cohen’s d ANS: A PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Comprehension 15 The level of risk or Type I error typically set for testing the level of significance of a correlation coefficient is which of the following? a .01 b .05 c .95 d .99 ANS: B PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Knowledge 16 Which of the following is the appropriate method for calculating the degrees of freedom associated with a correlation coefficient? a n - b n - c n - d n - ANS: B PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Knowledge 17 In the formula for calculating degrees of freedom for a correlation coefficient, what does the n represent? a Sample size b Number of groups c Number of pairs d Population ANS: C PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Knowledge 18 What is the name of the Greek letter a Phi b Rho c Chi d Alpha ? ANS: B PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge 19 Which of the following Greek symbols is used to represent the population estimate for a correlation coefficient? a  b  c  d  ANS: C PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge 20 Which of the following represents the test statistic for a correlation coefficient? a t b r c  d F ANS: B PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge 21 Which of the following is another use of correlation coefficients? a Testing mean differences b Testing causal relationships c Estimating reliability d Estimating power ANS: C PTS: DIF: Medium REF: So How Do I Interpret r(28) = 393, p < 05? OBJ: How to interpret the correlation coefficient COG: Knowledge 22 When computing the correlation coefficient, the _ between variables, not the _ between groups, is being examined a Relationship; difference b Difference; relationship c Means, reliability d Reliability; means ANS: A PTS: DIF: Medium REF: The Path to Wisdom and Knowledge OBJ: How to interpret the correlation coefficient COG: Knowledge 23 If the correlation between two variables is 496, how much of the variance has not been accounted for? a 24.6% b 49.6% c 50.4% d 75.4% ANS: REF: OBJ: COG: D PTS: DIF: Medium Significance Versus Meaningfulness (Again, Again!) The important distinction between significance and meaningfulness (again!) Application 24 If the correlation between two variables is 496, what is the coefficient of determination? a .246 b .496 c .504 d .754 ANS: REF: OBJ: COG: A PTS: DIF: Medium Significance Versus Meaningfulness (Again, Again!) The important distinction between significance and meaningfulness (again!) Application 25 What does the statement rxy  represent? a Null hypothesis b t statistic c Mean difference d Research hypothesis ANS: D PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Comprehension 26 If a research hypothesis does not predict the direction of a relationship, the test is _ a One tailed b Two tailed c Direct d Positive ANS: B PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Comprehension 27 If a research hypothesis posits that there is a direct relationship between two variables, the test is _ a One tailed b Two tailed c Negative d Nondirectional ANS: A PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Comprehension 28 In the equation r(65) = 45, p < 05, what does r represent? a Observed statistic b Experimental statistic c Test statistic d Critical statistic ANS: C PTS: DIF: Medium REF: So How Do I Interpret r(28) = 393, p < 05? OBJ: How to interpret the correlation coefficient COG: Application 29 In the equation r(65) = 45, p < 05, what are the degrees of freedom? a .45 b 45 c .65 d 65 ANS: D PTS: DIF: Medium REF: So How Do I Interpret r(28) = 393, p < 05? OBJ: How to interpret the correlation coefficient COG: Application 30 In the equation r(65) = 45, p < 05, what is the obtained value? a .45 b 45 c .65 d 65 ANS: A PTS: DIF: Medium REF: So How Do I Interpret r(28) = 393, p < 05? OBJ: How to interpret the correlation coefficient COG: Application 31 When computing a correlation coefficient, if you have 27 degrees of freedom, your sample size must be _ a 29 b 27 c 25 d 26 ANS: A PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Application 32 When computing a correlation coefficient, if you have 55 degrees of freedom, your sample size must be _ a 55 b 53 c 56 d 57 ANS: D PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Application 33 If a simple Pearson correlation value = 512, what percentage of variance is accounted for? a 26% b 49% c 51% d 74% ANS: REF: OBJ: COG: A PTS: DIF: Medium Significance Versus Meaningfulness (Again, Again!) The important distinction between significance and meaningfulness (again!) Application 34 If a simple Pearson correlation value = 685, what percentage of variance is accounted for? a 35% b 47% c 68% d 69% ANS: REF: OBJ: COG: B PTS: DIF: Medium Significance Versus Meaningfulness (Again, Again!) The important distinction between significance and meaningfulness (again!) Application 35 If a simple Pearson correlation value = 362, what percentage of variance is unaccounted for? a 25% b 36% c 56% d 87% ANS: REF: OBJ: COG: D PTS: DIF: Medium Significance Versus Meaningfulness (Again, Again!) The important distinction between significance and meaningfulness (again!) Application 36 If a simple Pearson correlation value = 75, what percentage of variance is unaccounted for? a 25% b 44% c 56% d 75% ANS: REF: OBJ: COG: B PTS: DIF: Medium Significance Versus Meaningfulness (Again, Again!) The important distinction between significance and meaningfulness (again!) Application 37 If you were looking to examine the relationship between chocolate sales and student happiness, you could test the relationship using the _ a Mean difference b t statistic c Error difference d c statistic ANS: REF: OBJ: COG: B PTS: DIF: Medium The Path to Wisdom and Knowledge How to test the significance of the correlation coefficient Application 38 You would like to examine the association between temperature and frozen yogurt sales You hypothesize that higher temperatures will be associated with increased frozen yogurt sales You have a _ a One-tailed hypothesis b Two-tailed hypothesis c Nondirectional hypothesis d Invalid hypothesis ANS: A PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Application 39 Which of the following indicates a significant correlation? a p = 21 b p < 05 c p < 20 d p < 50 ANS: B PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Comprehension 40 Which of the following indicates a NONsignificant correlation? a p < 05 b p < 01 c p = 02 d p = 30 ANS: D PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Comprehension 41 When computing a correlation coefficient, if you have 36 degrees of freedom, your sample size must be _ a 35 b 34 c 38 d 37 ANS: C PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Application 42 A professor hypothesizes that there will be a relationship between couples’ listening skills and length of marriage She has a _ a One-tailed hypothesis b Invalid hypothesis c Valid hypothesis d Two-tailed hypothesis ANS: D PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Application 43 A professor hypothesizes that there will be a positive relationship between couples’ listening skills and length of marriage She has a _ a One-tailed hypothesis b Invalid hypothesis c Valid hypothesis d Two-tailed hypothesis ANS: A PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Application 44 A _ correlation is also known as a _ correlation a Negative; direct b Negative; nondirectional c Positive; direct d Positive; nondirectional ANS: C PTS: DIF: Easy OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge TRUE/FALSE Correlation coefficients examine the relationship between variables ANS: T PTS: DIF: Medium REF: The Path to Wisdom and Knowledge OBJ: How to interpret the correlation coefficient COG: Knowledge A correlation coefficient can only test one variable at a time ANS: F PTS: DIF: Medium REF: The Path to Wisdom and Knowledge OBJ: How to interpret the correlation coefficient COG: Knowledge The appropriate test statistic to use is the t-test for the correlation coefficient ANS: T PTS: DIF: Medium REF: The Path to Wisdom and Knowledge OBJ: How to interpret the correlation coefficient COG: Knowledge With regard to correlations, tests can be either directional or nondirectional ANS: T PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Comprehension A significant correlation does not indicate causality ANS: T PTS: REF: Causes and Associations (Again!) COG: Comprehension DIF: Medium OBJ: How to interpret the correlation coefficient A significant correlation indicates a meaningful relationship ANS: REF: OBJ: COG: T PTS: DIF: Medium Significance Versus Meaningfulness (Again, Again!) The important distinction between significance and meaningfulness (again!) Application If two variables are significantly correlated, this means that one variable causes the other ANS: F PTS: REF: Causes and Associations (Again!) COG: Comprehension DIF: Medium OBJ: How to interpret the correlation coefficient The correlation coefficient can only be used for one-tailed tests ANS: F PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Application Correlations can be used to examine the differences between groups ANS: F PTS: DIF: Medium REF: The Path to Wisdom and Knowledge OBJ: How to interpret the correlation coefficient COG: Knowledge 10 A single correlation can be computed in order to determine the relationship between three variables ANS: REF: OBJ: COG: F PTS: DIF: Medium The Path to Wisdom and Knowledge How to test the significance of the correlation coefficient Comprehension 11 Dr Moo would like to examine differences in milk production between goats that listen to soft-jazz music and goats that listen to heavy-metal music She will be able to test this using a correlation coefficient ANS: F PTS: DIF: Medium REF: The Path to Wisdom and Knowledge OBJ: How to interpret the correlation coefficient COG: Comprehension 12 The Greek letter rho represents the sample estimate of the correlation coefficient ANS: F PTS: DIF: Medium OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Comprehension 13 For your purposes, you may use the CORREL function, Correlation tool, and PEARSON function in Excel interchangeably ANS: T PTS: DIF: Easy OBJ: How to interpret the correlation coefficient REF: Computing the Test Statistic COG: Knowledge SHORT ANSWER Give an example of a one-tailed hypothesis that may be tested through a correlation ANS: Example: Higher crime rates will be associated with lower income levels PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Application Think about the t-test for the correlation coefficient Write the equations for a research hypothesis with a one-tailed test and for a research hypothesis with a two-tailed test Write the equation for the null hypothesis ANS: One-tailed test H1: rxy > or H1: rxy < Two-tailed test H1: rxy  Null hypothesis H0: xy = PTS: DIF: Hard REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Application Write an example of a research hypothesis for a one-tailed t-test for the correlation coefficient ANS: An example of a research hypothesis for a one-tailed t-test for the correlation coefficient would be that there will be a positive correlation between number of hours studied and one’s grade on a test PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Application Write an example of a research hypothesis for a two-tailed t-test for the correlation coefficient ANS: An example of a research hypothesis for a two-tailed t-test for the correlation coefficient would be that there will be a relationship between number of hours studied and one’s grade on a test PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Application Write an example of a null hypothesis for a t-test for the correlation coefficient ANS: An example of a null hypothesis for a t-test for the correlation coefficient would be that there is no relationship between number of hours studied and one’s grade on a test PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Application What are the eight steps involved when examining a research question? ANS: Step 1: State the null and research hypothesis Step 2: Set the level of significance associated with the null hypothesis Steps and 4: Select the appropriate test statistic Step 5: Determine the critical value (using appropriate tables) Step 6: Compare the obtained value and the critical value Steps and 8: Make a decision (as to whether to accept or reject the null hypothesis) PTS: DIF: Hard REF: Computing the Test Statistic OBJ: How to test the significance of the correlation coefficient COG: Knowledge The research hypothesis posits that the relationship between two variables will be greater than zero (H1: rxy > 0) What would be concluded for r(29) = 467, p < 05? ANS: The obtained value (.467) is greater than the critical value (.296), so it can be concluded that the relationship between the two variables occurred by something other than chance (the treatment effect) Furthermore, the research hypothesis, which posits a positive relationship between the variables, is also supported PTS: DIF: Hard REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Application The research hypothesis posits that there will be a relationship between the number of hours a student studies and their result on a test (H1: rxy ?0? 0) What would be concluded for r(45) = 213, p > 05? ANS: The obtained value (.213) is less than the critical value (.2875), so it cannot be concluded that the relationship between the two variables occurred by something other than chance Furthermore, the research hypothesis, which posits a relationship between the variables, is also not supported PTS: DIF: Hard REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Application The research hypothesis posits that the more caffeine consumed by a subject, the longer a subject will stay awake (H1: rxy > 0) What would be concluded for r(10)= 653, p < 05? ANS: The obtained value (.653) is greater than the critical value (.4973), so it can be concluded that the relationship between the two variables occurred by something other than chance Furthermore, the research hypothesis, which posits a positive relationship between the variables, is also supported PTS: DIF: Hard REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Application 10 Give an example of a situation when it would be appropriate to use the t-test for the correlation coefficient test statistic ANS: A study comparing the relationship of the satisfaction level of dog owners to the degree to which they liked cats would use the t-test for the correlation coefficient test statistic PTS: DIF: Hard REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Application 11 Students participated in a study of the relationship between confidence and college success, with the results, r = 78, indicating that 61% of the variance in college success was accounted for by the students’ confidence Upon learning this, your statistics classmate decided that if he worked to increase his confidence, he would certainly become more successful in college What would you say to him in response to his idea? ANS: You could remind your classmate that although the correlation was strong, and much of the variance was accounted for by confidence, confidence still does not cause college success PTS: DIF: Hard REF: Causes and Associations (Again!) OBJ: How to interpret the correlation coefficient COG: Analysis 12 Dr Moo hypothesizes that there will be an association between grass consumption and milk production among goats What kind of hypothesis is this (one tailed or two tailed), and why? ANS: This is a two-tailed hypothesis because Dr Moo has not predicted a direction for the hypothesized relationship PTS: DIF: Hard REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Analysis 13 The research hypothesis posits that the treatment association between two variables will be greater than zero (H1: rxy > 0) What would be concluded for r(29) = 267, p > 05? ANS: The obtained value (.267) is less than the critical value (.296), so it can be concluded that the relationship between the two variables may have occurred due to chance PTS: DIF: Hard REF: Computing the Test Statistic OBJ: How to interpret the correlation coefficient COG: Application ... The appropriate test statistic to use is the _ a t -test for the correlation coefficient b p -test for the correlation coefficient c r -test for the correlation coefficient d t -test for statistical... with a one-tailed test and for a research hypothesis with a two-tailed test Write the equation for the null hypothesis ANS: One-tailed test H1: rxy > or H1: rxy < Two-tailed test H1: rxy  Null... for testing the level of significance of a correlation coefficient is which of the following? a .01 b .05 c .95 d .99 ANS: B PTS: DIF: Medium REF: Computing the Test Statistic OBJ: How to test