Statistics salkind 4e test bank ch05

Chapter 5: Ice Cream and Crime: Computing Correlation Coefficients Test Bank MULTIPLE CHOICE Who is responsible for the invention of the Pearson product–moment correlation coefficient? a Pearson Fisher b Karl Pearson c Karl Fisher d Fisher Pearson ANS: B PTS: REF: What Are Correlations All About? COG: Knowledge DIF: Easy OBJ: What correlations are and how they work When interested in examining how one variable changes in relation to another, which of the following descriptive statistics would you want to use? a Mean b Variance c Correlation d Standard Deviation ANS: C PTS: REF: What Are Correlations All About? COG: Knowledge DIF: Easy OBJ: What correlations are and how they work Which of the following is an example of a correlation? a Mean b Variance c Phi coefficient d Standard Deviation ANS: C PTS: DIF: Easy REF: Other Cool Correlations OBJ: What other types of correlations exist and when to use them COG: Knowledge Correlation coefficients are used to describe a A group b Individuals c Individuals as well as the group d This depends on the correlation coefficient used ANS: A PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: How to interpret the value of the correlation coefficient COG: Knowledge Which of the following refers to a correlation between two variables? a Bicorrelate b Bivariate c Two-way variance d Two-way analysis ANS: B PTS: REF: What Are Correlations All About? COG: Knowledge DIF: Medium OBJ: What correlations are and how they work Which of the following illustrates the range of possible values of Pearson’s product–moment correlation coefficient? a -.01 to 01 b -1.0 to 1.0 c -2.0 to 2.0 d -3.0 to 3.0 ANS: B PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: How to interpret the value of the correlation coefficient COG: Knowledge If variables change in the same direction, what type of correlation is this called? a Positive correlation b Negative correlation c Positive causation d Negative causation ANS: A PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge If variables change in the opposite direction, what type of correlation is this called? a Positive correlation b Negative correlation c Positive causation d Negative causation ANS: B PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge The correlation between variable X and variable Y is represented by which of the following? a R(xy)2 b rxy c rx(y) d Rx / y ANS: B PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge 10 Pearson’s product–moment correlation coefficient is represented by the following letter: a r b p c c d z ANS: A PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge 11 What would you use to visually represent a correlation? a Histogram b Polygon c Line graph d Scatterplot ANS: D PTS: DIF: Easy REF: A Visual Picture of a Correlation: The Scatterplot OBJ: What correlations are and how they work COG: Knowledge 12 When data points group together in a cluster from the lower left-hand side of the xy axis to the upper right-hand side, what is this? a Negative slope b Positive slope c Negative intercept d Positive intercept ANS: B PTS: DIF: Medium REF: A Visual Picture of a Correlation: The Scatterplot OBJ: What correlations are and how they work COG: Knowledge 13 When data points group together in a cluster from the upper left-hand side of the xy axis to the lower right-hand side, what is this? a Negative slope b Positive slope c Positive intercept d Negative intercept ANS: A PTS: DIF: Medium REF: A Visual Picture of a Correlation: The Scatterplot OBJ: What correlations are and how they work COG: Knowledge 14 If the correlation between variables is 70, what percentage of the variance is shared variance? a 70% b 51% c 49% d 30% ANS: C PTS: DIF: Medium REF: A Determined Effort: Squaring the Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Application 15 If the correlation between variables is 70, what percentage of the variance is not shared variance? a 70% b 51% c 49% d 30% ANS: B PTS: DIF: Medium REF: A Determined Effort: Squaring the Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Application 16 If the correlation between variables is 80, what is the coefficient of determination? a .20 b .34 c .64 d .80 ANS: C PTS: DIF: Medium REF: A Determined Effort: Squaring the Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Application 17 If the correlation between variables is 60, what is the coefficient of alienation? a .36 b .40 c .60 d .64 ANS: D PTS: DIF: Medium REF: A Determined Effort: Squaring the Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Application 18 Which of the following correlations would be interpreted as a very strong relationship? a .80 b .70 c .60 d .50 ANS: A PTS: DIF: Medium OBJ: How to interpret the value of the correlation coefficient REF: Using-Your-Thumb Rule COG: Application 19 Which of the following correlations would be interpreted a strong relationship? a .39 b .59 c .79 d .89 ANS: C PTS: DIF: Medium OBJ: How to interpret the value of the correlation coefficient REF: Using-Your-Thumb Rule COG: Application 20 Which of the following correlations would be interpreted a moderate relationship? a .25 b .35 c .45 d .65 ANS: C PTS: DIF: Medium OBJ: How to interpret the value of the correlation coefficient REF: Using-Your-Thumb Rule COG: Application 21 Which of the following correlations would be interpreted as a weak relationship? a -.26 b -.46 c -.66 d -.86 ANS: A PTS: DIF: Medium OBJ: How to interpret the value of the correlation coefficient REF: Using-Your-Thumb Rule COG: Application 22 Which of the following is the strongest correlation? a .21 b .87 c .44 d -.92 ANS: D PTS: DIF: Medium OBJ: How to interpret the value of the correlation coefficient REF: Using-Your-Thumb Rule COG: Application 23 Which of the following is the weakest correlation? a -.24 b -.22 c .19 d -.96 ANS: C PTS: DIF: Medium OBJ: How to interpret the value of the correlation coefficient REF: Using-Your-Thumb Rule COG: Application 24 This is another word for a positive correlation: a Inverse correlation b Negative correlation c Strong correlation d Direct correlation ANS: D PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge 25 This is another word for a negative correlation: a Direct correlation b Weak correlation c Strong correlation d Indirect correlation ANS: D PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge 26 This is a correlation that is best expressed as a straight line: a Line correlation b Direct correlation c Strong correlation d Linear correlation ANS: D PTS: DIF: Easy REF: Using Excel to Create a Scatterplot OBJ: What correlations are and how they work COG: Comprehension 27 This is a situation in which the correlation between two variables begins as a direct correlation, then becomes an indirect correlation, or vice versa a Direct relationship b Linear relationship c Curvilinear relationship d Reverse relationship ANS: C PTS: DIF: Easy REF: Using Excel to Create a Scatterplot OBJ: What correlations are and how they work COG: Comprehension 28 The coefficient of determination is equal to a The square of the Pearson product–moment correlation coefficient b The square of the phi coefficient c The square root of the Pearson product–moment correlation coefficient d The square root of the phi coefficient ANS: A PTS: DIF: Medium REF: A Determined Effort: Squaring the Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Knowledge 29 The amount of unexplained variance in a relationship between two variables is called _ a Coefficient of determination b Coefficient of alienation c Pearson’s product–moment correlation coefficient d Phi coefficient ANS: B PTS: DIF: Medium REF: A Determined Effort: Squaring the Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Knowledge 30 A positive correlation between two variables would be represented in a scatterplot as a A line sloping upward b A line sloping downward c A horizontal line d A vertical line ANS: A PTS: DIF: Medium REF: A Visual Picture of a Correlation: The Scatterplot OBJ: What correlations are and how they work COG: Knowledge 31 A negative correlation between two variables would be represented in a scatterplot as a A line sloping upward b A line sloping downward c A horizontal line d A vertical line ANS: B PTS: DIF: Medium REF: A Visual Picture of a Correlation: A Scatterplot OBJ: What correlations are and how they work COG: Knowledge 32 If the correlation between two variables was equal to 0, the scatterplot between these two variables would be represented as a A line sloping upward b A line sloping downward c A horizontal line d A vertical line ANS: C PTS: DIF: Medium REF: A Visual Picture of a Correlation: The Scatterplot OBJ: What correlations are and how they work COG: Application 33 This is used to summarize the correlations between a set of variables: a Scatterplot b Correlation c Correlation matrix d Scatterplot matrix ANS: C PTS: DIF: Medium REF: Bunches of Correlations: The Correlation Matrix OBJ: Using the Correlation tool in the Data Analysis tools to compute a correlation and a correlation matrix COG: Knowledge 34 If the range of one or both of the variables is restricted, the correlation will be _ a Strengthened b Reduced c The same d It cannot be determined ANS: B PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Comprehension 35 If you wanted to compute the correlation between two interval-level variables, which type of correlation should you use? a Point biserial b Phi c Spearman rank d Pearson ANS: D PTS: DIF: Medium REF: Other Cool Correlations OBJ: What other types of correlations exist and when to use them COG: Comprehension 36 If you wanted to compute the correlation between two nominal-level variables, which type of correlation should you use? a Point biserial b Phi c Spearman rank d Pearson ANS: B PTS: DIF: Medium REF: Other Cool Correlations OBJ: What other types of correlations exist and when to use them COG: Comprehension 37 If you wanted to compute the correlation between two ordinal-level variables, which type of correlation should you use? a Point biserial b Phi c Spearman rank d Pearson ANS: C PTS: DIF: Medium REF: Other Cool Correlations OBJ: What other types of correlations exist and when to use them COG: Comprehension 38 If you wanted to compute the correlation between one nominal-level variable and one interval-level variable, which type of correlation should you use? a Point biserial b Phi c Spearman rank d Pearson ANS: A PTS: DIF: Medium REF: Other Cool Correlations OBJ: What other types of correlations exist and when to use them COG: Comprehension 39 If the coefficient of determination between two variables is 81, what is the Pearson correlation coefficient? a .19 b .34 c .66 d .90 ANS: D PTS: DIF: Medium REF: A Determined Effort: Squaring the Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Application 40 If the coefficient of determination between two variables is 81, what is the coefficient of alienation? a .19 b .34 c .66 d .90 ANS: A PTS: DIF: Medium REF: A Determined Effort: Squaring the Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Application 41 What is the numerical index that describes the relationships between two variables? a Regression coefficient b Chi index c Correlation coefficient d Psi index ANS: C PTS: REF: What Are Correlations All About? DIF: Medium OBJ: How to interpret the value of the correlation coefficient COG: Knowledge 42 The Pearson product–moment correlation examines the relationship between what type of variables? a Discontinuous b Continuous c Nominal level d Large ANS: B PTS: REF: What Are Correlations All About? COG: Knowledge DIF: Medium OBJ: What correlations are and how they work 43 This measure is equal to the percentage of variance in one variable that is accounted for by the variance in a second variable a Correlation coefficient b Pearson’s product–moment correlation coefficient c Coefficient of determination d Coefficient of alienation ANS: C PTS: DIF: Medium REF: A Determined Effort: The Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Knowledge 44 If X increases in value as Y decreases in value, what type of correlation exists? a Positive b Negative c Neutral d None ANS: B PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge 45 If X decreases in value as Y increases in value, what type of correlation exists? a Positive correlation b Direct correlation c Negative correlation d No correlation ANS: C PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge 46 If X decreases in value as Y decreases, what type of correlation exists? a Positive correlation b Negative correlation c Neutral correlation d No correlation ANS: A PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge 47 If X increases in value as Y increases, what type of correlation exists? a Positive correlation b Negative correlation c No correlation d Inverse correlation ANS: A PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge 48 “The better your time management skills are, the more work you are able to do” is an example of a _ a Continuous correlation b Biserial correlation c Positive correlation d Negative correlation ANS: C PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Application 49 “The more oatmeal you eat, the lower your blood cholesterol level” is an example of a _ a Continuous correlation b Biserial correlation c Positive correlation d Negative correlation ANS: D PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Application 50 If X increases in value as Y increases in value, what type of correlation exists? a Positive correlation b Absolute correlation c Negative correlation d Nonabsolute correlation ANS: A PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Comprehension 51 If X decreases in value as Y increases in value, what type of correlation exists? a Positive correlation b Absolute correlation c Negative correlation d Nonabsolute correlation ANS: C PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Comprehension TRUE/FALSE You can use Pearson’s correlation coefficient if one or more of your variables are ordinal or nominal ANS: F PTS: DIF: Medium OBJ: What correlations are and how they work REF: Other Cool Correlations COG: Comprehension When you have a direct correlation, both variables change in the same direction ANS: T PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge A negative correlation indicates that variables change in opposite directions ANS: T PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge Correlation coefficients describe every individual person in your data set ANS: F PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Knowledge The coefficient of determination is more precise than using a correlation coefficient alone ANS: T PTS: DIF: Medium REF: A Determined Effort: Squaring the Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Comprehension If two variables are correlated, this implies that one variable causes the other ANS: F PTS: DIF: Medium REF: As More Ice Cream Is Eaten, the Crime Rate Goes Up (or Association Versus Causality) OBJ: What correlations are and how they work COG: Comprehension In certain cases, Pearson’s product–moment correlation coefficient can have values greater than ANS: F PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: How to interpret the value of the correlation coefficient COG: Comprehension It is better to find a positive correlation as opposed to a negative correlation ANS: F PTS: DIF: Easy REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Comprehension In a correlation matrix, the numbers above and below the diagonal row of 1.00s are a mirror image of themselves ANS: T PTS: DIF: Easy REF: Bunches of Correlations: The Correlation Matrix OBJ: Using the Correlation tool in the Data Analysis tools to compute a correlation and a correlation matrix COG: Knowledge SHORT ANSWER How is a direct correlation different from an indirect correlation? ANS: If variables change in the same direction, then there is a direct (or positive) correlation If variables change in opposite directions, then there is an indirect (or negative) correlation PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Comprehension Is a correlation of 0.6 stronger than a correlation of -0.9? Why or why not? ANS: A correlation of -0.9 is stronger than a correlation of 0.6 because the absolute value of the correlation reflects the strength of the correlation PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: How to interpret the value of the correlation coefficient COG: Application A correlation coefficient comparing exercise and body mass is -.67 What does this say about the relationship between exercise and weight? ANS: If exercise / body mass = -.67, then there is a strong indirect or negative relationship; greater exercise is associated with less body mass PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: How to interpret the value of the correlation coefficient COG: Application A correlation coefficient comparing study time to grades is +.80 Can one then conclude that greater study time causes good grades? Why or why not? ANS: No, one could not conclude that greater study time causes good grades because correlations only reflect association, not causality One could say that greater study time is associated with good grades PTS: DIF: Medium REF: As More Ice Cream Is Eaten, the Crime Rate Goes Up (or Association Versus Causality) OBJ: How to interpret the value of the correlation coefficient COG: Application In the formula for the Pearson correlation coefficient, what is the difference between the sum of a set of values squared and the sum of the squared values? ANS: The sum of a set of values squared adds the values together before squaring them, whereas the sum of the squared values squares the values before adding them together PTS: DIF: Medium REF: Computing a Simple Correlation Coefficient OBJ: How to compute a single correlation coefficient COG: Comprehension What is the purpose of a scatterplot? ANS: The shape of the plotted data points on a scatterplot or scattergram can indicate if the relationship between the variables is positive (direct), negative (indirect), if there is no relationship, or if the relationship is curvilinear PTS: DIF: Medium REF: A Visual Picture of a Correlation: The Scatterplot OBJ: What correlations are and how they work COG: Comprehension Why will you rarely find a perfect correlation between any two variables? ANS: You will rarely find a perfect correlation between any two variables because few variables are exactly alike PTS: DIF: Medium REF: A Visual Picture of a Correlation: The Scatterplot OBJ: What correlations are and how they work COG: Comprehension Give an example of two variables that may have a curvilinear relationship instead of a linear one ANS: The relationship between caffeine intake and performance, anxiety and performance, or many others PTS: DIF: Medium REF: Using Excel to Create a Scatterplot OBJ: What correlations are and how they work COG: Comprehension What information does the coefficient of determination provide? ANS: The coefficient of determination is the percentage of variance in one variable that is accounted for by the variance in the other variable In other words, it tells how much of one “thing” explains or “overlaps” with something else; the stronger the relationship between two variables, the greater the coefficient of determination PTS: DIF: Medium REF: A Determined Effort: The Correlation Coefficient OBJ: How to interpret the value of the correlation coefficient COG: Knowledge 10 How does a positive slope differ from a negative slope? ANS: A positive slope indicates a positive (or direct) relationship between two variables A negative slope indicates a negative (or indirect) relationship PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Comprehension 11 What is a correlation coefficient, and what is its range? ANS: A correlation coefficient is a numerical index that reflects the relationship between two variables The value of the correlation coefficient ranges from -1.0 to +1.0 PTS: DIF: Medium REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: How to interpret the value of the correlation coefficient COG: Knowledge 12 Under what circumstances would you use the phi coefficient? ANS: X = nominal variable and Y = nominal variable PTS: DIF: Medium REF: Other Cool Correlations OBJ: What other types of correlations exist and when to use them COG: Comprehension 13 Under what circumstances would you use the Pearson correlation? ANS: X = interval variable and Y = interval variable PTS: DIF: Medium REF: Other Cool Correlations OBJ: What correlations are and how they work COG: Comprehension 14 Under what circumstances would you use the rank biserial? ANS: X = nominal variable and Y= ordinal variable PTS: DIF: Medium REF: Other Cool Correlations OBJ: What correlations are and how they work COG: Comprehension 15 Under what circumstances would you use the point biserial? ANS: X = nominal variable and Y = interval variable PTS: DIF: Medium REF: Other Cool Correlations OBJ: What other types of correlations exist and when to use them COG: Comprehension 16 Under what circumstances would you use the Spearman rank? ANS: X = ordinal variable and Y = ordinal variable PTS: DIF: Medium REF: Other Cool Correlations OBJ: What other types of correlations exist and when to use them COG: Comprehension 17 In order to calculate a Pearson’s r between the hours college students study in a week and their GPAs, it would be best to have the students report their cumulative GPA as a number out to the hundredths rather than as pre-established categories (A = 4, B = 3, C = 2, D = 1, F = 0) Please explain why that is ANS: Pearson’s correlations need to be conducted with continuous variables, and the numerical equivalent of a letter grade is categorical data PTS: DIF: Medium REF: Other Cool Correlations OBJ: What correlations are and how they work COG: Application 18 A sample of typical undergraduate students is very likely to have a range of GPAs from 0.0 to 4.0, whereas graduate students are often required to have good grades (e.g., from 3.0 to 4.0) Please explain what influence these two different ranges of GPA would have on any correlations calculated on these two separate groups of students ANS: Correlations reflect the amount of variability that is shared between two variables and what they have in common The graduate students’ GPAs not vary nearly as much as the undergraduate students (the data are more restricted), so correlations using the graduate students’ GPAs are more likely to be close to zero than correlations using the undergraduates’ GPAs PTS: DIF: Hard REF: Types of Correlation Coefficients: Flavor and Flavor OBJ: What correlations are and how they work COG: Analysis 19 If you expected a strong correlation between the anxiety students have and how well they perform on their statistics exam—and it turns out that the correlation is not that strong—plotting out a _ could assist you in understanding your results ANS: scatterplot (or scattergram) PTS: DIF: Medium REF: Using Excel to Create a Scatterplot OBJ: What correlations are and how they work COG: Application 20 When you review the image plotted in the correlation of test anxiety scores and statistics exam scores (in the above item), you notice that the data points not appear to show a linear correlation What type of relationship might be shown instead, and what does it say about the relationship between test anxiety and exam scores? ANS: The relationship could be curvilinear In other words, too little anxiety or too much anxiety could be associated with poor statistics exam scores, but optimal levels of anxiety could be associated with high scores PTS: DIF: Hard REF: Using Excel to Create a Scatterplot OBJ: What correlations are and how they work COG: Application ... they work COG: Application 20 When you review the image plotted in the correlation of test anxiety scores and statistics exam scores (in the above item), you notice that the data points not appear... relationship between test anxiety and exam scores? ANS: The relationship could be curvilinear In other words, too little anxiety or too much anxiety could be associated with poor statistics exam scores,... expected a strong correlation between the anxiety students have and how well they perform on their statistics exam—and it turns out that the correlation is not that strong—plotting out a _ could