Deck 15: Correlation

Question 1

The results from a research study indicate that adolescents who watch more violent content on television also tend to engage in more violent behavior than their peers.The correlation between amount of TV violent content and amount of violent behavior is an example of a ____.​

A)​positive correlation
B)​negative correlation
C)​correlation near zero
D)​correlation near one

Answer 1

​positive correlation

Question 2

Which of the following best describes the Pearson correlation for these data?? $$\begin{array} { l l } \mathrm { X } & \mathrm { Y } \\2 & 5 \\5 & 1 \\3 & 4 \\4 & 2 \\\hline\end{array}$$

A)?It is positive.
B)?It is negative.
C)?It is close to zero.
D)?It is equal to zero.

Answer 2

?It is negative.

Question 3

What would the scatterplot show for data that produce a correlation of +0.88?​

A)​points clustered close to a line that slopes up to the right
B)​points clustered close to a line that slopes down to the right
C)​points widely scattered around a line that slopes up to the right
D)​points widely scattered around a line that slopes down to the right

Answer 3

​points clustered close to a line that slopes up to the right

Question 4

A scatter plot shows data points that are widely scattered around a line that slopes down to the right.Which value would be closest to the correlation for these data?​

A)​-0.80
B)-0.40
C)​0.40
D)​0.80

Question 5

A set of n = 10 pairs of scores has ΣX = 20,ΣY = 30,and ΣXY = 74.What is the value of SP for these data?​

A)74​
B)​24
C)​14
D)​-14

Question 6

A set of n = 15 pairs of scores (X and Y values)has SS_X = 4,SS_Y = 25,and SP = 6.The Pearson correlation for these data is ____.?

A)6/100?
B)?6/10
C)?6/(100/15)
D)?6/(10/ $\sqrt { 15 }$ )

Question 7

A college professor reports that students who finish exams early tend to get better grades than students who hold on to exams until the last possible moment.The correlation between exam score and amount of time spent on the exam is an example of a ____.​

A)​positive correlation
B)​negative correlation
C)​correlation near zero
D)​correlation near one

Question 8

What is indicated by a positive value for a correlation?​

A)​Increases in X tend to be accompanied by increases in Y.
B)​Increases in X tend to be accompanied by decreases in Y.
C)​A much stronger relationship exists than if the correlation were negative.
D)​A much weaker relationship exists than if the correlation were negative.

Question 9

The term correlation refers to a statistical technique that is used to ____.​

A)​measure and describe the linear relationship between two variables
B)​measure the magnitude of a variable
C)​measure the significance of a variable
D)​measure the fit of a model

Question 10

​For which of the following correlations would the data points be clustered most closely around a straight line?

A)​r = -0.10
B)​r = +0.40
C)​r = -0.70
D)​r = -0.00

Question 11

The scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle.For these data,what is the most likely value for the correlation?​

A)a positive correlation near 0​
B)​a negative correlation near 0
C)​either positive or negative near 0
D)​a value near +1.00 or 1.00

Question 12

A set of n = 5 pairs of X and Y scores has ΣX = 15,ΣY = 5,and ΣXY = 10.For these data,the value of SP is ____.​

A)-5​
B)​5
C)​10
D)​25

Question 13

A researcher records the odometer reading and age of used Hondas.What kind of correlation is likely to be obtained for these two variables?​

A)​a positive correlation
B)​a negative correlation
C)​a correlation near zero
D)​a correlation near one

Question 14

A researcher measures driving distance from college and weekly expense on gas for a group of commuting college students.What kind of correlation is likely to be obtained for these two variables?​

A)​a positive correlation
B)​a negative correlation
C)​a correlation near zero
D)​a correlation near one

Question 15

What is the value of SP for the following set of data?? $$\begin{array} { l l } X & Y \\4 & 3 \\1 & 2 \\1 & 5 \\2 & 6 \\\hline\end{array}$$

A)-1?
B)?-5
C)?5
D)?1

Question 16

The numerical value for a correlation can ____.​

A)never be greater than 1.00​
B)​never be less than 1.00
C)​never be greater than 1.00 and can never be less than -1.00
D)​be greater than 1.00 and can be less than -1.00

Question 17

A researcher measures IQ and weight for a group of college students.What kind of correlation is likely to be obtained for these two variables?​

A)a positive correlation​
B)​a negative correlation
C)​a correlation near zero
D)​a correlation near one

Question 18

What is the value of SP for the following set of data?? $$\begin{array} { l l } \mathrm { X } & \mathrm { Y } \\\hline 1 & 4 \\2 & 4 \\9 & 1 \\\hline\end{array}$$

A)?-5
B)?5
C)?-15
D)?15

Question 19

​Which of the following sets of correlations is correctly ordered from the highest to the lowest degree of relationship?

A)​0.91, +0.83, +0.10, 0.03
B)​0.91, +0.83, 0.03, 0.10
C)​+0.83, +0.10, 0.91, 0.03
D)​+0.83, +0.10, 0.03, 0.91

Question 20

Which correlation value shows the greatest strength or consistency of relationship?​

A)-0.90​
B)​+0.74
C)​+0.85
D)​-0.33

Question 21

For a sample of n = 16 individuals,how large a Pearson correlation is necessary to be statistically significant for a two-tailed test with α = .05?​

A)0.497​
B)​0.482
C)​0.468
D)​0.456

Question 22

How large a sample is needed for a correlation of r = 0.550 to be significant using a two-tailed test with α = .05?​

A)​n = 14
B)​n = 13
C)​n = 12
D)​n = 11

Question 23

For a two-tailed hypothesis test evaluating a Pearson correlation,what is stated by the null hypothesis?​

A)​There is a non-zero correlation for the general population.
B)​The population correlation is zero.
C)​There is a non-zero correlation for the sample.
D)​The sample correlation is zero.

Question 24

If the following seven scores are ranked from smallest to largest,then what rank should be assigned to a score of X = 1?Scores: 1,1,1,1,3,6,6,6,9​

A)1​
B)​2
C)​2.5
D)​4

Question 25

What correlation is obtained when the Pearson correlation is computed for data that have been converted to ranks?​

A)​the Spearman correlation
B)​the point-biserial correlation
C)​the phi coefficient
D)​the simple correlation

Question 26

A set of n = 5 pairs of X and Y values has SS_X = 16,SS_Y = 4 and SP = 2.For these data,the Pearson correlation is ____.​

A)​r = 2/64
B)​r = 2/8
C)​r = 8/8
D)​r = 64/8

Question 27

The Pearson and the Spearman correlations are both computed for the same set of data.If the Spearman correlation is r_S = +1.00,then what can you conclude about the Pearson correlation?​

A)It will be positive.​
B)​It will be negative and have a value of -1.00.
C)​It will be positive and have a value of 1.00.
D)​It will be negative.

Question 28

Which correlation should be used to measure the relationship between gender and grade point average for a group of college students?​

A)​Pearson correlation
B)​Spearman correlation
C)​point-biserial correlation
D)​phi-coefficient

Question 29

Under what circumstances is the point-biserial correlation used?​

A)​in the same circumstances when a repeated-measures t test would be used
B)​when X consists of regular, numerical scores but Y is dichotomous
C)​when both X and Y are dichotomous variables
D)​when both X and Y are measured on an ordinal scale (ranks)

Question 30

As the sample size gets larger,what happens to the size of the correlation that is needed for significance?​

A)​It also gets larger.
B)​It gets smaller.
C)​It stays constant.
D)​There is no consistent relationship between sample size and the critical value for a significant correlation.

Question 31

The Pearson and the Spearman correlations are both computed for the same set of data.If the Pearson correlation is r = +1.00,then what can you conclude about the Spearman correlation?​

A)​It will be negative.
B)​It will have a value of -1.00.
C)​It will be positive and have a value of 1.00.
D)​There is no predictable relationship between the Pearson and the Spearman correlations.

Question 32

The effect size for the data from an independent-measures t test can be measured by r².Which of the following also produces the value for r²?​

A)​squaring the Spearman correlation for the same data
B)​squaring the point-biserial correlation for the same data
C)​squaring the Pearson correlation for the same data
D)​taking the square root of the Pearson correlation

Question 33

If the Pearson correlation is calculated for a sample of n = 20 individuals,what value for df should be used to determine whether or not the correlation is significant?​

A)​18
B)​19
C)​20
D)​21

Question 34

A researcher obtains a Pearson correlation of r = 0.43 for a sample of n = 20 participants.For a two-tailed test,which of the following accurately describes the significance of the correlation?​

A)​The correlation is significant with α = .05 but not with α = .01.
B)​The correlation is significant with either α = .05 or α = .01.
C)​The correlation is not significant with either α = .05 or α = .01.
D)​The correlation is equal to zero.

Question 35

For a group of graduating college seniors,a researcher records each student's rank in his/her high school graduating class and the student's rank in the college graduating class.Which correlation should be used to measure the relationship between these two variables?​

A)​Pearson correlation
B)​Spearman correlation
C)​point-biserial correlation
D)​phi-coefficient

Question 36

Suppose that the correlation between height and weight for adults is +0.40.What proportion (or percent)of the variability in weight can be explained by the relationship with height?​

A)​40%
B)​60%
C)​16%
D)​84%

Question 37

A Pearson correlation is computed for a sample of n = 18 pairs of X and Y values.What correlations are statistically significant with α = .05,two tails?​

A)​correlations between 0.468 and -0.468
B)​correlations greater than or equal to 0.468 and correlation less than or equal to -0.468
C)​correlations between 0.456 and -0.456
D)​correlations greater than or equal to 0.456 and correlation less than or equal to -0.456

Question 38

Under what circumstances is the phi-coefficient used?​

A)​when one variable consists of ranks and the other is regular, numerical scores
B)​when both variables consists of ranks
C)​when both X and Y are dichotomous variables
D)​when one variable is dichotomous and the other is regular, numerical scores

Question 39

​If the following seven scores are ranked from smallest to largest,then what rank should be assigned to a score of X = 6?Scores: 1,1,3,6,6,6,9

A)3​
B)​4
C)​5
D)​6

Question 40

A set of n = 15 pairs of scores (X and Y values)produces a correlation of r = 0.40.If each of the X values is multiplied by 2 and the correlation is computed for the new scores,what value will be obtained for the new correlation?​

A)​r = 0.20
B)​r = 0.40
C)​r = 0.80
D)​This cannot be determined without knowing all the X and Y scores.

Question 41

The value for the sum of products (SP)is always greater than or equal to zero.

Question 42

The value r² is called the coefficient of determination because it measures the proportion of variability in one variable that can be determined from the relationship with the other variable.

Question 43

For a set of n = 10 pairs of scores with ΣX = 10,ΣY = 40,and ΣXY = 50,the sum of products of deviation is SP = 10.

Question 44

A negative correlation means that decreases in the X variable tend to be accompanied by decreases in the Y variable.

Question 45

For a positive correlation,decreases in X tend to be accompanied by decreases in Y.

Question 46

Suppose that there is a correlation of +0.41 between the amount of time that each student spends on social media and the student's grade on the exam.This correlation clearly indicates that people who spend more time on social media receive better grades.

Question 47

The sign (+ or -)and the strength of a correlation are independent of each other.

Question 48

A researcher obtains SS_X = 20,SS_Y = 5,and SP = 7 for a set of n = 25 pairs of scores.The Pearson correlation for these scores is r = 7/10 = 0.70.

Question 49

The value obtained for the sum of products,SP,determines the sign (+/)for the correlation.

Question 50

The value for a correlation can never be greater than +1.00.

Question 51

If the data points in a scatter plot show a nearly circular pattern,then the correlation is near zero.

Question 52

The sum of products (SP)is used to measure the amount of covariability between two variables.

Question 53

There is a statistical technique,known as partial correlation,which allows a researcher to measure the relationship between two variables while eliminating or holding constant the influence of a third variable.

Question 54

The Pearson correlation measures the degree and the direction of the linear relationship between two variables.

Question 55

Whenever a correlation is computed from scores that do not represent the full range of possible values,one is working with a restricted range and caution should be used when interpreting the correlation.

Question 56

A correlation of +0.95 means that there is essentially no consistent relationship between X and Y.

Question 57

Assuming that other factors are constant,a correlation of r = 0.95 will result in more accurate predictions than a correlation of r = +0.70.​

Question 58

If you measured hearing acuity and age for a group of people who are 50 to 90 years old,you should obtain a negative correlation between the two variables.

Question 59

A correlation of +0.90 indicates that the data points are clustered close to a line that slopes down to the right.

Question 60

If the value of the Pearson correlation between two variables is r = +1.00 or 1.00,then all data points in a scatter plot will fit perfectly on a straight line.

Question 61

Compute the Pearson correlation for the following data.​

Question 62

The Spearman correlation can be +1.00 or 1.00 even when there is no linear relationship between the two variables.

Question 63

Compute the Pearson correlation for the following data.​

Question 64

A psychologist would like to evaluate the relationship between verbal skills as measured by the Scholastic Achievement Test (SAT)and performance on an anagram task.(Anagrams are words with the letters scrambled.The task is to unscramble the letters and identify the word.)Each subject is given a set of 10 anagrams,and the psychologist records how much time is needed to solve all 10.The anagram times and each subject's SAT score are as follows.(Note that two subjects failed to complete all 10 anagrams.)Use a Spearman correlation to measure and describe the relationship between SAT and anagram performance.​

Question 65

A sample of n = 25 pairs of scores (X and Y values)produces a correlation of r = -0.40.Are these sample data sufficient to conclude that there is a significant non-zero correlation between X and Y in the population? Use a two-tailed test at the .05 level of significance.

Question 66

The Spearman correlation is used to measure the relationship when both variables have been measured on an ordinal scale (both are ranks).

Question 67

If participants in a study are classified by age (over 30/under 30)and by political affiliation (Democrat/Republican),then the point-biserial correlation would be the proper technique to measure the relationship between the two variables.

Question 68

A researcher classifies people by gender and by whether or not they routinely watch the evening news on television.For the resulting data,the correct method for measuring the relationship between the two variables would be the phi-coefficient.

Question 69

​The sign of the correlation (+/)is generally meaningless for the point-biserial correlation and the phi-coefficient.

Question 70

In a test for significance of a Pearson correlation for a sample of n = 30 individuals,one determines the critical value by using df = 29.​

Question 71

Describe what is meant by a negative relationship and a positive relationship between two variables.

Question 72

The phi-coefficient is used to measure relationships for data that would also be appropriate for an independent-measures t test.

Question 73

The following data show the results from an independent-measures study comparing two treatments.
a. Compute the independent-measures t statistic for these data.
b. Compute the percentage of variance explained by the treatment effect (r²).
b.)​Treatment
c. Convert the data into a form suitable for calculating the point-biserial correlation, and compute the correlation. (You should find that squaring the point-biserial correlation will produce the same r² value that you obtained in part

Question 74

The phi-coefficient is the correct correlation to use when both X and Y are dichotomous variables.

Question 75

Using a two-tailed test with α = .05,a sample correlation of r = 0.355 for a sample of n = 30 individuals is large enough to conclude that there is a real correlation in the general population.​

Question 76

If the Pearson correlation for a set of scores is equal to +1.00,then the Spearman correlation for the same scores would also be equal to +1.00.