Deck 18: Understanding Correlation Coefficients in Statistical Analysis

Question 1

The correlation coefficient measures the extent to which changes in one factor are _______ in a second factor.

A)related to changes
B)causing changes
C)causing variability
D)all of the above

Answer 1

related to changes

Question 2

A researcher measures the relationship between narcissism and willingness to help.If = 240, = 320,and = 410,then what is the value of the correlation coefficient?

A)0.002
B)0.02
C)0.66
D)0.69

Answer 2

0.66

Question 3

The numerator of the correlation coefficient measures the extent to which two variables

A)vary together
B)vary independently
C)covary
D)both A and C

Answer 3

both A and C

Question 4

The coefficient of determination is mathematically equivalent to

A)the correlation coefficient
B)omega-squared
C)eta-squared
D)both B and C

Question 5

If = 5.32 and n = 40,then what is the value of the coefficient of determination?

A)0.133
B)0.36
C)0.64
D)There is not enough information to answer this question.

Question 6

A researcher measures the following correlation between cost of produce and number of units sold.Which description best explains the relationship between these two factors?

A)As the cost of produce increases,so also do the number of units sold.
B)Less expensive produce is associated with an increased number of units sold.
C)Less expensive produce is associated with a decreased number of units sold.
D)No linear pattern is evident.

Question 7

Which of the following indicates the strongest correlation?

A)r = -0.57
B)r = +0.78
C)r = -0.90
D)r = +0.88

Question 8

The correlation coefficient is used to measure the ________ and ________ of the linear relationship between two factors.

A)date;time
B)mean;variance
C)significance;effect size
D)strength;direction

Question 9

A statistical procedure used to describe the strength and direction of the linear relationship between two factors is called

A)effect size
B)power
C)a correlation
D)coincidence

Question 10

A researcher measures the following correlation between cups of coffee consumed daily and daily work schedule.Which description best explains the relationship between these two factors?

A)The more a person works,the more coffee he or she tends to drink.
B)The less a person works,the more coffee he or she tends to drink.
C)The more a person works,the less coffee he or she tends to drink.
D)No linear pattern is evident.

Question 11

A researcher measures the following correlation: r = -0.21.What is the value of the coefficient of determination?

A)0.04
B)-0.04
C)0.42
D)-0.42

Question 12

The coefficient of determination is

A)a measure of effect size
B)mathematically equivalent to eta-squared
C)equal to the correlation coefficient squared
D)all of the above

Question 13

Suppose a correlation is computed in each of two samples.If the value of is the same in each sample,and is larger in Sample 1,then in which sample will the value of the correlation coefficient be larger?

A)Sample 1
B)Sample 2
C)None;the correlation coefficient will be the same in both samples.
D)There is not enough information to answer this question.

Question 14

The most common measure of effect size for the correlation coefficient is called

A)the correlation coefficient
B)the coefficient of determination
C)estimated Cohen's d
D)the test statistic

Question 15

The correlation coefficient ranges between ____ and ____.

A)0;+1
B)-1;0
C)-1;+1
D)- $\infty$ ;+ $\infty$

Question 16

A researcher measures the following correlation between number of years of education and life satisfaction: r = +0.08.What is the value of the coefficient of determination?

A)0.08
B)0.16
C)0.01
D)0.11

Question 17

The following graphs display the data points for two linear correlations.Based on the information provided in these graphs,________ displays a negative correlation and ________ displays a stronger correlation.

A)Graph A;Graph B
B)Graph B;Graph A
C)Graph A;Graph A
D)Graph B;Graph B

Question 18

The denominator of the correlation coefficient measures the extent to which two variables

A)vary together
B)vary independently
C)covary
D)both A and C

Question 19

The correlation coefficient ranges from -1.0 to +1.0,with values closer to ±1.0 indicating

A)a more positive relationship between two factors
B)a stronger relationship between two factors
C)that two factors are less likely to be related
D)that the correlation is due to outliers

Question 20

A researcher measures the relationship between two variables,X and Y.If = 340 and = 320,000,then what is the value of the correlation coefficient?

A)0.32
B)0.34
C)0.60
D)almost a zero correlation

Question 21

The assumption that there is an equal variance or scatter of data points dispersed along the regression line is referred to as

A)normality
B)linearity
C)homoscedasticity
D)restriction of range

Question 22

Which of the following is a limitation for interpreting a correlation?

A)Correlations do not demonstrate cause-and-effect.
B)Outliers can change the direction and/or strength of the correlation.
C)Conclusions should not be drawn beyond the range of scores measured.
D)all of the above

Question 23

A researcher measures the correlation between self-esteem (high,low)and physical fitness scores among school athletes.In the study,12 participants reported high self-esteem and 12 reported low self-esteem.If = 9.06 and = 11,then what is the value of the correlation coefficient?

A)0.61
B)0.30
C)0.39
D)There is not enough information to answer this question.

Question 24

The normality assumption states that the population of X and Y scores form a bivariate ("two variable")normal distribution,such that

A)the population of X and Y scores are normally distributed
B)for each X score,the distribution of Y scores is normally distributed
C)for each Y score,the distribution of X scores is normally distributed
D)all of the above

Question 25

The point-biserial correlation coefficient is a measure of the direction and strength of the linear relationship between two variables,where

A)one is continuous,and one is dichotomous
B)both variables are on an ordinal scale
C)one is at interval level or higher and one is ordinal
D)both variables are on a nominal scale

Question 26

The Spearman rank-order correlation coefficient is a measure of the direction and strength of the linear relationship between two ________ variables.

A)nominal
B)ordinal
C)interval
D)ratio

Question 27

The appropriate correlation coefficient for measuring the direction and strength of the linear relationship between one continuous and one dichotomous variable is

A)the Spearman rank-order correlation coefficient
B)the point-biserial correlation coefficient
C)the phi correlation coefficient
D)none of the above

Question 28

A researcher observes a correlation of values from 2 to 10 points and draws conclusions about the full range of values in the population from 0 to 21 points.Which limitation for correctly interpreting a correlation coefficient did the researcher violate?

A)reverse causality
B)restriction of range
C)a confound variable
D)homoscedasticity

Question 29

A researcher measures the correlation in rankings for a sample of restaurants and consumers' rankings of their favorite restaurants.If = 96 and n = 12,then what is the value of the correlation coefficient?

A)0.07
B)0.34
C)0.66
D)0.94

Question 30

Which of the following is the assumption that the best way to describe the pattern of data is using a straight line?

A)normality
B)linearity
C)homoscedasticity
D)restriction of range

Question 31

Outliers can change the _____ of a correlation.

A)direction
B)strength
C)sign (+,-)
D)all of the above

Question 32

A researcher measures the correlation of the time it take participants to complete two tasks purported to measure the same cognitive skill.Participant times are converted to ranks from fastest to slowest.If = 165 and n = 20,then what is the decision for this correlation test?

A)Retain the null hypothesis.
B)Reject the null hypothesis.
C)There is not enough information to answer this question.

Question 33

The appropriate correlation coefficient for measuring for the direction and strength of the linear relationship between two dichotomous variables is

A)the Spearman rank-order correlation coefficient
B)the point-biserial correlation coefficient
C)the phi correlation coefficient
D)none of the above

Question 34

What is the problem with the following data for computing a correlation?

A)The correlation coefficient will equal 0 because it violates the assumption of normality.
B)The correlation coefficient will equal 1.0 because it violates the assumption of normality.
C)The correlation coefficient will equal 0 because it violates the assumption of linearity.
D)The correlation coefficient will equal 1.0 because it violates the assumption of linearity.

Question 35

An unanticipated variable not accounted for in a research study that could be causing or associated with observed changes in one or more measured variables is called

A)reverse causality
B)restriction of range
C)a confound variable
D)homoscedasticity

Question 36

The phi correlation coefficient is a measure for the direction and strength of the linear relationship between two ________ variables.

A)dichotomous
B)curvilinear
C)ordinal
D)significant

Question 37

A researcher measures the correlation between gender and student aptitude scores from 0 to 100 among 20 participants.If = 0.49,then what is the decision for this correlation test?

A)Retain the null hypothesis.
B)Reject the null hypothesis.
C)There is not enough information to answer this question.

Question 38

The appropriate correlation coefficient for measuring the direction and strength of the linear relationship between two ranked or ordinal variables is

A)the Spearman correlation coefficient
B)the point-biserial correlation coefficient
C)the phi correlation coefficient
D)none of the above

Question 39

A correlation coefficient can ______ demonstrate cause.

A)always
B)never
C)mostly
D)intermittently

Question 40

Which of the following is the assumption that there is an equal variance of data points dispersed along the regression line?

A)normality
B)linearity
C)homoscedasticity
D)restriction of range

Question 41

Select the description below that identifies the following correlation: r = .28,p < .01.

A)the correlation is positive
B)the correlation is statistically significant
C)the coefficient of determination is .08
D)all of the above

Question 42

We convert r to a chi-square statistic for which of the following correlation tests?

A)Pearson
B)Spearman
C)point-biserial
D)phi

Question 43

If r = 0.65 and n = 36,then what is the value of ?

A)3.84
B)5.99
C)15.21
D)23.40

Question 44

A correlation of r = .38 in a sample of 30 participants is statistically significant for a two-tailed test at a .05 level of significance.

Question 45

A researcher determines that = 3.76 to test for significance for a phi correlation coefficient.What was the decision for this phi correlation test?

A)Retain the null hypothesis.
B)Reject the null hypothesis
C)There is not enough information to answer this question.

Question 46

We convert r to a t statistic for which of the following correlation tests?

A)Pearson
B)Spearman
C)point-biserial
D)phi

Question 47

A positive correlation is always stronger than a negative correlation.

Question 48

The coefficient of determination is a measure of significance.

Question 49

A correlation of r = .50 in a sample of 15 participants is statistically significant for a two-tailed test at a .05 level of significance.

Question 50

To summarize correlations,we report:

A)the strength of the correlation
B)the direction of the correlation
C)the p value
D)all of the above

Question 51

The value of the sum of products can be positive or negative.

Question 52

The sign (+ or -)of a correlation coefficient indicates the direction of a relationship between two factors.

Question 53

The correlation coefficient varies between 0 and 1 and can never be negative.

Question 54

A researcher measures the correlation between the frequency of self-esteem (high,low)and health status (lean/healthy,overweight/obese).Based on the frequencies for each nominal category given below,what is the value of the phi correlation coefficient?

A)0.08
B)0.28
C)0.52
D)0.56

Question 55

The coefficient of determination is mathematically equivalent to eta-squared.

Question 56

The denominator of the Pearson correlation coefficient measures the extent to which two factors vary together.

Question 57

If = 3.84 and n = 36,then what is the value of r?

A)0.11
B)0.16
C)0.33
D)0.36

Question 58

The closer that data points fall to the regression line,the more closely two factors are related.

Question 59

A researcher computes the following phi correlation coefficient: = 0.42.If the sample size was 20,then what is the decision for this correlation test?

A)Retain the null hypothesis.
B)Reject the null hypothesis.
C)There is not enough information to answer this question.

Question 60

Which of the following would not be reported for a correlation?

A)the sample size
B)the coefficient of determination
C)the critical values for each test
D)the strength and direction of the correlation

Question 61

Outliers can change both the direction and strength of a correlation coefficient.

Question 62

Restriction of range occurs when an unanticipated variable not accounted for in a research study that could be causing or associated with observed changes in one or more measured variables.

Question 63

The correlation coefficient can be converted to a t statistic.

Question 64

The formula for the phi correlation coefficient was derived from the formula for the Pearson correlation coefficient.

Question 65

The formula for the Spearman correlation coefficient was derived from the formula for the Pearson correlation coefficient.

Question 66

The correlation coefficient can be converted to a chi-square statistic.

Question 67

If r = .25,then the coefficient of determination is .06.

Question 68

The formula for the point-biserial correlation coefficient was derived from the formula for the Pearson correlation coefficient.

Question 69

Homoscedasticity is the assumption that there is an equal variance of data points dispersed along the regression line.

Question 70

The coefficient of determination is the square root of the correlation coefficient.

Question 71

If r = 0.026 and df = 10,then t = 7.20.

Question 72

Correlation does not show causation.

Question 73

When we compute many correlations in a single study,we report each correlation coefficient in a table called a correlation matrix.

Question 74

The phi correlation coefficient is used to measure the correlation between two ordinal variables.

Question 75

Linearity is the assumption that the best way to describe a pattern of data is using a straight line.

Question 76

The assumption of normality requires that the range of scores observed in a sample is the same of the possible range of scores in the population.

Question 77

To summarize correlations,we report the strength,the direction,and the p value for each correlation coefficient.

Question 78

The Spearman correlation coefficient is used to measure the correlation between two nominal variables.

Question 79

The point-biserial correlation coefficient is used to measure the correlation between two dichotomous variables.

Question 80

Three assumptions for a correlation are homoscedasticity,linearity,and normality.