Deck 6: Correlation

Question 1

In a positive relationship, _________.

A) as X increases, Y increases
B) as X decreases, Y decreases
C) as X increases, Y increases and as X decreases, Y decreases
D) as X increases, Y decreases

Answer 1

as X increases, Y increases and as X decreases, Y decreases

Question 2

Which of the following is(are) correct interpretation(s) of correlation? Correlation _________.

A) indicates the degree of the relationship between two variables
B) indicates a causal relationship between two variables
C) is useful in deciding which variables to manipulate in an experimental study
D) a and b
E) a and c

Answer 2

a and c

Question 3

In an imperfect relationship, _________.

A) all the points fall on the line
B) a relationship exists, but all of the points do not fall on the line
C) no relationship exists
D) a relationship exists, but none of the points can fall on the line

Answer 3

a relationship exists, but all of the points do not fall on the line

Question 4

If the correlation between variables X and Y is 0.95, which of the following is true?

A) X is a cause of Y
B) Y is a cause of X
C) low scores on X are accompanied by high scores on Y
D) high scores on X are accompanied by high scores on Y
E) a and d

Question 5

Correlation and regression differ in that _________.

A) correlation is primarily concerned with the size and direction of relationships
B) regression is primarily used for prediction
C) both of these are true
D) neither of these are true

Question 6

The lowest degree of correlation shown below is _________.

A) 0.75
B) - 0.33
C) - 0.25
D) 0.15

Question 7

In the equation Y = bX + a , X and Y , a is _________.

A) a constant giving the value of the Y axis intercept
B) a constant giving the value of the slope of the line
C) a variable relating X to Y
D) a variable relating Y to X

Question 8

Y can be most accurately predicted from X if the correlation between X and Y is _________.

A) 0.80
B) 0.00
C) 0.45
D) - 0.98

Question 9

A scatter plot _________.

A) has to do with electron scatter
B) is a graph of paired X and Y values
C) must be linear
D) is a frequency graph of X values

Question 10

The correlation coefficient between heights from the ground of two people on the opposite ends of a seesaw would be _________.

A) 1.0
B) 0
C) - 1.0
D) cannot tell without further information

Question 11

In a perfect relationship, _________.

A) all the points fall on the line
B) none of the points fall on the line
C) some of the points fall on the line
D) the points form an ellipse around the line

Question 12

In a negative relationship, _________.

A) b is positive
B) b can be either positive or negative
C) a must be negative
D) b is negative

Question 13

In the equation Y = bX + a , X and Y are _________.

A) constants
B) statistics
C) population parameters
D) variables

Question 14

The closer the points on a scatter diagram fall to the regression line, the _________ between the scores.

A) higher the correlation
B) lower the correlation
C) correlation doesn't change
D) need more information

Question 15

Which Pearson correlation coefficient shows the strongest relationship between two variables?

A) - 0.80
B) 0.00
C) 0.75
D) 0.20
E) 0.03

Question 16

A relationship can be _________.

A) perfect
B) imperfect
C) nonexistant
D) all of these

Question 17

In the equation Y = bX + a , X and Y , b is _________.

A) a constant
B) the slope of the line
C) the Y axis intercept
D) a constant and slope of the line
E) a variable

Question 18

In a positive relationship, _________.

A) b is negative
B) b is positive
C) a must be positive
D) a must be negative

Question 19

In a negative relationship, _________.

A) as X increases, Y increases
B) as X decreases, Y decreases
C) as X increases, Y increases, and as X decreases, Y decreases
D) as X increases, Y decreases

Question 20

If a relationship is linear, _________.

A) the relation can be most accurately represented by a straight line
B) all the points fall on a curved line
C) the relationship is best represented by a curved line
D) all the points must fall on a straight line

Question 21

It is possible to compute a coefficient of correlation if one is given _________.

A) a single score
B) two sets of measurements on the same individuals
C) 50 scores of a clerical aptitude test
D) all of these
E) none of these

Question 22

When a correlation exists, lowering the range of either of the variables will _________.

A) raise the correlation
B) lower the correlation
C) not change the correlation
D) produce a causal relationship

Question 23

If the correlation between two variables is - 1.00 and the score of a given individual is 2.20 standard deviations above the mean on one of the variables, we would predict a score on the second variable of _________.

A) 2.20 standard deviations below the mean
B) 2.20 standard deviations above the mean
C) more than 2.20 standard deviations above the mean
D) more than 2.20 standard deviations below the mean

Question 24

A traffic safety officer conducted an experiment to determine whether there is a correlation between people's ages and driving speeds. Six individuals were randomly sampled and the following data were collected. The proportion of variability of Y accounted for by X is _________.

A) 0.49
B) 0.67
C) 0.40
D) - 0.49

Question 25

After several studies, Professor Smith concludes that there is a zero correlation between body weight and bad tempers. This means that _________.

A) heavy people tend to have bad tempers
B) skinny people tend to have bad tempers
C) no one has a bad temper
D) everyone has a bad temper
E) a person with a bad temper may be heavy or skinny

Question 26

Which of the following values of r represents the strongest degree of relationship between two variables?

A) 0.55
B) 0.00
C) 0.78
D) - 0.80

Question 27

If N is small, an extreme score _________.

A) won't affect r obt unduly
B) should be thrown out
C) might have a large effect on r obt
D) has no effect on the value of r obt

Question 28

A traffic safety officer conducted an experiment to determine whether there is a correlation between people's ages and driving speeds. Six individuals were randomly sampled and the following data were collected. The value of Pearson r equals _________.

A) - 0.82
B) - 0.70
C) - 0.63
D) +0.70

Question 29

A researcher wanted to know if the order in which runners finish a race is correlated with their weight. She conducts an experiment and the data are given below. What is the appropriate correlation coefficient for these data?

A) r
B) rho
C) phi
D) biserial

Question 30

Which of the following statements is true?

A) Correlation implies causation.
B) Causation implies correlation.
C) neither of these
D) both of these

Question 31

Which of the following is (are) not correct interpretations of Pearson r ?

A) ratio of the variability of Y to the variability of X
B) measure of extent to which paired scores occupy the same or opposite positions within their own distributions
C) difference between the variability of Y and the variability of X
D) square root of the proportion of the total variability of Y accounted for by X
E) a and c

Question 32

Rho is used _________.

A) when both variables are dichotomous
B) when both variables are of interval or ratio scaling
C) when one or both variables are only of ordinal scaling
D) when the data is nonlinear

Question 33

Which of the following is (are) not correlation coefficients?

A) Pearson r
B) eta
C) rho
D) phi
E) they all are correlation coefficients

Question 34

Knowing nothing more than that IQ and memory scores are correlated 0.84, you could validly conclude that _________.

A) good memory causes high IQ
B) high IQ causes good memory
C) neither good memory nor high IQ cause each other
D) a third variable causes both good memory and high IQ
E) none of these

Question 35

Which of the following statements concerning Pearson r is not true?

A) r = 0.00 represents the absence of a relationship.
B) The relationship between the two variables must be nonlinear.
C) r = 0.76 has the same predictive power as r = - 0.76.
D) r = 1.00 represents a perfect relationship.
E) All of these are true statements.

Question 36

What is the slope for the points X 1 = 30, Y 1 = 50 and X 2 = 25 and Y 2 = 40?

A) 2.00
B) 0.50
C) - 2.00
D) - 0.50

Question 37

A correlation between college entrance exam grades and scholastic achievement was found to be - 1.08. On the basis of this you would tell the university that _________.

A) the entrance exam is a good predictor of success
B) they should hire a new statistician
C) the exam is a poor predictor of success
D) students who do best on this exam will make the worst students
E) students are this school are underachieving

Question 38

A researcher wanted to know if the order in which runners finish a race is correlated with their weight. She conducts an experiment and the data are given below. The correlation for these data equals _________.

A) 0.31
B) 0.32
C) 0.41
D) 0.45

Question 39

When deciding which measure of correlation to employ with a specific set of data, you should consider _________.

A) whether the relationship is linear or nonlinear
B) type of scale of measurement for each variable
C) a and b
D) none of these

Question 40

The proportion of variance accounted for by a correlation between two variables is determined by _________.

A) Y 2
B) r 2
C) r
D) b

Question 41

Causation implies correlation.

Question 42

For the following X and Y scores, how much of the variability of Y is accounted for by knowledge of X ? Assume a linear relationship.

A) 68%
B) 34%
C) 58%
D) 27%

Question 43

If one calculates r for raw scores, and then calculates r on the z scores of the same data, the value of r will _______.

A) stay the same
B) decrease
C) increase
D) equal 1.00

Question 44

In order for the correlation coefficient to be negative, which of the following must be true?

A) ΣXY > ( ΣX )( Σ Y )/ N
B) ΣXY (ΣX )( ΣY )/ N
C) ΣXY = ( ΣX )( ΣY )/ N
D) ΣXY must be zero

Question 45

If one takes a sample of pairs of points over a narrow range of X or Y scores, what effect might this have on the value of r ?

A) inflate r
B) have no effect on r
C) reduce r
D) cannot be determined

Question 46

Pearson r is _______.

A) a measure of the extent to which paired scores occupy the same or opposite positions within their own distributions.
B) the square root of the proportion of the variability of Y that is accounted for by X .
C) used when both variables are of interval or ratio scaling.
D) All of these are true.

Question 47

For a linear relationship to exist, all the points must fall on a straight line.

Question 48

If a correlation is perfect,

A) all the points must fall on a straight line
B) all the points must fall on a curve line
C) most the points must fall on the line, but some can miss it.
D) all the points must fall on a straight or curved line,

Question 49

A correlation of r = 0.60 exists between a set of X and Y scores. If a constant of 10 is added to each score of both distributions, the value of r will _______.

A) remain the same
B) will increase
C) decrease
D) be less meaningful
E) will increase and be less meaningful

Question 50

If zX equals zY for each pair of points, r will equal _______.

A) 0.00
B) - 1.00
C) 1.00
D) 0.50

Question 51

You have noticed that as people eat more ice cream they also have darker suntans. From this observation, you conclude _______.

A) eating ice cream causes people to tan darker
B) when one's skin tans it causes an urge to eat ice cream
C) the results were spurious
D) perhaps a third variable is responsible for the correlation
E) all of these are possible

Question 52

If 49% of the total variability of Y is accounted for by X , what is the value of r ?

A) 0.49
B) 0.51
C) 0.70
D) 0.30

Question 53

Pearson r can be properly used on which of the following type(s) of relationships?

A) linear
B) curvilinear
C) exponential
D) all of these

Question 54

What is the value of r for the following relationship between height and weight?

A) 0.87
B) 0.76
C) 0.93
D) 0.56

Question 55

In a positive relationship as X increases, Y increases.

Question 56

You have conducted a brilliant study which correlates IQ score with income and find a value of r = 0.75. At the end of the study you find out all the IQ scores were scored 10 points too high. What will the value of r be with the corrected data?

A) r will be increased
B) r will be decreased
C) r will remain the same
D) cannot be determined

Question 57

Correlation implies causation.

Question 58

If two variables are ratio scaled and the relationship is linear, what type of correlation coefficient is most appropriate?

A) Pearson r
B) Spearman rho
C) eta
D) phi

Question 59

In order to properly use rho, the variables must be of at least _______ scaling.

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

Question 60

What is the value of the Spearman rank order correlation coefficient (rho) for the following pairs of ranks?

A) 0.40
B) 0.50
C) 0.60
D) 0.70

Question 61

If the relationship is imperfect, the value of the correlation coefficient must be negative.

Question 62

The use of z scores allows comparisons between variables measured on different scales and units.

Question 63

Assuming a correlation exists, as the range of one of the variables decreases, r increases.

Question 64

In order to compute r , we must first convert each score to its z score and then do our calculations with the z scores.

Question 65

The slope of the line reveals whether the relationship is positive or negative.

Question 66

A scatter plot is used to help determine if the relationship is linear or curvilinear.

Question 67

The range of a correlation coefficient is 0 to +1.

Question 68

r decreases as N decreases.

Question 69

As the value of r increases, the proportion of variability of Y that is accounted for by X decreases.

Question 70

r ² is called the coefficient of determination.

Question 71

Pearson r requires that the data be of interval or ratio scaling.

Question 72

The farther away the points on a scatter diagram fall from the regression line, the lower the correlation.

Question 73

Given a - 1.00 correlation coefficient, a raw score of 32 on one measure must be accompanied by a score of - 32 on the corresponding second measure.

Question 74

Correlation deals with the relationship between two variables.

Question 75

Spearman rho really derives from Pearson r .

Question 76

Causation implies correlation.

Question 77

Correlation implies causation.

Question 78

In a perfect positive correlation, each individual obtains the same z score on each variable.

Question 79

A correlation coefficient expresses quantitatively the degree of relationship between two variables.

Question 80

Rho is used where one or both variables are at least of interval scaling.