Deck 7: The Correlation Coefficient

Question 1

When plotting correlational data,the appropriate graph to use is the

A)line graph.
B)bar graph.
C)histogram.
D)scatterplot.

Answer 1

scatterplot.

Question 2

What does a correlation coefficient do?

A)It allows us to draw conclusions about whether one variable causes another variable.
B)It creates a correlational design,rather than an experimental design.
C)It quantifies the pattern in a relationship.
D)It summarizes the X scores and the Y scores separately.

Answer 2

It quantifies the pattern in a relationship.

Question 3

We should do a scatterplot of the data when we compute a correlation because the scatterplot allows us to

A)see the relationship between the two variables.
B)determine the exact value of the correlation coefficient.
C)determine whether a relationship is likely to exist in the population from which the sample is taken.
D)predict accurate Y scores for known X scores.

Answer 3

see the relationship between the two variables.

Question 4

If you see the notation ,what should you do?

A)First multiply each X by its partner Y,then sum the results.
B)First sum the Xs then multiply the sum of the Xs by each Y.
C)First sum the Ys,then multiply the sum of the Ys by each X.
D)First sum the Xs,then sum the Ys,then multiply the sums.

Question 5

Using a correlational design,a researcher found a relationship between the healthiness of one's heart and the amount of fish oil in one's diet.The researcher should conclude that

A)a healthier heart causes one to consume more fish oil.
B)the amount of fish oil in one's diet causes a healthier heart.
C)although a relationship exists,one cannot infer that changes in one variable are causing changes in the other variable.
D)the availability of fish causes changes in both the healthiness of one's heart and the amount of fish oil consumed.

Question 6

"The bigger they are,the harder they fall" describes

A)a positive linear correlation.
B)a negative linear correlation.
C)no correlation.
D)a nonlinear correlation.

Question 7

If we calculate a correlation coefficient and we find that there is a relationship between the two variables,we

A)know that the data must be interval or ratio.
B)know,without referring to the study,that a correlational design was used.
C)can conclude that changes in one variable cause changes in the other variable.
D)cannot conclude that changes in one variable cause changes in the other variable.

Question 8

In general,a positive correlation means that as the values of one variable _____,there is a tendency for the values of the other variable to _____.

A)increase;increase
B)increase;decrease
C)increase;remain the same
D)decrease;increase

Question 9

In an experimental design _____,whereas in a correlational design _____.

A)there is only one variable (the independent variable);there are two variables (X and Y)
B)there are two X variables;there are an X and a Y variable
C)researchers assign each person an X score and then measure the score on the Y variable;researchers measure scores on variables that a participant has already experienced
D)researchers measure scores on variables that a participant has already experienced;researchers assign each person an X score and then measure the score on the Y variable

Question 10

The best-fitting line through a scatterplot is known as the

A)scatterplot line.
B)correlation line.
C)variance line.
D)regression line.

Question 11

Professor Johnston has found a strong positive correlation between wearing neckties and the frequency of strokes (r = 0.89).He thinks that the necktie reduces blood flow to the brain,preventing the brain from receiving enough oxygen.Professor Johnston and his associates claim to have proven that wearing neckties causes strokes.What error has Professor Johnston made?

A)An r = 0.89 is not a very large r-value.
B)Professor Johnston is drawing a causal conclusion from correlational findings.
C)Not everyone who wears a necktie wears it very tight.
D)Professor Johnston should know that there are other ways for blood to reach the brain.

Question 12

In a correlational analysis,N stands for the

A)total number of pairs of scores.
B)total number of X scores plus the total number of Y scores.
C)total number of X scores times the total number of Y scores.
D)total number of pairs of scores minus 2.

Question 13

What type of relationship does the following regression line represent?

A)A positive relationship
B)A negative relationship
C)A curvilinear relationship
D)No relationship

Question 14

"The self-confidence of a group of students is positively correlated with their chances of getting through the course." What does this statement mean?

A)The students will pass the course if they can be made to be self-confident.
B)The chances of passing the course tend to increase as the self-confidence scores of the students increase.
C)The chances of passing the course tend to decrease as the self-confidence scores of the students increase.
D)Passing the course will make the students self-confident.

Question 15

What type of relationship does the following regression line represent?

A)A positive relationship
B)A negative relationship
C)A curvilinear relationship
D)No relationship

Question 16

If there is a relationship between "income" and "happiness," then as the amount of income increases,the amount of happiness

A)also increases.
B)decreases.
C)stays the same.
D)changes in some consistent manner.

Question 17

To know whether there is a relationship between two variables,you draw a line around the outer edges of a scatterplot.If there is a negative relationship,

A)the scatterplot is simultaneously elliptical and circular.
B)the scatterplot is elliptical and is slanted upward (left to right).
C)the scatterplot is elliptical and is slanted downward (left to right).
D)the scatterplot is either circular or elliptical,and the ellipse is parallel to the X axis.

Question 18

In a linear relationship,as the X scores increase,the Y scores change

A)in only one direction.
B)only in the negative direction.
C)only in the positive direction.
D)in the positive and then in the negative direction.

Question 19

If you see the notation ,what should you do?

A)First multiply each X by its partner Y,then sum the results.
B)First sum the Xs,then sum the Ys,then multiply the results.
C)First sum the Xs,then multiply the result by each Y.
D)First sum the Ys,then multiply the result by each X.

Question 20

"The more you save,the less you spend" describes

A)a positive linear correlation.
B)a negative linear correlation.
C)no correlation.
D)a nonlinear correlation.

Question 21

In general,a zero correlation means that

A)as the values of one variable increase,there is no tendency for the values of the other variable to change in any consistent,predictable fashion.
B)as the values of one variable increase,there is a tendency for the values of the other variable also to increase.
C)as the values of one variable increase,there is a tendency for the values of the other variable to decrease.
D)as the values of one variable decrease,there is a tendency for the values of the other variable also to decrease.

Question 22

What kind of relationship is depicted in the following graph?

A)A positive linear correlation
B)A negative linear correlation
C)No correlation
D)A nonlinear correlation

Question 23

Which relationship is stronger,r = +0.62 or r = -0.62?

A)An r = +0.62 represents a stronger relationship than r = -0.62.
B)An r = -0.62 represents a stronger relationship than r = +0.62.
C)There is no difference in the strength of the two relationships.
D)Without seeing a scatterplot of the data,there is no way to determine which is stronger.

Question 24

What type of relationship does the following regression line represent?

A)A positive relationship
B)A negative relationship
C)A curvilinear relationship
D)No relationship

Question 25

What kind of relationship is depicted in the following graph?

A)A positive linear correlation
B)A negative linear correlation
C)No correlation
D)A nonlinear correlation

Question 26

A "weak" relationship between two variables is represented by

A)a small spread of Y scores at each X score.
B)a large spread of Y scores at each X score.
C)only one value of Y at each X score.
D)an equal spread of Y scores at each X score.

Question 27

Which of the following r-values indicates the weakest relationship between two variables?

A)-0.45
B)-0.30
C)-0.03
D)-0.45.

Question 28

In a nonlinear or curvilinear relationship,as the X scores change,the Y scores

A)tend to increase.
B)change consistently,but in more than one direction.
C)tend to be the same as the X scores.
D)do not change in a consistent fashion.

Question 29

Professor Miller has found that the correlation between a person's "need for affiliation" (found by taking a test to determine the need to be with others)and the number of hours spent watching television is -0.69.He should conclude that

A)as we observe people with higher and higher need for affiliation,we see a tendency for those people to spend less and less time watching television.
B)there is not much of a relationship between the two variables because the r is negative.
C)as we observe people with higher and higher need for affiliation,we see a tendency for those people to spend more and more time watching television.
D)the people who watch more television tend to have more need to be around others.

Question 30

What statistic should be used to find out whether there is a relationship between hours spent participating in sports and GPA?

A)The Pearson correlation coefficient
B)The Spearman rank-order correlation coefficient
C)The point-biserial correlation coefficient
D)The nonlinear correlation coefficient

Question 31

Calculate the appropriate correlation coefficient for the following data.

A)-0.07
B)+0.95
C)+0.49
D)+0.23

Question 32

What kind of relationship is depicted in the following graph?

A)A positive linear correlation
B)A negative linear correlation
C)No correlation
D)A nonlinear correlation

Question 33

What statistic should be used to find out whether there is a relationship between years of education and annual income?

A)The Pearson correlation coefficient
B)The Spearman rank-order correlation coefficient
C)The point-biserial correlation coefficient
D)The nonlinear correlation coefficient

Question 34

What kind of relationship is depicted in the following graph?

A)A positive linear correlation
B)A negative linear correlation
C)No correlation
D)A nonlinear correlation

Question 35

Which of the following r-values indicates the strongest relationship between two variables?

A)+0.65
B)-0.89
C)+0.10
D)-0.10

Question 36

The strength of a relationship is indicated by the extent to which _____ paired with one and only one individual value of the _____ variable.

A)many values of the Y variable are;X
B)many values of the X variable are;Y
C)the entire range of the Y variable is;X
D)one value of the Y variable is;X

Question 37

Which of the following studies represents the weakest relationship?

A)Study A
B)Study B
C)Study C
D)Cannot determine

Question 38

Which correlation coefficient should we use if we want to find out whether a relationship exists between two variables that are both interval or ratio variables?

A)The Pearson correlation coefficient
B)The Spearman rank-order correlation coefficient
C)The point-biserial correlation coefficient
D)The nonlinear correlation coefficient

Question 39

Professor Helgin has found that the correlation between the length of a person's index finger and the person's IQ is -0.11.He should conclude that

A)as the length of the index finger goes up,there is a fairly strong tendency for a person to have a lower IQ.
B)there is no relationship between the two variables because the r is negative.
C)we can be confident in predicting that people with high IQs will tend to have long index fingers.
D)there is a very weak relationship between the length of the index finger and IQ because r is nearly 0.

Question 40

When the correlation coefficient representing the relationship between X and Y is intermediate,then all of the following are true except

A)there is not a perfectly consistent association.
B)there are different Y scores associated with a single X score.
C)prediction of Y from a known X score has some error.
D)all data points fall on the regression line.

Question 41

Calculate the appropriate correlation coefficient for the following data.

A)-0.92
B)-0.37
C)-0.06
D)+0.75

Question 42

Calculate the appropriate correlation coefficient for the following data.

A)-0.52
B)+0.52
C)+0.83
D)+0.94

Question 43

Which correlation coefficient should we use if we want to find out whether a relationship exists between scores from one interval variable and one ordinal variable?

A)The Pearson correlation coefficient
B)The Spearman rank-order correlation coefficient
C)The point-biserial correlation coefficient
D)The nonlinear correlation coefficient

Question 44

In a study about the relationship between their age and women's attitudes about marriage,you survey over 500 undergraduate women and calculate a Pearson correlation coefficient.What mistake have you made?

A)You have collected too much data.
B)There is no way a woman's attitude about marriage can affect her age.
C)You only surveyed young women in college causing a restriction of range.
D)You have used the wrong correlation coefficient the type of data.

Question 45

If we compute a correlation on data that come only from the middle of the X distribution (restricted range)rather than from the entire range,the correlation is likely to be _____ the correlation from the entire range.

A)smaller than
B)the same as
C)a little larger than
D)a lot larger than

Question 46

Calculate the appropriate correlation coefficient for the following data,assuming X is an interval variable and Y is a ratio variable.

A)-0.65
B)+0.09
C)+0.40
D)+0.59

Question 47

Suppose a researcher has trained two observers to rank participants according to their level of frustration when trying to solve a puzzle.What statistic should be used to determine the extent to which the two observers agree in their rankings of frustration?

A)The Pearson correlation coefficient
B)The Spearman rank-order correlation coefficient
C)The point-biserial correlation coefficient
D)The nonlinear correlation coefficient

Question 48

What statistic should be used to find out whether there is a relationship between high school class rank and first-semester college GPA rank?

A)The Pearson correlation coefficient
B)The Spearman rank-order correlation coefficient
C)The point-biserial correlation coefficient
D)The nonlinear correlation coefficient

Question 49

Which correlation coefficient should we use if we want to find out whether a relationship exists between two variables that represent pairs of ordinal scores?

A)The Pearson correlation coefficient
B)The Spearman rank-order correlation coefficient
C)The point-biserial correlation coefficient
D)The nonlinear correlation coefficient

Question 50

Calculate the appropriate correlation coefficient for the following data.

A)-0.97
B)-0.39
C)+0.11
D)+0.57

Question 51

Calculate the appropriate correlation coefficient for the following data

A)-0.68
B)+0.72
C)-0.41
D)-0.93

Question 52

As a part of her Master's Degree thesis in Geology,Candice needs to calculate a correlation coefficient between the amount of rainfall (measured in inches)and the height of the ground water table (measured in inches)in various parts of the continental U.S.Which formula should she use for this calculation?

A)
B)
C)
D)