Deck 16: Inference About Correlation Coefficients

Question 1

For each of the following cases, give the size of the sample r required for statistical significance:
(a)
one-tailed test;

(b)
two-tailed test;
(c)
two-tailed test;
(d)
two-tailed test;

(e)
one-tailed test.

Answer 1

(a).805
(b).404
(c).393
(d).16
(e).05.

Question 2

You read in a review article: "Milhous (1979) found a significant positive correlation between peer ratings of self-confidence and scores on the Milhous Self Confidence Scale for a large sample of college sorority members."
(a)How might such a statement be misinterpreted by the statistically unsophisticated reader
(b)What does the statement really mean? Be precise in your answer. Use appropriate symbols and statistical terminology
(c)What single piece of additional information would be most necessary to an adequate interpretation of Milhous' results?

Answer 2

(a)Misinterpreted as a large or "important" correlation
(b)

was tested and rejected; conclusion:

(c)the obtained value of r.

Question 3

The human resources director of a large bank conducts a study to evaluate a particular employment test for possible use in screening prospective applicants for the position of teller. A group of 16 applicants is administered the test, hired, and rated by their supervisors after 6 months on the job. A sample correlation of +.39 is obtained between test scores and supervisors' ratings. Use a significance testing approach to evaluate the sample result ( $\alpha$ = .05).

Answer 3

from Table G, (one-tailed); retain

Question 4

(a)Suppose the correlation between two variables is reported as "not significant" for a sample of 980 cases. Is it possible to make an adequate interpretation concerning the true degree of relationship from this information alone without knowing the actual value of r? Explain.
(b)Suppose the correlation between two variables is reported as "significant" for a sample of 980 cases. Is it possible to make an adequate interpretation concerning the true degree of relationship from this information alone without knowing the actual value of r? Explain.

Question 5

The test of a hypothesis about correlation coefficients is probably most frequently used to inquire whether

A) is zero

B) is some specified value other than zero

C) there is a difference between 's obtained from independent samples

D) there is a difference between 's obtained from dependent samples

Question 6

is to the sampling distribution of r as ____________ is to the sampling distribution of the mean.

A)
B)
C)
D)

Question 7

Values of r vary more when

A) n is small
B) is low
C) n is small and is low
D) n is small and is high

Question 8

The problem that makes the inference about correlation coefficients somewhat less straightforward than inference about means is that the sampling distribution of r

A) has an unknown mean
B) has an unknown standard deviation
C) varies in shape according to circumstance
D) is bimodal because r can be negative as well as positive

Question 9

When
, the sampling distribution of r is

A) skewed negatively
B) skewed positively
C) symmetrical
D) normal when

Question 10

The sampling distribution of r is most nearly normal when
is

A) positive
B) negative
C) near ±1.00
D) near zero

Question 11

A significant correlation indicates a conclusion that

A) is large
B) r is large
C) is not zero
D) r is not zero

Question 12

When n is very large, we may find that

A) the standard error of the sampling distribution cannot be determined
B) large values of r may suggest that we should retain the hypothesis that when it is false
C) the sampling distribution departs substantially from a normal distribution
D) the correlation coefficient is shown to be significantly different from zero when in fact the true value of is not importantly different from zero

Question 13

In which of the following cases could the sample r have been any value over a range from rather small to quite large?

A) significant r,
B) significant r,
C) nonsignificant r,
D) any of the above

Question 14

We can be fairly sure that
is very small in which of the following cases?

A) significant r,
B) nonsignificant r,
C) nonsignificant r,
D) none of the above

Question 15

A significant correlation ( $\alpha$ = .01). is obtained for a sample of 1,000 cases. From this we can infer that

A) is probably large
B) is not zero
C) is not zero but probably is small
D) none of the above

Question 16

A nonsignificant correlation is obtained for a random sample of 6 cases. From this we can infer that

A)
B) is very small
C) does not differ by an important amount from 0
D) none of the above

Question 17

If we want to know whether a test is predictive of success according to a given performance criterion, we can be certain that it is to some degree if r between these two variables is

A) +.25
B) +.50
C) +.75
D) without knowledge of n, we cannot be certain in any of these circumstances

Question 18

To test the hypothesis that
we need to remember that the number of degrees of freedom is

A) n
B)
C)
D)

Question 19

Fisher's
is

A) a kind of z score
B) a kind of standard score
C) a kind of normalized standard score
D) none of the above

Question 20

The standard error of
is

A)
B)

C)
D)

Question 21

The purpose of the
transformation is to correct for

A) an unknown mean of the sampling distribution of r
B) an unknown standard deviation of the sampling distribution of r
C) varying shape of the sampling distribution of r
D) differing values of n

Question 22

The
transformation yields values of

for corresponding values of r which are

A) increasingly larger than r as r becomes larger
B) increasingly smaller than r as r becomes larger
C) proportionately larger than r
D) proportionately smaller than r

Question 23

If the
transformation is used to evaluate inference about correlation coefficients, the referent distribution is

A) the normal distribution
B) Student's distribution of t
C) dependent on the number of degrees of freedom
D) a rectangular distribution

Question 24

Which procedure, if any, does not require the assumption of a normal bivariate distribution?

A) t test of the hypothesis of no correlation
B) estimation of the population correlation coefficient
C) test of the hypothesis of no difference between two correlation coefficients
D) the assumption is required for all of the above