Question 1

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 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

Accepted Answer

When the Spearman correlation is +1.00, it indicates a perfect monotonic relationship. The Pearson correlation will be positive, but it may not necessarily be 1.00 unless the relationship is also perfectly linear.

Question 2

The effect size for the data from an independent-measures t test can be measured by r² which is the percentage of variance accounted for.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)None of the other options will produce r².

Accepted Answer

The answer of The effect size for the data from...

Question 3

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

Accepted Answer

The point-biserial correlation is the best choice for measuring the relationship between gender (a dichotomous variable) and grade point average (a continuous variable). The Pearson correlation is used for two continuous variables, the Spearman correlation is used for two ordinal variables, and the phi-coefficient is used for two nominal variables.

Question 4

If the following seven scores are ranked from smallest (#1) 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

Accepted Answer

The answer of If the following seven scores are ranked...

Question 5

Under what circumstances is the point-biserial correlation used?
A)in the same circumstances when a repeated-measures t test would be used
B)in the same circumstances when an independent-measures t test would be used
C)when both X and Y are dichotomous variables
D)when both X and Y are measured on an ordinal scale (ranks)

Accepted Answer

The point-biserial correlation is used when one variable is dichotomous (binary) and the other is continuous, similar to the conditions for an independent-measures t test.

Question 6

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

Accepted Answer

The null hypothesis for a two-tailed hypothesis test evaluating a Pearson correlation states that the population correlation is zero.

Question 7

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

Accepted Answer

The correct order from highest to lowest degree of relationship is: -0.91, +0.83, +0.10, -0.03.

Question 8

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)There is not enough information to evaluate the significance of the correlation.

Accepted Answer

The answer of A researcher obtains a Pearson correlation of...

Question 9

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

Accepted Answer

The degrees of freedom (df) for a Pearson correlation is calculated as n - 2, where n is the sample size. For n = 20, df = 20 - 2 = 18.

Question 10

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)It is still called a Pearson correlation.

Accepted Answer

When data are converted to ranks and the Pearson correlation is computed, it is known as the Spearman correlation, which measures the strength and direction of association between two ranked variables.

Question 11

Suppose 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%

Accepted Answer

The proportion of variability in weight that can be explained by the relationship with height is found by squaring the correlation coefficient (r^2). So, 0.40^2 = 0.16, or 16%.

Question 12

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

Accepted Answer

The answer of How large a sample is needed for...

Question 13

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.

Accepted Answer

As the sample size increases, the size of the correlation needed to achieve statistical significance actually gets smaller. This is because with larger sample sizes, the statistical tests have more power to detect a true effect, allowing even smaller correlations to be considered statistically significant.

Question 14

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

Accepted Answer

Because the ranks in both high school and college graduation classes are ordinal data and not measured on a continuous scale, the best correlation to use would be the Spearman correlation. The Spearman correlation measures the strength and direction of a monotonic relationship between two variables, which is suitable for comparing the rankings of two groups.

Question 15

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.

Accepted Answer

The phi-coefficient is used when both X and Y are dichotomous variables.

Question 16

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)cannot be determined without knowing all the X and Y scores

Accepted Answer

Multiplying all X values by a constant does not change the correlation coefficient, so the correlation remains r = 0.40.

Question 17

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

Accepted Answer

With a significance level of α=.05 with two tails, the critical values for a Pearson correlation coefficient for n=18 is ±0.468. Therefore, any correlations greater than or equal to 0.468 and correlation less than or equal to -0.468 are statistically significant.

Question 18

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 positive.
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.

Accepted Answer

When the Pearson correlation is +1.00, it indicates a perfect linear relationship. The Spearman correlation, which measures monotonic relationships, will also be +1.00 in this case because a perfect linear relationship is also a perfect monotonic relationship.

Question 19

For a sample of n = 16 individuals, how large a Pearson correlation is necessary to be statistically significant for a two-tailed test with $\alpha=.05$ ?
A)0.497
B)0.482
C)0.468
D)0.456

Accepted Answer

For a sample size of n = 16, the degrees of freedom (df) is n - 2 = 14. Using a Pearson correlation table or calculator, the critical value for a two-tailed test with $\alpha = .05$ and df = 14 is approximately 0.497.

Question 20

If the following seven scores are ranked from smallest (#1) 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

Accepted Answer

The answer of If the following seven scores are ranked...

Quiz 15: Correlation

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

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

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

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

Under what circumstances is the point-biserial correlation used?

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

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

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?

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?

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

Suppose 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?

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

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

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?

Under what circumstances is the phi-coefficient used?

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 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.

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?

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\alpha=.05α=.05 ?

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

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?

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

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