Question 1

Correlation coefficients can test _______ variable(s) at a time.

Accepted Answer

Correlation coefficients are statistical measures that calculate the strength and direction of the relationship between two variables, hence they can test only two variables at a time.

Question 2

Correlation coefficients examine ______.

Accepted Answer

Correlation coefficients examine the relationship between variables, specifically how changes in one variable are associated with changes in another variable. They do not examine differences between groups or how variables can be arranged into higher-order factors.

Question 3

What is the most important characteristic of a correlation coefficient?

Accepted Answer

The absolute value is the most important characteristic of a correlation coefficient because it represents the strength and direction of the relationship between two variables, regardless of whether the correlation is positive or negative. The other choices (number of variables included, one tailed, and two tailed) do not directly relate to the characteristic of a correlation coefficient.

Question 4

When computing the correlation coefficient, the _______ between variables, not the _______ between groups, is being examined.

Accepted Answer

The correlation coefficient measures the strength of the relationship between two variables, not the difference between different groups.

Question 5

Correlations can be _______.

Accepted Answer

Correlations can be either directional or nondirectional depending on the nature of the relationship between the variables being studied. Directional correlation implies that there is a specific cause-and-effect relationship between two variables, while nondirectional correlation implies that there is a simple relationship between them without any specific cause-and-effect direction. Therefore, choice A is the best answer as it includes both possibilities.

Question 6

If the correlation between two variables is .496, how much of the variance has not been accounted for?

Accepted Answer

The coefficient of determination, which represents the proportion of variance accounted for, is the square of the correlation coefficient (0.496^2 = 0.246). Therefore, 24.6% of the variance is accounted for, and 75.4% (100% - 24.6%) is not accounted for.

Question 7

Which of the following is the appropriate method for calculating the degrees of freedom associated with a correlation coefficient?

Accepted Answer

The appropriate method for calculating the degrees of freedom associated with a correlation coefficient is n-2. This is because when calculating a correlation coefficient between two variables, we are estimating the population correlation coefficient based on a sample. We lose one degree of freedom for each variable used to calculate the correlation coefficient, which in this case is 2 (one variable for each of the two variables being correlated). Thus, the degrees of freedom associated with a correlation coefficient is n-2. Option B (n-2) is the correct answer.

Question 8

What is another term for a negative correlation?

Accepted Answer

A negative correlation is also known as an indirect correlation because as one variable increases, the other decreases.

Question 9

The level of risk or Type I error typically set for testing the level of significance of a correlation coefficient is which of the following?

Accepted Answer

The most commonly used level of risk for testing the level of significance of a correlation coefficient is 0.05 or 5%. This means that there is a 5% chance of making a Type I error or rejecting a true null hypothesis (no correlation) based on random chance. A level of 0.01 or 1% may be used in some cases where a stricter level of significance is needed, but this is less common. A level of 0.95 or 0.99 does not make sense in this context as it represents confidence levels rather than levels of risk or Type I error.

Question 10

If you do not predict that a relationship between two variables will be either positive or negative, what type of test should you use?

Accepted Answer

A two-tailed test is appropriate when there is no prior prediction about the direction of the relationship between two variables. It tests whether there is a significant difference between the two groups or conditions being compared, regardless of the direction of the effect. ANOVA and Cohen's d are not appropriate for this scenario, and a one-tailed test would be unnecessary since there is no directional prediction.

Question 11

While you can use the correlation coefficient as its own test statistic, what is the other appropriate test statistic often used to examine the significance of a correlation?

Accepted Answer

The t-test is often used to examine the significance of a correlation by testing whether the correlation coefficient is significantly different from zero.

Question 12

If you posit that a relationship between two variables will be either positive or negative, what type of test should you use?

Accepted Answer

A one-tailed test is used when the direction of the relationship between two variables is specified, such as positive or negative. In this case, we have posited that the relationship will be either positive or negative, so a one-tailed test is appropriate. A two-tailed test would be used if there were no direction specified, meaning we would be interested in testing whether there is any relationship (positive or negative) between the variables. ANOVA and Cohen's d are not appropriate for testing the direction of a relationship between two variables.

Question 13

The correlation coefficient is a measure of _______.

Accepted Answer

The correlation coefficient is a statistical measure that indicates the strength and direction of the relationship between two variables. It measures the degree of association between the two variables, but it does not indicate causation or the mean differences between them. It is used to predict one variable's value based on the other's value. Therefore, the best choice is D - association.

Question 14

Which of the following is another use of correlation coefficients?

Accepted Answer

Correlation coefficients can be used to estimate the reliability of a measurement by assessing the consistency of results across different instances.

Question 15

Significant correlations are not able to indicate _______.

Accepted Answer

Correlations can identify relationships between variables, but they cannot determine causation. Just because there is a significant correlation between two variables does not mean that one variable caused the other. Other factors could be involved in the relationship.

Question 16

What is another term for a positive correlation?

Accepted Answer

A positive correlation is a relationship between two variables in which they both increase or decrease together. It is sometimes referred to as a direct correlation. Therefore, the best choice is C.

Question 17

In the formula for calculating degrees of freedom for a correlation coefficient, what does the n represent?

Accepted Answer

The answer of In the formula for calculating degrees of...

Question 18

This chapter illustrates that you can also incorporate _____ into the correlation coefficient.

Accepted Answer

Incorporating statistical significance into the correlation coefficient provides information about the likelihood that the correlation coefficient is not due to chance. This can help determine the reliability of the correlation and whether it can be generalized to a larger population.

Question 19

The appropriate test statistic to use is the _______.

Accepted Answer

The t-test for the correlation coefficient is used to determine if the correlation between two variables is statistically significant.

Question 20

What is the name of the Greek letter ρ?

Accepted Answer

The name of the Greek letter ρ is rho.

Quiz 15: Cousins or Just Good Friends Testing Relationships Using Correlation Coefficient