Question 1

Professor Falls wants to determine if there is a relationship between frequent hearing of a startle stimulus and hearing loss. He ran a regression and obtained an r value of .60. Which of the following best summarizes what this result means?

Accepted Answer

The correlation coefficient (r) value of .60 indicates a moderate positive correlation between frequent hearing of a startle stimulus and hearing loss. However, it does not indicate a causal relationship. The correct interpretation is that 36% of the variability in hearing loss can be accounted for by variability in the hearing of startle stimuli. Therefore, choice B is the best summary.

Question 2

A scatterplot can be used to visualize the degree of association between 2 variables.

Accepted Answer

A scatterplot is a graph that displays the relationship between two variables. By plotting one variable on the x-axis and the other on the y-axis, we can see how the two variables are related. The pattern of the points on the graph can show if there is a positive, negative, or no association between the two variables. Therefore, a scatterplot can be used to visualize the degree of association between 2 variables.

Question 3

Which r-value represents the strongest correlation?

Accepted Answer

In correlation, the absolute value of the r-value represents the strength of the correlation. Therefore, the strongest correlation is represented by an r-value with an absolute value closest to 1. Option C has an r-value of -.75, which has the highest absolute value among the given options and is therefore the strongest correlation. Option D is not a valid choice as r-values can only range from -1 to +1.

Question 4

Correlation coefficients can range from -1 to 1.

Accepted Answer

Correlation coefficients can range from -1 to 1, with -1 indicating a strong negative correlation, 1 indicating a strong positive correlation, and 0 indicating no correlation.

Question 5

We look at a number of states and record the number of auto fatalities last year and the state's maximum speed limit, trying to show that high speed limits are dangerous. This is an example of

Accepted Answer

This is a correlational study because it is looking at the relationship between two variables (number of auto fatalities and maximum speed limit) without manipulating any variables.

Question 6

The correlation between amount of caffeine consumed and nervous behavior was found to be .30. What conclusion can be drawn from this finding?

Accepted Answer

The correct conclusion is that 9% of the variability in nervous behavior can be accounted for by variability in amount of caffeine consumed. This is because the square of the correlation coefficient (0.30^2 = 0.09 or 9%) represents the proportion of the variance in one variable that is predictable from the variance in the other variable.

Question 7

A researcher is predicting exam scores based on the amount of time spent studying. The criterion variable is exam scores.

Accepted Answer

The researcher is using the amount of time spent studying as the predictor variable to predict exam scores, which is the criterion variable.

Question 8

A correlation was computed between amount of exercise people do and people's overall happiness. A significant correlation was found, such that the more people exercise, the happier they are. What is the best conclusion to draw from this finding?

Accepted Answer

The finding shows that there is a positive relationship between exercise and happiness, meaning that as one increases, the other tends to increase as well. However, it does not necessarily mean that exercise directly causes happiness or that everyone who exercises will be happy. Additionally, while the finding suggests that exercise may contribute to overall happiness, it does not necessarily mean that people should exercise more or that exercise is the only way to achieve happiness.

Question 9

Correlations are typically used to examine mean differences between groups.

Accepted Answer

Correlations are used to examine the relationship between two variables, not mean differences between groups. Mean differences between groups are typically analyzed using t-tests, ANOVA, or other statistical tests.

Question 10

Restricted range has no effect on correlation coefficients.

Accepted Answer

Restricted range can have a significant effect on correlation coefficients by reducing the variability of the data and potentially leading to an underestimation of the correlation.

Question 11

A significant correlation is one which

Accepted Answer

A significant correlation is one in which the correlation coefficient is significantly different from 0, indicating that the variables are not linearly independent. Choice A implies subjective meaning, choice C implies difficulty, and choice D is incorrect as a true correlation near 0 would not be significant.

Question 12

The covariance measure is

Accepted Answer

The covariance measure is a statistical concept that measures the degree to which two variables vary together. In other words, it measures the degree to which the observations of one variable predict the observations of another variable. Therefore, option C is the correct choice. The other options are incorrect as they do not accurately reflect the definition or purpose of covariance.

Question 13

The following is an example of a negative correlation. As height increase, so does foot size.

Accepted Answer

This statement describes a positive correlation, where both variables (height and foot size) increase together.

Question 14

Correlation cannot be used to test associations between two dichotomous variables.

Accepted Answer

Correlation can be used to test associations between two dichotomous variables, typically using point-biserial correlation for one dichotomous and one continuous variable, or phi coefficient for two dichotomous variables.

Question 15

Which of the following is the most accurate statement?

Accepted Answer

Correlation and R squared or regression may indicate a relationship between variables, but they cannot prove causation. Other factors may be influencing the relationship observed. To establish causation, experimental designs and/or rigorous statistical methods, such as randomized controlled trials, are necessary.

Question 16

A correlation of .65 between depression and anxiety suggests that people who are highly depressed are reasonably likely to be highly anxious.

Accepted Answer

A correlation coefficient of .65 indicates a positive correlation between depression and anxiety, meaning that as one variable (depression) increases, the other variable (anxiety) is also likely to increase. Therefore, people who are highly depressed are reasonably likely to be highly anxious.

Question 17

Correlation coefficients closer to 0 reflect strong relationships.

Accepted Answer

Correlation coefficients closer to 1 or -1 reflect strong relationships, while coefficients closer to 0 reflect weak relationships.

Question 18

Which of the following pairs is most likely to be negatively correlated?

Accepted Answer

A volatile temper is generally seen as a negative trait in arbitrators, and therefore, there is likely to be a negative correlation between volatile temper and success as an arbitrator.

Question 19

We want to demonstrate that a relationship exists between optimism and happiness. We are not concerned with trying to demonstrate that one variable causes the other. What type of statistical test can be use to see if a relationship exists between the variables?

Accepted Answer

A correlation test would be appropriate to determine if there is a relationship between two variables without establishing causation. It will measure the strength and direction of the relationship between optimism and happiness.

Question 20

If the R squared between brain size and IQ is .09 then

Accepted Answer

The R squared value represents the proportion of variance in one variable (IQ) that can be explained by the other variable (brain size). Therefore, option C is the correct choice which states that 9% of the variability in IQ is accounted for by variability in brain size.

Quiz 9: Correlation