Question 1

A statistically significant correlation means that the correlation is large and strong.

Accepted Answer

A statistically significant correlation only means that the correlation is unlikely to occur by chance, it does not necessarily mean that the correlation is strong or large. The strength of the correlation is indicated by the magnitude of the correlation coefficient.

Question 2

Because there is a strong positive correlation between depression and risk of divorce, we can conclude that depression causes divorce.

Accepted Answer

Correlation does not equal causation. While there may be a relationship between depression and divorce, it is not necessarily a causal one. Other factors could be at play, such as stressors within the relationship or individual differences in coping mechanisms.

Question 3

With a very small sample, it is possible to have what appears to be a strong correlation when in fact there is no relationship between variables.

Accepted Answer

This is true because with a very small sample size, chance or coincidence can easily create the appearance of a correlation between variables even if there is no actual relationship between them. It is important to have a large enough sample size to ensure that any observed correlations are statistically significant and not just due to chance.

Question 4

A researcher obtained a correlation of r = +0.62 between the amount of time spent watching television and level of blood cholesterol. This means that there is a general tendency for people who watch more television also to have higher blood cholesterol.

Accepted Answer

A positive correlation coefficient indicates a positive relationship between the two variables, meaning that as one variable increases, the other tends to increase as well. In this case, the positive correlation indicates that people who spend more time watching television tend to have higher levels of blood cholesterol.

Question 5

For a positive correlation, decreases in X tend to be accompanied by decreases in Y.

Accepted Answer

The answer of For a positive correlation, decreases in X...

Question 6

A Pearson correlation of r = −1.00 means that all the data points fit perfectly on a straight line.

Accepted Answer

A Pearson correlation of -1.00 indicates a perfect negative linear relationship between two variables, meaning that as one variable increases, the other variable decreases in a perfectly predictable manner. This does not necessarily mean that all the data points fit perfectly on a straight line, but rather that they fit perfectly on a straight line with a negative slope.

Question 7

Suppose there is a correlation of +0.87 between the length of time a person is in prison and the amount of aggression the person displays on a psychological inventory. This means that spending a longer amount of time in prison causes people to become more aggressive.

Accepted Answer

Correlation does not imply causation, so we cannot conclude that longer time in prison causes people to become more aggressive. It is possible that there is a third variable that is causing both the length of time in prison and the aggression. Alternatively, it could be that more aggressive individuals are being sentenced to longer prison terms.

Question 8

Both correlational studies and differential research examine the relationship between two variables.

Accepted Answer

Both correlational studies and differential research investigate the association or relationship between two variables, although they differ in their methods and designs.

Question 9

A correlation of r = −0.90 means that there is essentially no consistent relationship between X and Y.

Accepted Answer

A correlation coefficient of -0.90 indicates a strong negative relationship between X and Y, meaning as one variable increases, the other variable decreases in a consistent manner.

Question 10

With a very large sample, even a very small correlation can be statistically significant.

Accepted Answer

This is because statistical significance is determined by both the size of the correlation coefficient and the sample size. As the sample size increases, the standard error of the correlation coefficient decreases, making it more likely to achieve statistical significance with even small correlations.

Question 11

If decreases in the X variable are accompanied by decreases in the Y variable, then the correlation between X and Y is negative.

Accepted Answer

If decreases in the X variable are accompanied by decreases in the Y variable, this indicates a positive correlation, as both variables move in the same direction.

Question 12

A researcher knows that there is a relationship between obesity and watching television for young children. However, it is not known whether children watch more TV because they are overweight, or whether they are overweight because they watch so much TV. This is an example of the directionality problem.

Accepted Answer

The directionality problem refers to the issue of not knowing the direction of causality between two variables. In this case, it is not known if watching TV causes obesity or if being obese causes children to watch more TV.

Question 13

The electric company uses the correlation between summer temperatures and energy consumption to anticipate energy demands. In this example, temperature is the criterion variable.

Accepted Answer

In this example, energy consumption is the criterion (or dependent) variable because it is being predicted or explained by the temperature, which is the predictor (or independent) variable.

Question 14

The coefficient of determination is computed by taking the square root of the correlation coefficient .

Accepted Answer

The coefficient of determination is equal to the correlation coefficient squared, not the square root of the correlation coefficient.

Question 15

Correlations are often used to help demonstrate the reliability and validity of measurement.

Accepted Answer

Correlations can help show the consistency (reliability) and accuracy (validity) of a measure by detecting whether there is a consistent relationship between the measure and another variable.

Question 16

Suppose it was observed that there is a correlation of r = −0.81 between a driver's age and the cost of the car insurance. This correlation would mean that, in general, older people pay more for car insurance.

Accepted Answer

A correlation of r = -0.81 indicates a strong negative relationship, meaning that as one variable increases, the other decreases. In this context, it suggests that as a driver's age increases, the cost of car insurance decreases.

Question 17

The Pearson correlation measures the degree to which the X and Y data points fit on a straight line.

Accepted Answer

The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two variables X and Y. It ranges between -1 and +1, where a value of +1 indicates a perfect positive linear relationship, 0 indicates no linear relationship, and -1 indicates a perfect negative linear relationship.

Question 18

The goal of the correlational research strategy is to demonstrate a cause-and-effect relationship between two variables.

Accepted Answer

The goal of the correlational research strategy is to identify a relationship between two variables, but it does not attempt to establish a cause-and-effect relationship. Other research strategies such as experimental design are used to establish cause-and-effect relationships.

Question 19

When the data for a correlational study consist of one or more scores that are not numerical values, the relationship between the variables cannot be evaluated.

Accepted Answer

Correlational studies can evaluate relationships between variables using non-numerical (categorical) data by employing methods such as Spearman's rank-order correlation or chi-square tests, which do not require all data to be numerical.

Question 20

A researcher knows that there is a relationship between obesity and watching television for young children. However, it is not known whether children watch more TV because they are overweight, or whether they are overweight because they watch so much TV. This is an example of the third-variable problem.

Accepted Answer

This is an example of the directionality problem, where the direction of cause-and-effect between two variables is unclear, not the third-variable problem which involves an additional variable that could be influencing both of the variables in question.

Quiz 12: The Correlational Research Strategy