Question

Which of the following correlation coefficients would indicate the strongest relationship between two variables? A. .58 C. -.97 B. .19 D. -.05

Short answer

Answer: -.97

Step-by-step solution

Understand the correlation coefficient

The correlation coefficient is a measure of the strength of the relationship between two variables. It ranges from -1 to 1. A positive correlation coefficient indicates that both variables tend to increase or decrease together, while a negative correlation coefficient indicates that one variable tends to increase as the other decreases. The closer the correlation coefficient is to 1 or -1, the stronger the relationship.

Compare the positive correlation coefficients

We have two positive correlation coefficients: .58 and .19. As correlation coefficients are closer to 1, the relationship is stronger. Therefore, .58 indicates a stronger relationship between variables when compared to .19.

Compare the negative correlation coefficients

We have two negative correlation coefficients: -.97 and -.05. As correlation coefficients are closer to -1, the relationship is stronger. Therefore, -.97 indicates a stronger relationship between variables when compared to -.05.

Determine the strongest relationship

Now we have compared the positive and negative correlation coefficients separately. We have found that .58 is the strongest positive correlation coefficient, and -.97 is the strongest negative correlation coefficient. To determine the overall strongest relationship, we need to compare both the positive and negative correlation coefficients. Since -.97 is closer to -1 than .58 is to 1, we have the strongest relationship with a correlation coefficient of -.97. So, the correct answer is C. -.97, which indicates the strongest relationship between two variables.

Key concepts

Understanding Positive Correlation

When exploring the concept of correlation in statistics, positive correlation is fundamental. It's a term used to describe the relationship between two variables where, as one variable increases, the other variable tends to increase as well. Similarly, as one variable decreases, the other follows in a decreasing fashion. This type of correlation is quantified using a correlation coefficient, which can range from +0.01 to +1.0.

A perfect positive correlation, represented by a coefficient of +1.0, means that for every increase in one variable, there is a proportional increase in the other. An example might be temperature and ice cream sales; as the temperature rises, so typically do the sales of ice cream. It's crucial for students to note that a positive coefficient implies a direct relationship, not necessarily that the variables are 'good' or desirable.

Interpreting Negative Correlation

In contrast, negative correlation is indicative of an inverse relationship between two variables. This means that when one variable increases, the other decreases, and vice versa. Negative correlation coefficients are measured between -0.01 and -1.0.

A perfect negative correlation, given by a coefficient of -1.0, implies that an increase in one variable results in a proportional decrease in the other. For example, the number of layers of clothing people wear is often negatively correlated with the outside temperature. As it becomes warmer, fewer layers are worn. Understanding this concept is critical in many fields, including economics and psychology, where interpreting relationships between factors directly impacts interpretations and conclusions.

Assessing Strength of Relationship

The strength of the relationship between two variables is expressed by the absolute value of the correlation coefficient, regardless of whether the correlation is positive or negative. The closer the value is to 1, either positive or negative, the stronger the relationship. Conversely, as this value approaches 0, it suggests a weaker relationship.

For example, a correlation coefficient of 0.8 indicates a substantially strong positive relationship, whereas a coefficient of -0.8 reflects a strong negative relationship. A coefficient close to 0, such as 0.2 or -0.2, would imply a very weak relationship. It is important to understand that correlation does not prove causation; it simply indicates that there is a relationship to be explored further, perhaps through causal research methods.

Variables in Psychology

In the realm of psychology, variables are elements that can be measured and can vary among participants. Variables can be anything from age to socio-economic status, to more abstract concepts such as levels of anxiety or happiness. When psychologists study behavior and mental processes, they often look for relationships between these variables.

Understanding how and why significant correlations exist between variables allows psychologists to make predictions and develop theories about human behavior. For instance, research might reveal a strong negative correlation between stress levels and sleep quality. Though this doesn't establish a cause-and-effect relationship, it does suggest an area worthy of intervention or deeper study.