Problem 8 - An Introduction to Psychological Statistics

Question

In the following correlation matrix, what is the relation (number, direction, and magnitude) between… a. Pay and Satisfaction b. Stress and Health $$ \begin{array}{llcll} \text { Workplace } & \text { Pay } & \text { Satisfaction } & \text { Stress } & \text { Health } \\ \hline \text { Pay } & 1.00 & & & \\ \text { Satisfaction } & 0.68 & 1.00 & & \\ \hline \text { Stress } & 0.02 & -0.23 & 1.00 & \\ & & & & \\ \text { Health } & 0.05 & 0.15 & -0.48 & 1.00 \end{array} $$

Step-by-Step Solution

Answer

Pay and Satisfaction: direct moderate (0.68). Stress and Health: inverse moderate (-0.48).

Step 1: Understanding Correlation Coefficient

A correlation coefficient quantifies the direction and magnitude of the linear relationship between two variables. The value will be between -1 and 1. A positive value indicates a direct relationship (both increase or decrease together), a negative value indicates an inverse relationship (one increases while the other decreases), and a magnitude closer to 1 means a stronger relationship.

Step 2: Identify Correlation between Pay and Satisfaction

Look at the correlation matrix and find the value at the intersection of Pay and Satisfaction. The value is 0.68, which indicates a positive relationship.

Step 3: Analyze the Pay and Satisfaction Relationship

This means that there is a direct, moderately strong relationship between Pay and Satisfaction. As Pay increases, Satisfaction tends to increase as well, and vice versa.

Step 4: Identify Correlation between Stress and Health

Find the value at the intersection of Stress and Health in the matrix. The value is -0.48, indicating a negative relationship.

Step 5: Analyze the Stress and Health Relationship

The coefficient -0.48 shows a moderate inverse relationship between Stress and Health. As Stress increases, Health tends to decrease, and vice versa.

Key Concepts

Correlation Coefficient

Understanding the correlation coefficient is key when analyzing relationships between variables. This coefficient is a numerical value, ranging from -1 to 1, which measures how two variables move in relation to each other. When you interpret this value, you're looking at two main things:

• Magnitude: This indicates the strength of a relationship. A value close to 1 or -1 signifies a strong relationship, while values near 0 suggest a weak relationship.
• Direction: If the correlation coefficient is positive, both variables tend to increase or decrease together, known as a positive relationship. If it's negative, one variable increases as the other decreases, indicating a negative relationship.

Hence, by understanding these two aspects, you can summarize the linear relationship between variables in the dataset, helping in predicting trends or making decisions based on the data.

Positive Relationship

A positive relationship in statistical terms indicates that as one variable increases, the other tends to increase too. In the context of our correlation matrix, the positive correlation coefficient of 0.68 between Pay and Satisfaction shows a positive relationship. This suggests that when pay increases, satisfaction tends to increase as well, and this applies when either decreases too. Such relationships can be particularly important in scenarios like workplace analysis, where variables like employee satisfaction are closely watched to ensure performance and retention.

Negative Relationship

A negative relationship is observed when one variable increases while the other decreases. The correlation between Stress and Health in the matrix is an example of this, with a correlation coefficient of -0.48. This number signifies a moderate inverse relationship, indicating that as stress levels go up, health condition tends to worsen and vice versa. Knowing about negative relationships can be quite useful in fields like healthcare, where managing stress could potentially lead to improved health outcomes.

Linear Relationship

The term 'linear relationship' refers to a consistent change in one variable accompanied by a consistent change in another. A correlation coefficient helps identify the strength and direction of this linear relationship. In our matrix, the variables relate to each other in a linear fashion, meaning a change in one is predictable by the change in the other. Remember:

• A correlation coefficient of 1 indicates a perfect positive linear relationship.
• A coefficient of -1 indicates a perfect negative linear relationship.

This concept allows for the prediction of one variable's behavior based on another's, which is invaluable in data analysis.