Final answer:
The correlation coefficient, represented by r, indicates the strength and direction of the relationship between two variables, with values ranging from -1 to +1. Positive correlations show that variables increase and decrease together, while negative correlations indicate they move in opposite directions. Correlational research establishes patterns between variables but does not imply causation.
Step-by-step explanation:
The correlation coefficient, often represented by the symbol r, is a numerical representation of the strength and direction of the relationship between two variables. This coefficient ranges between -1 and +1. A positive correlation implies that both variables move in the same direction, meaning as one variable increases, so does the other, and similarly, they decrease together. In contrast, a negative correlation indicates that the variables move in opposite directions; as one variable increases, the other decreases.
A key function of correlational research is to identify patterns of association between variables. However, it's crucial to understand its limitations: correlation does not establish causation. This means that even if two variables are strongly correlated, we cannot conclude that one variable causes the changes in the other without further experimental research. Additionally, correlational research may be affected by third-variable problems or spurious correlations.
An example of correlation could be the relationship between hours spent studying and exam scores; a positive correlation might be observed as more study time is associated with higher scores. The correlation coefficient here could be, for instance, +0.8, indicating a strong, positive relationship. However, we cannot say that increasing study hours causes better scores without controlling for other variables, such as prior knowledge or intelligence.
To conclude, while correlational research can be a powerful tool for understanding relationships between variables, its findings should be interpreted with caution, understanding the difference between correlation and causation, and recognizing potential limitations.