Brett's teacher observed Brett's behavior in class for a week and compared the minutes he stayed on task in class to the grade he earned on the homework that night. She found that the correlation coefficient was [tex]$r=0.97$[/tex]. What type of relationship has his teacher discovered?
A. positive correlation, likely causal
B. positive correlation, not likely causal
C. negative correlation, likely causal
D. negative correlation, not likely causal
Answer (1)
The correlation coefficient r = 0.97 indicates a strong positive correlation.
Positive correlation means that as time on task increases, homework grade tends to increase.
Correlation does not imply causation; other factors may be involved.
Therefore, the relationship is a positive correlation and not likely causal: positive correlation, not likely causal .
Explanation
Understanding the Correlation Coefficient The correlation coefficient, denoted as r , is a measure of the strength and direction of a linear relationship between two variables. In this case, the teacher observed Brett's behavior and compared the minutes he stayed on task with his homework grade, finding a correlation coefficient of r = 0.97 .
Interpreting the Positive Correlation A correlation coefficient close to +1 indicates a strong positive correlation. This means that as one variable increases, the other variable also tends to increase. In this scenario, as the minutes Brett stayed on task increased, his homework grade also tended to increase.
Correlation vs. Causation It's crucial to remember that correlation does not imply causation. Just because two variables are correlated doesn't mean that one causes the other. There might be other factors influencing both variables. For example, Brett's understanding of the material could influence both his time on task and his homework grade.
Conclusion Therefore, the teacher has discovered a positive correlation between Brett's time on task and his homework grade. However, it is not likely that the relationship is causal.
Examples
In educational research, correlation coefficients are often used to explore relationships between different variables, such as study habits and academic performance. For instance, a researcher might find a positive correlation between the amount of time students spend studying and their exam scores. While this suggests that studying more is associated with higher scores, it doesn't prove that studying directly causes the higher scores. Other factors, like prior knowledge or teaching quality, could also play a significant role. Understanding correlation helps educators identify potential areas for intervention, but further investigation is needed to establish causal relationships.
