Calculating and Interpreting the Correlation Coefficient ~adapted from walch education
Important Concepts: A correlation is a relationship between two events, where a change in one event implies a change in another event. Correlation doesn’t mean that a change in the first event caused a change in the other event. The strength of a linear correlation can be measured using a correlation coefficient. Before determining the correlation coefficient, look at the scatter plot of the data and make an initial assessment of the strength of a linear relationship between the two events.
Concepts, continued… A correlation coefficient of –1 indicates a strong negative correlation. A correlation coefficient of 1 indicates a strong positive correlation. A correlation coefficient of 0 indicates a very weak or no linear correlation. The correlation coefficient only assesses the strength of a linear relationship between two variables. The correlation coefficient does not assess causation—that one event causes the other.
Practice Caitlyn thinks that there may be a relationship between class size and student performance on standardized tests. She tracks the average test performance of students from 20 different classes, and notes the number of students in each class in the table on the next slide. Is there a linear relationship between class size and average test score? Use the correlation coefficient, r, to explain your answer.
Scatter Plot Average test score Number of students
Describe the relationship between the data As the class size increases, the average test score decreases. It appears that there is a linear relationship with a negative slope between the two variables. The correlation coefficient, r, is approximately –0.84 (calculated using a graphing calculator)
Use the correlation coefficient to describe the strength of the relationship between the data A correlation coefficient of –1 indicates a strong negative correlation, and a correlation of 0 indicates no correlation. A correlation coefficient of –0.84 is close to –1, and indicates that there is a strong negative linear relationship between class size and average test score.