Bill is doing a project for you in the marketing department. Ln conducting his analysis regarding consumer behavior and a new product that has come out, he tells you the correlation between these two variables is 1.09. What is your response to this analysis.
Judy conducted an analysis for her supervisor. The result she obtained was a correlation coefficient that was negative 0.86. Judy us confused by the number and feels that because it is negative and not positive, it means that it is bad. You are her supervisor. How would you clarify this result for Judy regarding the meaning of the correlation?
A) correlation coefficient is between -1 and +1 , not 1.09
B) negative coefficient means that y is pretty well correlated with negative x. It is pretty much a straight line but with negative slope. like y = -5x + 3
http://www.dmstat1.com/res/TheCorrelationCoefficientDefined.html
Judy has conducted an analysis for her supervisor. The result she obtained was a correlation coefficient that was negative 0.86. Judy is confused by this number and feels that because it is negative and not positive is means that it is bad. You are her supervisor. How would you clarify this result for Judy regarding the meaning of the correlation?
As the supervisor, here's how you can respond to both scenarios:
1. Bill's Analysis:
It's important to note that a correlation coefficient measures the relationship between two variables, indicating the strength and direction of the relationship. However, a correlation coefficient of 1.09 is not valid, as it exceeds the possible range of correlations, which is typically between -1 and +1. It suggests an error in calculation or data entry.
To address this, you can inform Bill about the range of possible correlation values and ask him to double-check his calculations or data. It's crucial to ensure the accuracy of the statistical analysis before drawing any conclusions based on incorrect results.
2. Judy's Confusion:
Negative correlations, such as the -0.86 coefficient obtained by Judy, do not necessarily indicate a "bad" relationship. In fact, negative correlations imply an inverse relationship between the two variables, meaning that as one variable increases, the other tends to decrease. It doesn't suggest that the relationship is unfavorable or detrimental.
To clarify this for Judy, explain that a negative correlation simply indicates an opposite movement between the variables being analyzed. The strength of the correlation (-0.86) suggests a relatively strong inverse relationship, demonstrating that as one variable increases, the other tends to decrease proportionally.
Emphasize that negative correlations are as important and meaningful as positive correlations, as they provide valuable insights about how the variables interact. It is crucial for Judy to understand that a negative correlation does not inherently imply a negative outcome, but rather highlights a different type of relationship between the variables.