Explain the concept of correlation and how to interpret correlation coefficients of 0.3,0, and -0.95
Correlation coefficient (r) is a number that indicates the degree of linear relationship between two variables.
I. Scatter diagram (scattergram, scatterplot) is graphic representation of r. Each dot on scattergram represents two measures on one unit.
II. Reference values
A. 1 or +1 indicates perfect predictability and that both variables increase/decrease together (height in inches vs. cm. example).
B. -1 also indicates perfect predictability, but that one variable increase while the other decreases (height in inches vs. distance between head and ceiling example).
C. 0 indicates random relationship with no predictability.
D. All r's are between these points. This is only an ordinal scale.
-1_______________0_______________+1
E. However, there are some limitations.
1. The decimals cannot be converted into percentages, because it is only an ordinal scale.
2. Absolute value can never be greater than 1 (see formula).
3. Correlation does not necessarily mean causation
r = .3 indicates mild relationship with minimal predictability.
r = .95 indicates strong relationship with great predictability.
Correlation is a statistical measure that describes the relationship between two variables. It provides information about how strongly, and in what direction, two variables are related to each other. The correlation coefficient, commonly denoted as "r," is used to quantify this relationship.
The correlation coefficient ranges from -1 to +1. A positive value indicates a positive relationship, meaning that as one variable increases, the other tends to increase as well. On the other hand, a negative value indicates a negative relationship, where one variable increases as the other decreases.
When interpreting correlation coefficients, it is helpful to consider the magnitude or strength of the correlation. Values closer to +1 or -1 indicate a stronger relationship, while values closer to 0 indicate a weaker relationship. Additionally, the sign of the correlation coefficient indicates the direction of the relationship, whether it is positive or negative.
Now, let's interpret the correlation coefficients you provided:
1. A correlation coefficient of 0.3: This indicates a relatively weak positive relationship between the two variables. It suggests that as one variable increases, the other tends to increase, but the relationship may not be very strong.
2. A correlation coefficient of 0: This suggests no linear relationship between the two variables. It indicates that there is no consistent pattern between the variables, and changes in one variable do not correspond to changes in the other.
3. A correlation coefficient of -0.95: This represents a very strong negative relationship between the variables. It suggests that as one variable increases, the other tends to decrease, or vice versa. This indicates a highly consistent and inverse relationship between the variables.
To obtain these interpretations, you would need to calculate the correlation coefficient using statistical software or manual calculations based on the covariance and standard deviation of the two variables.