What is the range of possible correlation coefficients?

The range of possible correlation coefficients is from -1 to +1. This reflects the nature of correlation measurements, which assess the strength and direction of a linear relationship between two variables.

A correlation coefficient of +1 indicates a perfect positive correlation, meaning that as one variable increases, the other variable also increases in a perfectly linear manner. In contrast, a correlation coefficient of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other variable decreases perfectly in a linear manner. A correlation coefficient of 0 signifies no linear relationship between the variables.

Understanding this range is crucial in statistics because it allows researchers to quantify the degree of association between variables and interpret data more effectively. Other ranges, such as between 0 and 1 or -1 and 0, do not encapsulate the full spectrum of relationships that can exist between two variables, thus invalidating the understanding of correlation as inherently unable to express both positive and negative relationships simultaneously. Furthermore, the range of 0 to 100 does not apply to correlation coefficients, as it suggests an entirely different scale, potentially creating confusion in statistical analysis.