Correlation analysis is an important statistical tool used to help us understand how two variables are related. It can be used to measure the strength of a relationship between two variables, the direction of the relationship, and the magnitude of the relationship. But, how do we know which of the following statements concerning correlation analysis is not true?

Statement 1: The Value of Correlation Coefficient is Always 2

False. The value of the correlation coefficient can range from -1 to +1, and its magnitude is always less than or equal to 1. A correlation coefficient of 1 indicates a perfect positive correlation between two variables, whereas a correlation coefficient of -1 indicates a perfect negative correlation. A correlation coefficient close to 0 indicates that there is no appreciable relationship between the two variables.

Statement 2: Not All Correlations Are Symmetrical

True. While it is possible for two variables to be perfectly correlated, it is not a requirement for a correlation to exist. In fact, not all correlations are symmetrical. That is, the relationship between two variables can be different in the two directions. For example, the stock market could be positively correlated to the GDP of a country, but could be negatively correlated to its interest rate.

Statement 3: A Correlation Coefficient Expresses Both the Effect Size and the Direction of the Relationship

True. A correlation coefficient can measure both the effect size and the direction of the relationship between two variables. The effect size is a measure of the strength of the relationship between two variables, whereas the direction measures the tendency of one variable to increase or decrease as the other variable increases or decreases. A positive correlation coefficient indicates a positive relationship between two variables, while a negative correlation coefficient suggests a negative relationship between the two variables.