Correlation is a statistical measure that describes the degree to which two variables move in relation to each other. It's used to gauge the mutual relationship and association between two or more variables.

In statistics, the correlation coefficient is a quantitative assessment that measures both the direction and the strength of this tendency to vary together. The correlation coefficient is measured on a scale that varies from + 1 through 0 to - 1.

• Complete positive correlation (+ 1) exists when as one variable increases, another variable increases by a consistent amount.

• No correlation (0) exists when there is no relationship between variables.

• Complete negative correlation (- 1) exists when as one variable increases, another variable decreases by a consistent amount.

Examples of Correlation

1. Positive Correlation: An example of positive correlation could be the relationship between time spent studying and the resulting exam scores. As the time spent studying increases, we would expect the exam score to increase as well.

2. Negative Correlation: An example of negative correlation could be the relationship between the amount of time spent watching TV and grades in school. As the time spent watching TV increases, the grades may decrease.

3. No Correlation: An example of no correlation could be the relationship between shoe size and intelligence. There is likely no relationship between the two; changing one probably does not affect the other.

Additional Context

In the context of the provided document, correlation is important in understanding the relationship between different metrics in an experiment. For example, in an A/B test, you might be interested in understanding the correlation between the version of a website a user sees (A or B) and their likelihood to make a purchase.