Correlation refers to a technique used to measure the relationship between two or more variables.When two things are correlated, it means that they vary together.Positive correlation means that high scores on one are associated with high scores on the other, and that low scores on one are associated with low scores on the other. Negative correlation, on the other hand, means that high scores on the first thing are associated with low scores on the second. Negative correlation also means that low scores on the first are associated with high scores on the second. An example is the correlation between body weight and the time spent on a weight-loss program. If the program is effective, the higher the amount of time spent on the program, the lower the body weight. Also, the lower the amount of time spent on the program, the higher the body weight.

Pearson

Pearson

*r*is a statistic that is commonly used to calculate bivariate correlations.
For an Example Pearson

*r*= -0.80,*p*< .01. What does this mean?
To interpret correlations, four pieces of information are necessary.

**1.**Correlation coefficients can vary numerically between 0.0 and 1.0. The closer the correlation is to 1.0, the stronger the relationship between the two variables. A correlation of 0.0 indicates the absence of a relationship. If the correlation coefficient is –0.80, which indicates the presence of a strong relationship.*The numerical value of the correlation coefficient.***2.**A positive correlation coefficient means that as variable 1 increases, variable 2 increases, and conversely, as variable 1 decreases, variable 2 decreases. In other words, the variables move in the same direction when there is a positive correlation. A negative correlation means that as variable 1 increases, variable 2 decreases and vice versa. In other words, the variables move in opposite directions when there is a negative correlation. The negative sign indicates that as class size increases, mean reading scores decrease.

*The sign of the correlation coefficient*.**3.**A statistically significant correlation is indicated by a probability value of less than 0.05. This means that the probability of obtaining such a correlation coefficient by chance is less than five times out of 100, so the result indicates the presence of a relationship. For -0.80 there is a statistically significant negative relationship between class size and reading score (

*The statistical significance of the correlation.**p*< .001), such that the probability of this correlation occurring by chance is less than one time out of 1000.

**4.**For correlations, the effect size is called the coefficient of determination and is defined as

*The effect size of the correlation.**r*

^{2}. The coefficient of determination can vary from 0 to 1.00 and indicates that the proportion of variation in the scores can be predicted from the relationship between the two variables. For

*r*= -0.80 the coefficient of determination is 0.65, which means that 65% of the variation in mean reading scores among the different classes can be predicted from the relationship between class size and reading scores. (Conversely, 35% of the variation in mean reading scores cannot be explained.)

A correlation can only indicate the presence or absence of a relationship, not the nature of the relationship.

*There is always the possibility that a third variable influenced the results. For example, perhaps the students in the small classes were higher in verbal ability than the students in the large classes or were from higher income families or had higher quality teachers.***Correlation is not causation**.