In a real-world example of negative correlation, student researchers at the University of Minnesota found a weak negative correlation ( r = -0.29) between the average number of days per week that students got fewer than 5 hours of sleep and their GPA (Lowry, Dean, & Manders, 2010). One might expect a negative correlation to exist between someone’s tiredness during the day and the number of hours they slept the previous night: the amount of sleep decreases as the feelings of tiredness increase. Other examples of positive correlations are the relationship between an individual’s height and weight or the relationship between a person’s age and number of wrinkles. The example of ice cream and crime rates is a positive correlation because both variables increase when temperatures are warmer. If two variables are negatively correlated, a decrease in one variable is associated with an increase in the other and vice versa. A negative correlation means that the variables move in opposite directions. Put another way, it means that as one variable increases so does the other, and conversely, when one variable decreases so does the other. A positive correlation means that the variables move in the same direction. The sign-positive or negative-of the correlation coefficient indicates the direction of the relationship (Figure 1). The example above about ice cream and crime is an example of two variables that we might expect to have no relationship to each other. If the variables are not related to one another at all, the correlation coefficient is 0. For instance, a correlation coefficient of 0.9 indicates a far stronger relationship than a correlation coefficient of 0.3. The closer the number is to zero, the weaker the relationship, and the less predictable the relationships between the variables becomes. The closer the number is to 1 (be it negative or positive), the more strongly related the variables are, and the more predictable changes in one variable will be as the other variable changes. The number portion of the correlation coefficient indicates the strength of the relationship. The correlation coefficient is usually represented by the letter r. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between variables.

We can measure correlation by calculating a statistic known as a correlation coefficient. When two variables are correlated, it simply means that as one variable changes, so does the other. How do we determine if there is indeed a relationship between two things? And when there is a relationship, how can we discern whether it is attributable to coincidence or causation? Correlational ResearchĬorrelation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. Also, when it is warm outside, we are more likely to seek a cool treat like ice cream. When the temperature is warm, there are lots of people out of their houses, interacting with each other, getting annoyed with one another, and sometimes committing crimes. It is much more likely that both ice cream sales and crime rates are related to the temperature outside. Describe why correlation does not mean causationĭid you know that as sales in ice cream increase, so does the overall rate of crime? Is it possible that indulging in your favorite flavor of ice cream could send you on a crime spree? Or, after committing crime do you think you might decide to treat yourself to a cone? There is no question that a relationship exists between ice cream and crime (e.g., Harper, 2013), but it would be pretty foolish to decide that one thing actually caused the other to occur.Explain what a correlation coefficient tells us about the relationship between variables.

A negative correlation exists between