One might wonder if the time spent studying for a test affects test score. These two variables would probably be positively related. As time studying for a test goes up, test score probably goes up too. Click on image for full size (3 Kb) Courtesy of Freeze Clip Art

One of the most common ways a scientist does this is by using a concept called correlation. Correlation is basically a measurement of how independent two different variables are, and is usually calculated using a formula that results in a coefficient of correlation ranging from -1 to 1.

A correlation of -1 indicates that the two variables are inversely related, and that as one variable increases the other always decreases. For example, the total sales in a given day for an ice cream truck and the total snowfall for that same day might have a correlation close to -1. On days with lots of snow, not many people are buying ice cream from the truck, and on days where the ice cream truck’s sales are really high, it’s probably not snowing. A correlation of 1, on the other hand, indicates that the two variables are directly related, and that as one variable goes up the other does also. For example, the amount of time a basketball player spends practicing is usually closely related to the number of points he or she scores in games, and this relationship would probably have a correlation coefficient close to 1.

Many times a calculated correlation will be close to 0, and this indicates that there is no obvious relationship between the two variables (there may still be a relationship; in some rare cases two variables can be closely related but have a correlation coefficient of 0). It’s important to remember that even when two variables are correlated, this does not mean that a change in one variable causes the other one to change—it just means that they’re related. For instance, when it’s raining you can see people using umbrellas a lot more often, and you can see cars using their wipers a lot more often. So umbrella use and windshield wiper use are correlated, but neither causes the other—we don’t use umbrellas because other people are using wipers, or vice versa. We use both because it’s raining.

One might wonder if the time spent studying for a test affects test score. These two variables would probably be positively related. As time studying for a test goes up, test score probably goes up too. Click on image for full size (3 Kb) Courtesy of Freeze Clip Art

One of the most common ways a scientist does this is by noting correlation. Correlation tells if two different variables vary together - that is, if one goes up, does the other one also go up? Correlation is usually calculated using a formula that results in a number ranging from -1 to 1.

A correlation of -1 says that the two variables are inversely related. As one variable increases the other always decreases. For example, the total sales in a given day for an ice cream truck and the total snowfall for that same day might have a correlation close to -1. On days with lots of snow, not many people are buying ice cream from the truck. On days where the ice cream truck’s sales are really high, it’s probably not snowing.

A correlation of 1 says that the two variables are directly related. That is as one variable goes up the other does also. For example, the amount of time a basketball player spends practicing is usually closely related to the number of points he or she scores in games. This correlation would be close to 1.

Many times a correlation will be close to 0. This means that there is no obvious relationship between the two variables.

It’s important to remember that even when two variables are correlated, this does not mean that a change in one variable causes the other one to change. It just means they’re related. For instance, when it’s raining you can see people using umbrellas a lot more often, and you can see cars using their wipers a lot more often. So umbrella use and windshield wiper use are correlated, but neither causes the other. We don’t use umbrellas because other people are using wipers, or vice versa. We use both because it’s raining.

A student studying for a test. As time studying for the test goes up, so should test score. Click on image for full size (3 Kb) Courtesy of Freeze Clip Art

Sometimes variables are related (or correlated) in a positive way. That is, as one variable goes up, the other one goes up too. In an experiment to see if amount of time studying for a test affects student test score, the two variables are probably positively related. As time studying for a test goes up, test score probably goes up too.

Sometimes two variables can have a negative correlation. As one variable goes up the other always goes down. For example, the total sales in a day for an ice cream truck and the total snowfall for that same day might have negative correlation. On days with lots of snow, not many people are buying ice cream from the truck. On days where the ice cream truck’s sales are really high, it’s probably not snowing.

Finally, some variables will have no clear relationship or correlation.