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*Explore the characteristics of positive correlations. Learn about strength and direction, the difference between positive and negative correlations, and more.*

We also recommend watching Correlational Research: Definition, Purpose & Examples and Interpreting the Correlation Coefficient

Imagine that you are conducting research on school achievement. You want to know if a relationship exists between school achievement and attendance. You collect the grade point average (GPA) and days present during the school year from 75 high school students. Your findings are reported in the table below.

If you look at the data closely, you will begin to notice that as the days present increases, GPA also increases. In other words, there is a positive correlation between school achievement and attendance.

What does it mean when we say that two variables are correlated with each other? It means that there is a relationship between them. A correlation is a single numerical value that is used to describe the relationship. Correlation is most commonly measured by the Pearson Product Moment Correlation, which is commonly referred to as Pearson's r. Because of this, a correlation is usually represented by the letter *r*.

Every correlation has two qualities: **strength** and **direction**. The direction of a correlation is either positive or negative. In a **negative correlation**, the variables move in inverse or opposite directions. In other words, as one variable increases, the other variable decreases. For example, there is a negative correlation between self-esteem and depression. In other words, the higher your self-esteem, the lower your feelings of depression.

When two variables have a **positive correlation**, they move in the same direction. This means that as one variable increases, so does the other one. In the example above, we noted that the students who attended school more frequently had the highest GPAs. As the days present at school decreased, so did GPA.

Some other examples of variables that have a positive correlation are:

- GPA and SAT score: The students with the higher GPAs are usually the ones who perform best on the SAT
- Education and salary: The more years of schooling you have, the higher your income will likely be
- Depression and suicide: Those suffer from depression tend to have higher rates of suicide than those who do not

We determine the strength of a relationship between two correlated variables by looking at the numbers. A correlation of 0 means that no relationship exists between the two variables, whereas a correlation of 1 indicates a perfect positive relationship. It is uncommon to find a perfect positive relationship in the real world. Chances are that if you find a positive correlation between two variables that the correlation will lie somewhere between 0 and 1.

The further away from 1 that a positive correlation lies, the weaker the correlation. Similarly, the further a negative correlation lies from -1, the weaker the correlation. A correlation of 0.5 is not stronger than a correlation of 0.8. A correlation of -0.5 is not stronger than a correlation of -0.8.

Two correlations with the same numerical value have the same strength whether or not the correlation is positive or negative. This means that a correlation of -0.8 has the same strength as a correlation of 0.8.

The following guidelines are useful when determining the strength of a positive correlation:

- 1: perfect positive correlation
- .70 to .99: very strong positive relationship
- .40 to .69: strong positive relationship
- .30 to .39: moderate positive relationship
- .20 to .29: weak positive relationship
- .01 to .19: no or negligible relationship
- 0: no relationship exists

The easiest way to spot a positive correlation is to create a scatterplot. We can put the GPA on the *x*-axis and the days present during the school year on the *y*-axis to create a scatterplot.

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Each point on a scatterplot represents one student's GPA and days present during the school year. There is one point on the scatterplot for each of the 75 high school students. The **line of best fit** is a straight line drawn through the center of the data on a scatterplot that best represents the data set. All positive correlations have a line of best fit that goes in the exact same direction as the one in this example.

So what does this graph tell us? We can see from the direction of the line of best fit that there is a positive correlation between GPA and days present during the school year. We could also use the line of best fit to predict where a student might fall on one variable in relation to the other. For example, we could look at the line and see that a student with a 2.63 GPA will likely attend 148 days in the school year.

If you look in the upper right hand corner, you also see that *r = 0.84*. Since *r* signifies a correlation, we can conclude that there is a very strong positive relationship between GPA and days present during the school year.

Could we say that attending more days at school leads to a boost in your GPA? No, we cannot. This is because **correlation does not equal causation**. All a correlation signifies is a relationship between two variables. The only way for causation to be established is by conducting an experiment.

A correlation is a single numerical value that is used to describe the relationship between two variables. All correlations have strength and direction. Two variables that are positively correlated move in the same direction. The closer a positive correlation is to 1, the stronger it is. A positive correlation can be easily observed by creating a scatterplot of your data. So the next time your friend gives you a hard time about skipping a workout to watch television, you can tell her that watching television will not cause you to be obese but going to work out will definitely interfere with your show.

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