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Research Methods in Psychology: Help and Review15 chapters | 158 lessons
Yolanda has taught college information technology and literacy, and has a master's in counseling psychology and business administration.
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 15 high school students. Your findings are reported in this table.
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 two variables are correlated with each other? It means that two variables have 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, it means the variables 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 the GPA.
Some other examples of variables that have a positive correlation are:
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:
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.
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 15 high school students. The line of best fit is a straight line drawn through the center of the data on the 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.
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 will 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. When two variables have a positive correlation, that means the two variables 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.
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Research Methods in Psychology: Help and Review15 chapters | 158 lessons