See the Effect Size review for more information. If asked to use effect size, you can report and interpret r. * r is also one of the two most commonly reported measures of Effect Size, or strength of relationship. You can use Excel to create a scatter plot, called a frequency polygon, by using these directions. Using a scatter plot, we plot the intersection of two measures (math and science score for a group of students) and examine the pattern. Most often, it is abbreviated as Pearson’s r, and usually noted as simply, r.* Pearson’s r is the most widely used statistical measure of association. The long title for this measure is called the Pearson Product Moment Correlation Coefficient. In the second, the pattern seems negative, as the plotted scores suggest a downward trend.įinally, we can calculate a percentage that represents how close the scores are to the perfect line. In the first graph, the pattern seems positive, as the plotted scores suggest an upward trend. We chose which line to add based on the pattern we see in scores. Notice that the perfect correlation line is still there. The next two graphs are called scatter plots, and they show the intersection of 10 student scores (Student 1: math = 80 science = 57, for example). However, while research tells us that there is a relationship between math and science scores, we know that it will not be perfect. Alternately, using the perfect negative relationship example, a student scoring a 90 in math would have a 60 in science. Repeat this in increments of 10 and you get a perfect relationship. Using the perfect positive relationship example, a student scoring a 90 in math would also score a 90 in science. Imagine individual dots for each student along a line representing the intersection between a math and a science score. The above graphs show lines with perfect relationships. The following graphs show the same relationships: Negative as Math Score declines,Science Score improves Negative as Math Score improves,Science Score declines Positive as Math Score declines,Science Score declines Positive as Math Score improves,Science Score improves This and other possibilities are listed below: Variable 1 For example, as one value (in this case, math score) improves, the other (in this case, science score) also improves. This relation, statistically, is referred to as a linear trend. Therefore, the question: “Among 7 th graders, what is the correlation between math and science scores?” is the same as asking, “Among 7 th graders, what is the relationship between math and science scores?” Why would this be useful?ĭepending on your research question, you may want to know if two things are related (or not). A synonym for correlation is relationship.
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