The introductory text follows: A correlation indicates a relationship between two variables, such as the amount of time you spend studying and the grade you get on a test. is relationship is often indicated using a correlation coefficient, symbolized as r. To interpret the relationship using a correlation coefficient (r), ask yourself two questions:
A scatterplot helps us see what the relationship looks like. And remember, a correlation between two variables does not necessarily mean that one variable caused the change in the other variable.
An equation is drawn, expressing: r = + .73
A callout to the + in the equation reads:
What Is the Direction of the Correlation?
A graphic showing a note reads, “Example: +.73 is a positive number, showing a positive correlation. As hours spent studying increase, test grades also increase.”
A callout to the value .73 in the expression reads:
What Is the Strength of the Correlation?
strength ranges from +1.00 to −1.00
A graphic showing a note reads, “Example: +.73 is close to 1.00. This shows a strong correlation between hours spent studying and test grades.”
A triangle at the bottom of the infographic shows a caution ! icon, and text reading, “BEWARE of the potential Third Variable. Correlation does not indicate that one variable causes a change in the other. A third variable may have influenced the results. Example: Although time spent studying and exam grades are strongly and positively correlated, attendance is another variable. Students who attend classes regularly tend to spend more hours studying. Likewise, students who attend classes regularly know what to expect on the test and are therefore likely to get better grades.” A sidebar at the right shows four scatterplots and is titled, “What does the Correlation look like?” The introductory text in the sidebar reads, “Using a scatterplot, we can express the relationship between two variables. One variable is labeled on the horizontal axis, and the second variable is labeled on the vertical axis. Each dot represents one participant's scores on the two variables. Notice how the shape of the graph changes depending on the direction and strength of the relationship between the variables.” The first graph is labeled “example: +.73 (strong positive correlation).” The graph shows an upward-sloping line starting at 0,0 on the X,Y point and ending about 2/3 the height of the Y-axis at the right of the X-axis. The dots are scattered above and below the sloping line.
The second graph is labeled, “perfect positive correlation (+1.00).” The graph shows a precise set of dots slanting upward from 0,0 on the X,Y point, and ending at 100 on the Y-axis. The third graph is labeled, “no relationship (.00).” The dots are scattered randomly across the graph area. The fourth graph is labeled, “perfect negative correlation (−1.00).” The graph shows a precise set of dots slanting downward from 0,100 on the X,Y point, across and down to end at 0 on the Y-axis.