The introductory text reads, 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. This 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 scatter plot 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 equals positive point 73
A callout pointing to the plus sign in the equation reads:
What Is the Direction of the Correlation? Positive correlation: as one variable increases, the other also increases. Negative correlation: as one variable increases, the other decreases (an inverse relationship).
A graphic showing a note reads, Example: positive point 73 is a positive number, showing a positive correlation. As hours spent studying increase, test grades also increase.
A callout to the value point 73 in the expression reads:
What Is the Strength of the Correlation?
Strength ranges from positive 1 point 00 to negative 1 point 00; a value close to positive 1 point 00 or negative 1 point 00 is a strong correlation; a value close to 0 point 00 is a weak correlation.
A graphic showing a note reads, Example: positive point 73 is close to 1 point 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 scatter plots and is titled, What does the Correlation look like? The introductory text in the sidebar reads, Using a scatter plot, 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: positive point 73 (strong positive correlation). The graph shows an upward-sloping line starting at 0, 0 on the X, Y point and ending about 2 over 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 (positive 1 point 00). The graph shows a precise set of dots slanting upward from 0, 0 on the X, Y point, and ending at positive 100 on the Y-axis.
The third graph is labeled, no relationship (point 00). The dots are scattered randomly across the graph area.
The fourth graph is labeled, perfect negative correlation (negative 1 point 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.