An 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. 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:
1, What is the direction of the relationship?
2, What is the strength of the relationship?
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 reads r equals plus point 7 3.
A callout pointing the plus symbol reads, what is the Direction of the Correlation? Positive, plus sign, correlation: as one variable increases, the other also increases; negative, minus sign, correlation as one variable increases, the other decreases (an inverse relationship).” A note at the bottom reads Example: plus point 7 3 is a positive number, showing a positive correlation. As hours spent studying increase, test grades also increase.
A callout pointing toward point 7 3 reads what is the Strength of the Correlation? Strength ranges from plus 1.00 to negative 1.00; a value close to plus 1.00 or negative 1.00 is a strong correlation; a value close to 0.00 is a weak correlation.).” A note at the bottom reads Example: point 7 3 is close to 1.00. This shows a strong correlation between hours spent studying and test grades.
An illustration shows an alert icon within a dashed triangle. The text within the triangle reads 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. A sticky note below the dashed triangle reads, 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 rectangular box from the equation r equals plus point 7 3 shows an eye icon accompanied by text that reads, what does the correlation look like? 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 rectangular box consists of four scatter plots as follows: In the first graph the line of best fit is a gradually ascending line. Text on the horizontal axis reads example: point 7 3 (strong positive correlation).
The second graph plots 20 points from origin to the top right corner. Text on the horizontal axis reads perfect positive correlation (plus 1.00).
The third graph has random plots all over. Text on the horizontal axis reads no relationship (0.00). The fourth graph plots 20 points from the top left corner to bottom right of the graph. Text on the horizontal axis reads perfect negative correlation (negative 1.00).