How to Comment on Scatter Graphs

If you wanted to see if your swimming was related to weight loss, you could plot your results. on a scatter graph.

Graphs provide an excellent way to visually represent data. Scatter graphs demonstrate the relationship between two continuous variables --- for example, length of time spent swimming and amount of weight loss. One of the variables, length of time swimming, is plotted on the "x" or horizontal axis and the other, weight loss, is plotted on the "y" or vertical axis. A scatter graph is well-suited to large data sets in which you are interested in learning if two variables are correlated. When examining any scatter graph, you will want to comment on its shape, direction and pattern.

Instructions

1. Examine how the data is dispersed. Look to see if most of the values are in the middle, to the left or right side, or evenly dispersed. If the values are not evenly dispersed, you do not have a correlation between your variables and you would say, "The scatter graph demonstrates little consistent relationship between swim time and weight loss." This would be the end of your interpretation. If the dots on the scatter graph are evenly distributed across the x and y axes, you would say, "The scatter graph suggests there is a relationship between swim time and weight loss."

2. Look for positive direction. If the line of dots rises up and to the right, you would say that the two variables are positively correlated by stating, "There appears to be a positive relationship between time spent swimming and weight loss." In other words, the the more time you spent swimming, the more weight you lost.

3. Look for negative direction. If the line of dots descends down and to the right, then statisticians say that the two variables are negatively correlated. In this case you would say: "There appears to be a negative relationship between swimming and weight loss; the more this person swam, the less weight they lost." Keep in mind that you are talking about correlation, meaning that as one variable increases the other variable either increases or decreases. You are not talking about one variable causing another.

4. Look for a curvilinear relationship --- when your data resembles either an upright or an upside-down "U". If this is the case, you would say, "The relationship between the two variables appears to be curvilinear." If the "U" is right side up you would say something like, "The relationship between swimming and weight loss appears negatively related until the critical value is reached, then the relationship becomes positive." If the critical value was 20 minutes you would say: "When the time spent swimming was less than 20 minutes, greater time spent swimming was associated with less weight loss until the 20 minute mark; at this value and beyond, more time swimming was associated with greater weight loss." If the "U" is upside down you would say the opposite: "When the time spent swimming was less 20 minutes, greater time spent swimming was associated with greater weight loss until the 20 minute mark; at this value and beyond, more time spent swimming was associated with less weight loss."

5. Look at the strength of the relationship by examining the slope of the line. A steep slope would indicate a positive relationship, while a shallow slope would indicate a weak relationship. Your examination of the scatter graph tells you visually whether you want to calculate further statistics, such as slope and correlation. You would say, "The slope of the line appears to be steep, suggesting that a correlational analysis should be completed."

References

• University of Illinois: Scatter Plots
• Rossmanchance.com; Grapical Summaries; Allan J. Rossman and Beth L. Chance
• University of Dayton: How to Calculate the Slope of a Line