The scatter plot is one of Six Sigma’s main tools for structured problem solving. You may already be asking: What Is a Scatter Plot? Given two numerical variables, X and Y, measured on the same sample of n items, a scatter plot uses axes X-Y: each sample item is represented by a pair of values (xi, yi) and its corresponding point on the Cartesian plane X-Y.
What Is It Used For?
The graph helps analyze how two variables are related. For example, it can show the relationship between students’ height (X) and weight (Y), or between a process input variable (X) and a quality characteristic (Y) of the final product. Plotting all points—that is, all pairs of values (xi, yi), a clear pattern in the points provides evidence of a possible relationship between the two variables.
How Do I Interpret a Scatter Plot?
| Panel | Relationship | Correlation Coefficient |
|---|---|---|
| a | Positive linear correlation | r = 0.97 |
| b | Negative linear correlation | r = −0.99 |
| c | No correlation | r = 0.06 |
| d | Parabolic relationship | r = −0.33 |
The figure above shows common scatter plot patterns. In figure c, points lie in a horizontal band without apparent order, suggesting no correlation. Figures a, b and d show clear patterns suggesting a relationship. Figure a shows positive linear correlation: as X increases, Y increases. Figure b shows negative linear correlation: as X increases, Y decreases, and vice versa. If a relationship is suspected but the graph suggests otherwise, verify that the data were collected correctly.
Scatter Plot: Horizontal axis: Speed. Vertical axis: Impurities.
Some scatter plots show a weaker, less defined pattern. This is called weak correlation and should be checked by calculating the correlation coefficient. Relationships may also be nonlinear. Figure d shows a parabolic curve: as X increases, Y initially increases and then decreases. Isolated points outside the general pattern should be investigated: they may reflect unusual process behavior or measurement, recording or typing errors. Identify their cause, since they may provide valuable information.
A relationship between two variables does not necessarily mean that one causes the other. A scatter plot shows association; the user must investigate why it exists. To verify whether X affects Y, use both process knowledge and testing. Anyone interpreting a scatter plot should consider that variables X and Y may appear significantly related for the following reasons:
- X affects Y (the case usually of greatest interest).
- Y affects X.
- X and Y interact with each other.
- A third variable, Z affects both and causes the observed relationship.
- X and Y behave similarly by chance.
- X and Y appear related because the sample is not representative.
How often do you use this tool to solve the problems you face every day?
Reference: Control estadístico de la calidad y seis sigma, by Humberto Gutiérrez and Román De la Vara.
