Continuous Improvement Toolkit Scatter Diagram www. citoolkit .com
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Scatter Diagram Many situations require the investigating whether a relationship exists between two or more variables www. citoolkit .com
Scatter Diagram A line manager may want to check the relationship between the number of training hours and employee productivity Or if the number of defects is a function of the experience of the person causing it www. citoolkit .com
Scatter Diagram Other Examples The relationship between equipment downtime and its cost of maintenance www. citoolkit .com
Scatter Diagram Other Examples The relationship between driving speed and fuel consumption www. citoolkit .com
Scatter Diagram Other Examples The relationship between the number of people working on a shift and the average answer time in a call center www. citoolkit .com
Scatter Diagram Other Examples The relationship between the number of years of education someone has and the annual income of that person www. citoolkit .com
Scatter Diagram A diagram that shows whether two variables are correlated or related to each other It shows patterns in the relationship that cannot be seen by just looking at the data www. citoolkit .com
Scatter Diagram It works with both continuous and count data www. citoolkit .com
Scatter Diagram Primarily used to visually investigate the relationship between two variables Often an output and an input variables 0 1 0 0 1 1 0 1 0 0 1 X Y 1 0 0 0 1 1 0 1 0 1 0 www. citoolkit .com
Scatter Diagram This is useful to verify that a change in one variable can affect the other variable It helps detecting the primary factors that are really causing a problem and hence eliminating non-critical factors from consideration www. citoolkit .com
Scatter Diagram Often used as a first step when analyzing and communicating the correlation between pairs of variables Before conducting advanced statistical techniques www. citoolkit .com
Scatter Diagram Often used with statistical tools (such as regression) to support or reject hypotheses about the data www. citoolkit .com
Scatter Diagram Where do scatter diagrams fit? Graph the data Scatter diagram Check the correlations Use Pearson Coefficient 1 st regression Linear / Multiple regression Evaluate regression R-squared and analyze residuals Simple: With different model (Cubic) Re-run regression Multiple: Remove unnecessary items (If necessary) Control critical process inputs and Use the results select best operating levels www. citoolkit .com
Scatter Diagram The input variable is normally placed on the horizontal axis while the output variable is placed on the vertical axis Output or response or dependent variable Input or explanatory or independent variable www. citoolkit .com
Scatter Diagram You may also compare two input or output variables to each other X & Y X 1 & X 2 Y 1 & Y 2 In this case, it doesn’t matter which variable goes on the horizontal axis and which goes on the vertical axis www. citoolkit .com
Scatter Diagram Scatter diagrams can indicate several types of correlation No correlation when the data X X X X points are scattered randomly X X X without showing any particular X X X X pattern. Note that the width of the scattered pattern reflects the strength of the relationship www. citoolkit .com
Scatter Diagram Scatter diagrams can indicate several types of correlation A positive correlation occurs X X X when the values of one variable X X X X increase as the values of the X X X X other also increase. The fitted line slopes from bottom left to top right www. citoolkit .com
Scatter Diagram Scatter diagrams can indicate several types of correlation A negative correlation occurs X X X X X when the values of one variable X X X increase as the values of the X X X X other decrease. The fitted line slopes from upper left to lower right www. citoolkit .com
Scatter Diagram Scatter diagrams can indicate several types of correlation Scatter diagrams can also X X indicate nonlinear relationships X X X X between variables. X XX X X www. citoolkit .com
Scatter Diagram Example – Forest Trees 80 Shows the relationship between 70 the volume and the diameter of sample trees in a forest. 60 50 Volume 40 30 20 1 0 Data source: Minitab 0 Both are output 1 0.0 1 2.5 1 5.0 1 7.5 20.0 variables Diameter www. citoolkit .com
Scatter Diagram Example – Presence of Diabetes at a Workplace An analysis that was conducted for diagnosing the presence of diabetes at a workplace. The population was generally young (75.8% were below thirty). www. citoolkit .com
Scatter Diagram Example – Presence of Diabetes This scatter diagram illustrates that there is no obvious relationship between age and glucose levels. High glucose levels are found in all ages, and normal glucose levels are found in higher ages. www. citoolkit .com
Scatter Diagram Example – The amount of sales per month generated at two locations The plotted points form a negative slope. Location B The sales at location B is inversely related to the sales at location A. Location A www. citoolkit .com
Scatter Diagram Example – The amount of sales per month generated at two locations Does this mean that location A caused the decrease in sales at location B, or vice Location B versa? Answer: Not necessarily, unless the two locations are direct competitors. Location A www. citoolkit .com
Scatter Diagram How to Construct a Scatter Diagram Collect the two paired sets of data C r e a t e a s u m m a r y t a b l e o f t h e d a t a Variable 1 Variable 2 www. citoolkit .com
Scatter Diagram How to Construct a Scatter Diagram Draw and label the horizontal and vertical axes with variable names and scale values Xxxx Xxxx www. citoolkit .com
Scatter Diagram How to Construct a Scatter Diagram Plot the data pairs on the diagram by placing a dot at the intersection of each data pair Look at how the pattern appears and how the two variables vary together Y X X X X X X www. citoolkit .com
Scatter Diagram Matrix Plots Summarizes the relationship between pairs of multiple variables in one graph X 1 & X 2 & Y 3 variables Allows to visually assess the variables that might be related www. citoolkit .com
Scatter Diagram Matrix Plots Produces a scatter diagram for every combination of variables X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Potential correlations between pairs of variables can then be identified www. citoolkit .com
Scatter Diagram Matrix Plots – Example 3 6 9 1 00 Salary 80 60 9 6 Publication 3 20 Years 1 0 0 60 80 1 00 0 1 0 20 # of publications doesn't appear to be correlated with the years of experience There may be a relationship between the years of experience and salaries www. citoolkit .com
Scatter Diagram Matrix Plots – Example 3 6 9 1 00 Salary 80 60 9 6 Publication 3 20 Years 1 0 0 60 80 1 00 0 1 0 20 Is there a correlation between the number of publication and salaries? www. citoolkit .com
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