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Continuous Improvement Toolkit Scatter Diagram
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The Continuous Improvement Map
Multivariate Brainstorming IDEF0 Document control Check Sheets** Flowcharting Flow Process Charts** KPIs SCAMPER*** Pugh Matrix Lateral Thinking Reliability Service Blueprints Affinity Diagrams Mind Mapping* Attribute Analysis Morphological Analysis How-How Diagram*** Control Charts Waste Analysis** Time Value Map** Value Stream Mapping** Value Analysis** Suggestion Systems Histograms Activity Networks RACI Matrix Stakeholder Analysis Improvement Roadmaps DMAIC SWOT Analysis Policy Deployment Project Charter PDCA Gantt Charts MOST PERT/CPM Daily Planning Delphi Method Payoff Matrix Relations Mapping Data Mining Just in Time Automation Product Family Matrix Flow Spaghetti** Multi-vari Studies Decision Tree FMEA PDPC RAID Log* Fault Tree Analysis Paired Comparison Traffic Light Assessment TPN Analysis Risk Analysis* Run Charts Scatter Diagram A3 Thinking Importance Urgency Matrix Four Field Matrix Critical-to X Portfolio Matrix Force Field Analysis Decision Balance Sheet Break-even Analysis Voting Quality Function Deployment Pick Chart Gap Analysis* Bottleneck Analysis Cost Benefit Analysis Kaizen Events Control Planning Standard Work Mistake Proofing Quick Changeover Visual Management Simulation TPM 5S Health & Safety Best Practices Pareto Analysis 5 Whys Prioritization Matrix Hypothesis SIPOC* Matrix Diagram Fishbone Diagrams Tree Diagram* Root Cause Analysis Correlation DOE ANOVA Nonparametric Chi-Square Regression Observations Kano Lean Measures Benchmarking*** Interviews Graphical Methods Data collection planner* Questionnaires Probability Distributions MSA Descriptive Statistics Cost of Quality* Sampling Focus Groups Capability Indices Process Yield Project KPIs Normal Distribution
Data Collection Understanding Performance** Implementing Solutions*** Planning & Project Management* Managing Risk Understanding Cause & Effect Designing & Analyzing Processes Group Creativity Selecting & Decision Making
Five Ws Process Redesign Pull Process Mapping OEE
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Scatter Diagram
Many situations require the investigating whether a relationship exists between two or more variables
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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
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Scatter Diagram
Other Examples
The relationship between equipment downtime and its cost of maintenance
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Scatter Diagram
Other Examples
The relationship between driving speed and fuel consumption
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Scatter Diagram
Other Examples
The relationship between the number of people working on a shift and the average answer time in a call center
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Scatter Diagram
Other Examples
The relationship between the number of years of education someone has and the annual income of that person
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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
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Scatter Diagram
It works with both continuous and count data
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Scatter Diagram
Primarily used to visually investigate the relationship between two variables
Often an output and an input variables
Y
0 1 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0
X
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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
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Scatter Diagram
Often used as a first step when analyzing and communicating the correlation between pairs of variables
Before conducting advanced statistical techniques
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Scatter Diagram
Often used with statistical tools (such as regression) to support or reject hypotheses about the data
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Scatter Diagram
Where do scatter diagrams fit?
Graph the data Scatter diagram Check the correlations Use Pearson Coefficient 1st regression Linear / Multiple regression Evaluate regression R-squared and analyze residuals Re-run regression
(If necessary)
Simple: With different model (Cubic) Multiple: Remove unnecessary items Use the results Control critical process inputs and select best operating levels
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Scatter Diagram
The input variable is normally placed on the horizontal axis while the output variable is placed on the vertical axis
Input or explanatory or independent variable Output or response or dependent variable
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Scatter Diagram
You may also compare two input or output variables to each other
In this case, it doesn’t matter which variable goes on the horizontal axis and which goes on the vertical axis
X1 X2 & Y1 Y2 & X Y &
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Scatter Diagram
Scatter diagrams can indicate several types of correlation
X X X X X X X X X X X
No correlation when the data points are scattered randomly without showing any particular pattern.
Note that the width of the scattered pattern reflects the strength of the relationship
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Scatter Diagram
A positive correlation occurs when the values of one variable increase as the values of the
X X X X X X X X X X X
Scatter diagrams can indicate several types of correlation
The fitted line slopes from bottom left to top right
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Scatter Diagram
Scatter diagrams can indicate several types of correlation A negative correlation occurs when the values of one variable increase as the values of the
X X X X X X X X X X X X
The fitted line slopes from upper left to lower right
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Scatter Diagram
Scatter diagrams can indicate several types of correlation Scatter diagrams can also indicate nonlinear relationships between variables.
X X X X X X X X X XX
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Scatter Diagram
Example – Forest Trees
Both are output variables
20.0 1 7.5 1 5.0 1 2.5 1 0.0 80 70 60 50 40 30 20 1 0
Diameter Volume
Shows the relationship between the volume and the diameter of sample trees in a forest.
Data source: Minitab
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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).
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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.
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Scatter Diagram
Example – The amount of sales per month generated at two locations
Location A Location B
The plotted points form a negative slope. The sales at location B is inversely related to the sales at location A.
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Scatter Diagram
Example – The amount of sales per month generated at two locations
Location A Location B
Does this mean that location A caused the decrease in sales at location B, or vice versa? Answer: Not necessarily, unless the two locations are direct competitors.
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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
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Scatter Diagram
How to Construct a Scatter Diagram
Draw and label the horizontal and vertical axes with variable names and scale values
Xxxx Xxxx
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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
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Scatter Diagram
Matrix Plots
Summarizes the relationship between pairs of multiple variables in one graph
Allows to visually assess the variables that might be related 3 variables
X1 X2 & Y &
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Scatter Diagram
Matrix Plots
Produces a scatter diagram for every combination of variables
Potential correlations between pairs of variables can then be identified
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
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Scatter Diagram
Matrix Plots – Example
1 00 80 60 20 1 0 9 6 3 9 6 3 1 00 80 60 20 1 0
Salary Publication Years
There may be a relationship between the years of experience and salaries # of publications doesn't appear to be correlated with the years of experience
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Scatter Diagram
Matrix Plots – Example
1 00 80 60 20 1 0 9 6 3 9 6 3 1 00 80 60 20 1 0
Salary Publication Years
Is there a correlation between the number of publication and salaries?
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Scatter Diagram
Further Information – One of the 7 Basic Tools of Quality
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Scatter Diagram
Further Information
When the relationship is not so clear, Correlation can be used to help validate if a relationship exists between the variables Regression techniques go a step further by defining the relationship in a mathematical format
# of Defects Years of experience
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Scatter Diagram
Further Information
Be careful before concluding that there is a direct cause-and- effect relationship between the variables There might be a third factor that is causing the change in the two variables
Y=f(x)
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Scatter Diagram
Further Information
You can also illustrate a stratification factor in scatter diagrams For example, the relationship between a process output and a process input for two different settings
