Tutorial on Tukey Charts

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Tutorial on Tukey Charts

• Farrokh Alemi, Ph.D.
• Sunday, 11/25/2007

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(No Transcript)
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Why Chart Data?

• To discipline intuitions
• Only points outside the limit are real changes
• To communicate data in vivid graphical ways

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Steps in Creating a Chart

1. Check assumptions select time period
2. Calculate Median and Fourths
3. Calculate Fourth Spread
4. Calculate control limits
5. Plot observations and control limits
6. Interpret findings
7. Distribute control chart

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Step 1 Check Assumptions

• Observations must be measured on an interval
  scale.
• There must be at least 7 observations in the time
  period where control limits are calculated

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Separate Pre Post Intervention Data
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Select Control Limits that Are Tighter
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Select Control Limits that Are Tighter
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Select Control Limits that Are Tighter
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Select Control Limits that Are Tighter
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Step 2 Calculating Limits

• UCL Upper Fourth 1.5 Fourth Spreads
• LCL Lower Fourth 1.5 Fourth Spreads
• Upper Fourth is value where ¼ of data above it
• Lower Fourth is value where ¼ of data below it
• Fourth Spread is difference of Upper and Lower
  Fourths

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Calculating Median

• Median is a value where 50 of data are below if
  and 50 above it.
• List observations from smallest to largest
• If odd number of observations, take the data
  point in the middle, where 50 of data are below
  it.
• If even number of observations, take average of
  the two middle ranked numbers.

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Calculating Limits by Using Median

• List values from smallest to largest
• Calculate median, divide the data into two halves
• If Median is one of the data points, include it
  in both the upper and lower half of data
• Lower Fourth is the Median of lower half of data
• Upper Fourth is the median of the upper half of
  the data
• Fourth Spread is the difference between the two
  Fourths
• Calculate limits as
• LCL Lower Fourth - 1.5 Fourth Spread
• UCL Upper Fourth 1.5 Fourth Spread

No need for Calculator
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Example Exercise Data
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Analysis of Exercise Data Step 1
Lower half of data
Upper half of data
Two halves both include Median because it is an
observed data point
Median
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Analysis of Exercise Data Step 2
Lower Fourth is Median of lower data set, it is a
value between 25 30, so it is 27.5
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Analysis of Exercise Data Step 3
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Analysis of Exercise Data Step 4

• Fourth Spread 37.5-27.5 10
• UCL 37.51.510 52.5

Upper Fourth
Fourth Spread
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Analysis of Exercise Data Step 4

• Fourth Spread 37.5-27.5 10
• LCL 27.5-1.510 12.5

Lower Fourth
Fourth Spread
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Control Chart for Exercise Data
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Example Data Budget Deviations
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Analysis of Budget Data Step 1
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Analysis of Budget Data Continued
Lower Fourth is Median of lower half and is -4.5
Lower half
Fourth spread is 23.5 minus -4.5 29
Upper Fourth is Median of upper half and is 23.5
Upper Half
UCL is 23.5 1.5 29 LCL is
-4.5 - 1.5 29
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Control Chart for Budget data
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Take Home Message

• Tukey Chart can work with small number of data
  points with no assumptions regarding data
  distribution