Tutorial on Tukey Charts

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Tutorial on Tukey Charts

• Farrokh Alemi, Ph.D.
• Friday, 12 March 2003

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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

• Check assumptions
• Calculate Median and Fourths
• Calculate Fourth spread
• Calculate control limits
• Plot observations and control limits
• Interpret findings
• 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 time periods in the
  pre-intervention period
• Control limits are calculated based on
  pre-intervention data and extrapolated to post
  intervention period

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Separate Pre Post Intervention Data
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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
Upper half of data
Lower 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
• LCL 27.5-1.510 12.5

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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 -6
Lower half
Fourth spread is 23.5 minus -6 29.5
Upper Fourth is Median of upper half and is 23.5
Upper Half
UCL is 23.5 1.5 29.5 LCL is
-6.5 - 1.5 29.5
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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