Tutorial on Tukey Charts Farrokh Alemi, Ph.D. Sunday, 11/25/2007.

Tutorial on Tukey ChartsTutorial on Tukey Charts

Farrokh Alemi, Ph.D.Farrokh Alemi, Ph.D.

Sunday, 11/25/2007Sunday, 11/25/2007

Why Chart Data?Why Chart Data?

• To discipline intuitions– Only points outside the

limit are real changes

• To communicate data in vivid graphical ways

Steps in Creating a ChartSteps 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

Step 1: Check AssumptionsStep 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

Separate Pre & Post Intervention DataSeparate Pre & Post Intervention Data

Select Control Limits that Are TighterSelect Control Limits that Are Tighter

Step 2: Calculating LimitsStep 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

Calculating MedianCalculating 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.

Calculating Limits by Using MedianCalculating Limits by Using Median

1. List values from smallest to largest2. 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

3. Lower Fourth is the Median of lower half of data4. Upper Fourth is the median of the upper half of the

data 5. Fourth Spread is the difference between the two

Fourths 6. Calculate limits as:

LCL = Lower Fourth - 1.5 * Fourth SpreadUCL = Upper Fourth + 1.5 *Fourth Spread

No need for Calculator

Example: Exercise DataExample: Exercise DataMinutes

of exercise

1 302 03 254 305 356 407 508 459 31

10 2011 4012 6013 4514 6015 4516 3217 5018 60

Day of observation

Pre-intervention

Analysis of Exercise Data: Step 1Analysis of Exercise Data: Step 1

Minutes

of exercise Rank

Day of observation

Minutes of exercise

1 30 1 2 02 0 2 3 253 25 3 1 304 30 4 4 305 35 5 5 356 40 6 6 407 50 7 7 50

Day of observation

Sorted in order of length of exercise

Median

Upper half of data

Lower half of data

Two halves both include Median because it is an observed data point


Minutes

of exercise Rank

Day of observation

Minutes of exercise

1 30 1 2 02 0 2 3 253 25 3 1 304 30 4 4 305 35 5 5 356 40 6 6 407 50 7 7 50

Day of observation


Lower Fourth is Median of lower data set, it is a value between 25 & 30, so it is 27.5


Upper Fourth is Median of upper data set, it is a value between 35 & 40, so it is 37.5

Minutes

of exercise Rank

Day of observation

Minutes of exercise

1 30 1 2 02 0 2 3 253 25 3 1 304 30 4 4 305 35 5 5 356 40 6 6 407 50 7 7 50

Day of observation



• Fourth Spread = 37.5-27.5 = 10

• UCL = 37.5+1.5*10 = 52.5

Upper Fourth

Fourth Spread


• Fourth Spread = 37.5-27.5 = 10

• LCL = 27.5-1.5*10 = 12.5

Lower Fourth

Fourth Spread

Control Chart for Exercise DataControl Chart for Exercise Data

0

20

40

60

80

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Days of observation

Min

utes

of e

xerc

ise

MonthBudget

deviation in 1000s

1 232 -53 -704 -75 -86 97 128 308 2410 2511 -412 -2

Example Data: Budget DeviationsExample Data: Budget Deviations

Analysis of Budget Data: Step 1Analysis of Budget Data: Step 1

MonthBudget

deviation in 1000s

1 232 -53 -704 -75 -86 97 128 308 2410 2511 -412 -2

RankBudget

deviation in 1000s

1 -702 -83 -74 -55 -46 -27 98 129 2310 2411 2512 30

Sort the data from lowest to highest value

Analysis of Budget Data ContinuedAnalysis of Budget Data Continued

RankBudget

deviation in 1000s

1 -702 -83 -74 -55 -46 -27 98 129 2310 2411 2512 30

Median

Upper Half

Lower half

Lower Fourth is Median of lower half and is -4.5

Upper Fourth is Median of upper half and is 23.5

Fourth spread is 23.5 minus -4.5 = 29

UCL is 23.5 + 1.5 * 29 LCL is -4.5 - 1.5* 29

Control Chart for Budget dataControl Chart for Budget data

Take Home MessageTake Home Message

Tukey Chart can work with Tukey Chart can work with small number of data points small number of data points

with no assumptions regarding with no assumptions regarding data distributiondata distribution

Tutorial on Tukey Charts Farrokh Alemi, Ph.D. Sunday, 11/25/2007.

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