Tukey Control Chart in Health Informatics Program at GMU
Tukey Control Chart
Farrokh Alemi, Ph.D.
Seven Steps
1. Assumptions
Assumption
1 per Period
Assumption
Outliers
Seven Steps
2. Median & Fourths
2. Median & Fourths
Median, ½ Below
2. Median & Fourths
Median, ½ Below
1.
Order
2.
Equal halves
3.
Odd or Even?
2. Median & Fourths
Lower Fourth, ¼ Below
2. Median & Fourths
Upper Fourth, ¾ Below
Seven Steps
3. Fourth Spread
3. Fourth Spread
Upper Fourth-lower Fourth
Seven Steps
4. Control Limits
UCL = Upper Fourth + 1.5 * Fourth Spreads
LCL = Lower Fourth – 1.5 * Fourth Spreads
Seven Steps
5. Plot Chart
Seven Steps
6. Interpret Findings
Seven Steps
7. Distribute
E
XAMPLE
: E
XERCISE
D
ATA
A
NALYSIS
OF
E
XERCISE
D
ATA
: S
TEP
1
Median
Upper half of
data
Lower half of
data
Two halves both include
Median because it is an
observed data point
A
NALYSIS
OF
E
XERCISE
D
ATA
: S
TEP
2
Lower Fourth is
Median of
lower data set,
it is a value
between 25 &
30, so it is 27.5
A
NALYSIS
OF
E
XERCISE
D
ATA
: S
TEP
3
Upper
Fourth
Lower
Fourth
Fourth Spread = 37.5-27.5 = 10
Upper
Fourth
Fourth
Spread
UCL = 37.5+1.5*10 = 52.5
Lower
Fourth
Fourth
Spread
UCL = 37.5-1.5*10 = 52.5
C
ONTROL
C
HART
FOR
E
XERCISE
D
ATA
A
NALYSIS
OF
B
UDGET
D
ATA
: S
TEP
1
A
NALYSIS
OF
B
UDGET
D
ATA
C
ONTINUED
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
C
ONTROL
C
HART
FOR
B
UDGET
DATA
Tukey control chart works with
medians and is less sensitive to
outliers than mean-based
charts
These slides were organized by Dr. Alemi. These slides discuss a control chart based on median’s distribution, as organized by Tukey and first proposed by Alemi.
Explore the Tukey Control Chart methodology as part of the Health Informatics Program at George Mason University (GMU). Learn about the seven essential steps including assumptions, outliers, median, fourths, and control limits to enhance data analysis and decision-making in healthcare settings.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
Presentation Transcript
Tukey Control Chart Farrokh Alemi, Ph.D. HEALTH INFORMATICS PROGRAM HI.GMU.EDU
Seven Steps 1. Assumptions HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Assumption 1 per Period HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Assumption Outliers HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Seven Steps 2. Median & Fourths HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
2. Median & Fourths Median, Below HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
2. Median & Fourths Median, Below 1. Order 2. Equal halves 3. Odd or Even? HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
2. Median & Fourths Lower Fourth, Below HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
2. Median & Fourths Upper Fourth, Below HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Seven Steps 3. Fourth Spread HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
3. Fourth Spread Upper Fourth-lower Fourth HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Seven Steps 4. Control Limits HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
UCL = Upper Fourth + 1.5 * Fourth Spreads LCL = Lower Fourth 1.5 * Fourth Spreads HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Seven Steps 5. Plot Chart HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Seven Steps 6. Interpret Findings HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Seven Steps 7. Distribute HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
EXAMPLE: EXERCISE DATA Pre- intervention HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
ANALYSISOF 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 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
ANALYSISOF EXERCISE DATA: STEP 2 Lower Fourth is Median of lower data set, it is a value between 25 & 30, so it is 27.5 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
ANALYSISOF EXERCISE DATA: STEP 3 Upper Fourth is Median of upper data set, it is a value between 35 & 40, so it is 37.5 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Fourth Spread = 37.5-27.5 = 10 Upper Fourth Lower Fourth HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
UCL = 37.5+1.5*10 = 52.5 Upper Fourth Fourth Spread HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
UCL = 37.5-1.5*10 = 52.5 Fourth Spread Lower Fourth HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
CONTROL CHARTFOR EXERCISE DATA Figure 3: Seven-day limits for data in Table 1 Minutes of exercise 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Days of observation HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Budget deviation in 1000s 23 -5 -70 -7 -8 9 12 30 24 25 -4 -2 Month 1 2 3 4 5 6 7 8 8 10 11 12 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
ANALYSISOF BUDGET DATA: STEP 1 Budget deviation in 1000s 23 -5 -70 -7 -8 9 12 30 24 25 -4 -2 Budget deviation in 1000s -70 -8 -7 -5 -4 -2 9 12 23 24 25 30 Month Rank 1 2 3 4 5 6 7 8 8 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 Sort the data from lowest to highest value HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
ANALYSISOF BUDGET DATA CONTINUED Budget deviation in 1000s -70 -8 -7 -5 -4 -2 9 12 23 24 25 30 Rank 1 2 3 4 5 6 7 8 9 10 11 12 Lower Fourth is Median of lower half and is -4.5 Lower half Fourth spread is 23.5 minus - 4.5 = 29 Median 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 HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
CONTROL CHARTFOR BUDGETDATA HEALTH INFORMATICS PROGRAM GEORGE MASON UNIVERSITY
Tukey control chart works with medians and is less sensitive to outliers than mean-based charts
