Statistics - Designs - Differences between Orthogonality and Confounding

v9991

Trusted Information Resource
#1
Elsmar Forum Sponsor

Miner

Forum Moderator
Staff member
Admin
#2
This is a tricky concept. An easy way to test whether your design is orthogonal is to run a correlation of each factors levels (using -1, 1 level coding) against every other factors levels. If all correlations are 0, the design is orthogonal.

Confounding (a.k.a. aliasing) can occur in two ways.
  • First, if there is some correlation between the levels of different factors (non-orthogonal design) you can have partial confounding.
  • Second, in an orthogonal fractional factorial you may have partial confounding between main effects and interactions as in a Plackett-Burmann design to complete confounding as in a main effect with a 2-way interaction in a Resolution III fractional factorial or between interactions in a Resolution IV design.
The two are actually separate concepts.
 

Attachments

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#3
There are two good examples of confounding in the wikipedia writeup for confounding at http://en.wikipedia.org/wiki/Confounding

As an example, suppose that there is a statistical relationship between ice-cream consumption and number of drowning deaths for a given period. These two variables have a positive correlation with each other. An evaluator might attempt to explain this correlation by inferring a causal relationship between the two variables (either that ice-cream causes drowning, or that drowning causes ice-cream consumption). However, a more likely explanation is that the relationship between ice-cream consumption and drowning is spurious and that a third, confounding, variable (the season) influences both variables: during the summer, warmer temperatures lead to increased ice-cream consumption as well as more people swimming and thus more drowning deaths.

In another concrete example, say one is studying the relation between birth order (1st child, 2nd child, etc.) and the presence of Down's Syndrome in the child. In this scenario, maternal age would be a confounding variable:
1.Higher maternal age is directly associated with Down's Syndrome in the child
2.Higher maternal age is directly associated with Down's Syndrome, regardless of birth order (a mother having her 1st vs 3rd child at age 50 confers the same risk)
3.Maternal age is directly associated with birth order (the 2nd child, except in the case of twins, is born when the mother is older than she was for the birth of the 1st child)
4.Maternal age is not a consequence of birth order (having a 2nd child does not change the mother's age)
 

v9991

Trusted Information Resource
#4
will it be right to say that, balanced design need not be orthogonal, but orthogonal design necessary be balanced!.

and further, does the power of design change for orthogonal and non orthogonal design! (although, statistically the technique/formula might be different, but my understanding is that, it should not matter, i.e., because the power is function of signal-noise-runs)
 
Last edited:

Miner

Forum Moderator
Staff member
Admin
#5
will it be right to say that, balanced design need not be orthogonal, but orthogonal design necessary be balanced!.
No. It is possible to have an orthogonal design that was originally balanced (i.e. 5 repeats per experiment), but due to insufficient materials, one experiment only has 3 repeats. This creates an unbalanced orthogonal design.
and further, does the power of design change for orthogonal and non orthogonal design! (although, statistically the technique/formula might be different, but my understanding is that, it should not matter, i.e., because the power is function of signal-noise-runs)
Good question! I'll have to research that one. The biggest impact is in the increased complexity of the analysis and in the potential for confounding(aliasing).
 

Miner

Forum Moderator
Staff member
Admin
#6
I did research your question regarding power of orthogonal versus non-orthogonal designs.

If all things are equal (i.e., number of runs, number of replicates, number of factors, etc.) the two designs will have the same power.

However, orthogonal designs have a special property called the Projective Property. As terms are removed from the model, this property increases the resolution of the design until it becomes a full factorial. If additional terms are removed it becomes a replicated full factorial. This is called hidden replication.

A non-orthogonal design does not have these properties. Therefore, even though both types have the same power initially, as terms are removed an orthogonal design may increase in power while the non-orthogonal design will not.
 
Thread starter Similar threads Forum Replies Date
Richard Regalado What could go wrong with information: Ransomware statistics and facts (2018 to present) IEC 27001 - Information Security Management Systems (ISMS) 0
I Good resources for learning statistics (quality engineering related) Statistical Analysis Tools, Techniques and SPC 10
qualprod Statistics - Where to start in ISO 9001? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 5
Ninja Visitor Statistics - How to see a poster's stats easily? Elsmar Xenforo Forum Software Instructions and Help 3
D How do you use statistics in your job Statistical Analysis Tools, Techniques and SPC 6
J Excellent Resource on Statistics / Lean / Six Sigma Book, Video, Blog and Web Site Reviews and Recommendations 2
V Accelerated Learning and Simulations / Scenarios - Statistics Statistical Analysis Tools, Techniques and SPC 0
P Where to find conformance statistics for ISO 15189 Other Medical Device Regulations World-Wide 1
M Statistics Question - What percent falls above 105? Statistical Analysis Tools, Techniques and SPC 2
A Assessing a Preventive Maintenance Strategy - Reliability or Maintenance Statistics Reliability Analysis - Predictions, Testing and Standards 2
S Statistics and Sampling - Accounting for Failed Tests Statistical Analysis Tools, Techniques and SPC 10
T Metrics and Statistics for Improvement - Easy to implement Statistical Analysis Tools, Techniques and SPC 4
C Statistics equation to determine the number of samples in a lot Statistical Analysis Tools, Techniques and SPC 8
A ASQ CQE statistics training in Australia? Training - Internal, External, Online and Distance Learning 2
E Online Degrees and Graduate Certificates in Statistics Training - Internal, External, Online and Distance Learning 1
AnaMariaVR2 Guide to Microsoft Excel for Calculations, Statistics, and Plotting Data Excel .xls Spreadsheet Templates and Tools 11
C Basic Statistics Template .xls Document Control Systems, Procedures, Forms and Templates 0
S Statistics in Check/Replicate Analysis - HPLC Assay (Sample Duplicates) Statistical Analysis Tools, Techniques and SPC 1
R Student Question - Help needed with statistics questions Statistical Analysis Tools, Techniques and SPC 6
M The Statistical Meaning of "Muddy Middle" - Statistics Terminology Statistical Analysis Tools, Techniques and SPC 6
B Descriptive Statistics where the Data Type is Text? Using Minitab Software 4
R Industry Statistics on the benefits of Quality Management Systems ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 8
Jim Wynne xkcd on Statistics and Mainstream Media Funny Stuff - Jokes and Humour 2
A R using RExcel - Non GUI Statistics Program Statistical Analysis Tools, Techniques and SPC 1
Wes Bucey Job recovery? or "statistics don't lie, people do" Career and Occupation Discussions 37
G Statistics Question from Production and Operations Management Course Statistical Analysis Tools, Techniques and SPC 3
O Information on the extent of Statistics in the Six Sigma Green Belt Exam Professional Certifications and Degrees 9
J Gage R&R Module for R (Statistics Program) Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 4
T Survey or Statistics on the use of OHSAS 18001 Worldwide Occupational Health & Safety Management Standards 66
T Survey or Statistics on the use of the AS 9100 Standard Worldwide AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 2
H Elsmar Cove Statistics Found Online Coffee Break and Water Cooler Discussions 2
Chennaiite Quotable Quotes - Statistics Funny Stuff - Jokes and Humour 10
S Statistics of Gage R&R & Boundary Specifications Statistical Analysis Tools, Techniques and SPC 15
K Sample Statistics on HR (Human Resources) Key Processes ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 3
bio_subbu FDA released guidance on use of Bayesian statistics in Clinical Studies 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 0
O Weighting Problems (Statistics) - Weight distribution for a machine setup Capability, Accuracy and Stability - Processes, Machines, etc. 5
S "Human Error" statistics Quality Manager and Management Related Issues 3
S ASQ CSSBB Exam & Knowledge of Statistics Professional Certifications and Degrees 3
J Are there PPM statistics kept by Industry Manufacturing and Related Processes 4
Marc Battery-Life Statistics After Work and Weekend Discussion Topics 4
F Error in Minitab (no statistics can be calculated with these data) Using Minitab Software 10
O The Basis of %GRR (% Gage R&R) and other Statistics - Minitab Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 21
V Management Review Meeting - Statistics for Customer Complaints and Non Conformances ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 2
T The use of Statistics at a Medical Device Manufacturer US Food and Drug Administration (FDA) 16
Y Statistics and MiniTab - Example Problems Using Minitab Software 4
W Application of Statistics/ SPC tools in Oil Refineries Statistical Analysis Tools, Techniques and SPC 11
Q Specific requirements for Statistics in CQE exam Professional Certifications and Degrees 3
A Best certification combination with Masters in Statistics Professional Certifications and Degrees 2
BradM Use of Non-Parametric Statistics and Non-Normal Data Statistical Analysis Tools, Techniques and SPC 33
A Statistics Sampling Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1

Similar threads

Top Bottom