Here is a piece of detailed information about the experimental design used in the field of statistics. This also features some information on the three most widely accepted and most widely used designs.
Here is a piece of detailed information about the experimental design used in the field of statistics. This also features some information on the three most widely accepted and most widely used designs.
BUS 308 Week 5 Lecture 3 A Different View Effect Sizes .docxcurwenmichaela
BUS 308 Week 5 Lecture 3
A Different View: Effect Sizes
Expected Outcomes
After reading this lecture, the student should be familiar with:
1. What effect size measures exist for different statistical tests.
2. How to interpret an effect size measure.
3. How to calculate an effect size measure for different tests.
Overview
While confidence intervals can give us a sense of how much variation is in our decisions,
effect size measures help us understand the practical significance of our decision to reject the
null hypothesis. Not all statistically significant results are of the same importance in decision
making. A difference in means of 25 cents is more important with means around a dollar than
with means in the millions of dollars, yet with the right sample size both groups can have this
difference be statistically significant.
Effect size measures help us understand the practice importance of our decision to reject
the null hypothesis.
Excel has limited functions available for us to use on Effect Size measures. We generally
need to take the output from the other functions and generate our Effect Size values.
Effect Sizes
One issue many have with statistical significance is the influence of sample size on the
decision to reject the null hypothesis. If the average difference in preference for a soft drink was
found to be ½ of 1%; most of us would not expect this to be statistically significant. And,
indeed, with typical sample sizes (even up to 100), a statistical test is unlikely to find any
significant difference. However, if the sample size were much larger; for example, 100,000; we
would suddenly find this miniscule difference to be significant!
Statistical significance is not the same as practical significance. If for example, our
sample of 100,000 was 1% more in favor of an expensive product change, would it really be
worthwhile making the change? Regardless of how large the sample was, it does not seem
reasonable to base a business decision on such a small difference.
Enter the idea of Effect Size. The name is descriptive but at the same time not very
illuminating on what this measure does. We will get to specific measures shortly, but for now,
let’s look at how an Effect Size measure can help us understand our findings. First, the name:
Effect Size. What effect? What size? In very general terms, the effect we are monitoring is the
effect that occurs when we change one of the variables. For example, is there an effect on the
average compa-ratio when we change from male to female. Certainly, but not all that much, as
we found no significant difference between the average male and female compa-ratios. Is there
an effect when we change from male to female on the average salary? Definitely. And it is
much larger than what we observed on the compa-ratio means. We found a significant
difference in the average salary for males than females – around $14,000.
The Effect Siz.
Sensitivity Analysis, Optimal Design, Population Modeling.pptxAditiChauhan701637
Sensitivity analysis is the study of the unreliability related to output and input of mathematical model or numerical system which can be divided and allocated to various sources.
The process of outcome under possible speculation to find out the impact of a variable under sensitivity analysis can be useful for a range of purpose, consisting -
1. In the existence of unreliability, prefer testing of the results of a model or system.
2. Enhanced understanding of correlation between input and output variables in a model or system.
Sensitivity analysis methods:
There are many number of methods to study the sensitivity analysis, many of which have been developed to address one or more of the limitations discussed above. By the type sensitivity analysis measurement they are differentiate, be it based on variance decompositions, partial derivatives or elementary effects.
Chapter 8
Sampling
Sampling
Sampling involves decisions about who or what will be tested, observed, or interviewed in your study (Morse, 2007)
Key questions to address:
Who should and should not be included?
How many should be included?
Probability
Probability is the likelihood that an event or a condition will occur
You can express probability in terms of the chance the event will occur or in percentages
Levels of Significance
Levels of significance are the difference that will be accepted as too large to be attributed to chance
These levels are set by the researcher at the outset of a study
Probability Samples
Probability samples are formed to ensure that each subject has an equal chance of being included so an unbiased sample can be used
Probability Samples
A sampling design explains how the subjects are chosen and should include:
Number of subjects
How they will be assessed, screened, and selected
Inclusion and exclusion criteria
Probability Samples
Random selection is accomplished by having:
Identification of all possible participants
Every potential participant is given an equal chance of being selected
Probability Samples
Variations of random sampling include:
Stratified: randomly select from each stratum
Cluster: sample groups rather than individuals
Multistage: sample from multiple sets of clusters
Nonprobability Sampling
Reasons why researchers use nonprobability samples are:
Limited resources for developing an accurate sampling frame or purchase lists of potential subjects
Information needed to identify all potential subjects is not available
Nonprobability Sampling
Reasons why researchers use nonprobability samples are:
Limited number of subjects
Subjects are difficult to find or difficult to persuade to participate in study
Subjects do not complete study
Experimental mortality
Nonprobability Sampling
Types of nonprobability samples include:
Quota sampling: select a specified number of participants from each group
Convenience sampling: enroll those who are available
Snowball network or referral sampling: begin with known individuals and ask them to refer others who meet selection criteria
Tracking and Reporting
Sample Development
In order to improve the reporting of randomized controlled trials (RCTs), the Consolidated Standards of Reporting Trials (CONSORT) were developed
A flow diagram that can be used for tracking sample development
CONSORT Flow Diagram
Source: Altman, D.G., Schulz, K.F., Moher, D., Egger, M.. Davidoff, F., Elbourne, D., Gøtzsche, P.C., & Lang, T. (2001). The revised CONSORT statement for reporting randomized trials: Explanation and elaboration. Annuals of Internal Medicine; 134(8), 663-694.
Example of Flowchart
Source: Buchbinder, R., Osborne, R.H., Ebeling, P. R., Wark, J.D., Mitchell, P.M., Wriedt, C., Graves, S.D., Staples, M.P., & Murphy, B. (2009). A randomized trial of vertebroplasty for painful osteoporotic vertebral factures. The New England Journal of Medicine, 361 ...
BUS 308 Week 5 Lecture 3 A Different View Effect Sizes .docxcurwenmichaela
BUS 308 Week 5 Lecture 3
A Different View: Effect Sizes
Expected Outcomes
After reading this lecture, the student should be familiar with:
1. What effect size measures exist for different statistical tests.
2. How to interpret an effect size measure.
3. How to calculate an effect size measure for different tests.
Overview
While confidence intervals can give us a sense of how much variation is in our decisions,
effect size measures help us understand the practical significance of our decision to reject the
null hypothesis. Not all statistically significant results are of the same importance in decision
making. A difference in means of 25 cents is more important with means around a dollar than
with means in the millions of dollars, yet with the right sample size both groups can have this
difference be statistically significant.
Effect size measures help us understand the practice importance of our decision to reject
the null hypothesis.
Excel has limited functions available for us to use on Effect Size measures. We generally
need to take the output from the other functions and generate our Effect Size values.
Effect Sizes
One issue many have with statistical significance is the influence of sample size on the
decision to reject the null hypothesis. If the average difference in preference for a soft drink was
found to be ½ of 1%; most of us would not expect this to be statistically significant. And,
indeed, with typical sample sizes (even up to 100), a statistical test is unlikely to find any
significant difference. However, if the sample size were much larger; for example, 100,000; we
would suddenly find this miniscule difference to be significant!
Statistical significance is not the same as practical significance. If for example, our
sample of 100,000 was 1% more in favor of an expensive product change, would it really be
worthwhile making the change? Regardless of how large the sample was, it does not seem
reasonable to base a business decision on such a small difference.
Enter the idea of Effect Size. The name is descriptive but at the same time not very
illuminating on what this measure does. We will get to specific measures shortly, but for now,
let’s look at how an Effect Size measure can help us understand our findings. First, the name:
Effect Size. What effect? What size? In very general terms, the effect we are monitoring is the
effect that occurs when we change one of the variables. For example, is there an effect on the
average compa-ratio when we change from male to female. Certainly, but not all that much, as
we found no significant difference between the average male and female compa-ratios. Is there
an effect when we change from male to female on the average salary? Definitely. And it is
much larger than what we observed on the compa-ratio means. We found a significant
difference in the average salary for males than females – around $14,000.
The Effect Siz.
Sensitivity Analysis, Optimal Design, Population Modeling.pptxAditiChauhan701637
Sensitivity analysis is the study of the unreliability related to output and input of mathematical model or numerical system which can be divided and allocated to various sources.
The process of outcome under possible speculation to find out the impact of a variable under sensitivity analysis can be useful for a range of purpose, consisting -
1. In the existence of unreliability, prefer testing of the results of a model or system.
2. Enhanced understanding of correlation between input and output variables in a model or system.
Sensitivity analysis methods:
There are many number of methods to study the sensitivity analysis, many of which have been developed to address one or more of the limitations discussed above. By the type sensitivity analysis measurement they are differentiate, be it based on variance decompositions, partial derivatives or elementary effects.
Chapter 8
Sampling
Sampling
Sampling involves decisions about who or what will be tested, observed, or interviewed in your study (Morse, 2007)
Key questions to address:
Who should and should not be included?
How many should be included?
Probability
Probability is the likelihood that an event or a condition will occur
You can express probability in terms of the chance the event will occur or in percentages
Levels of Significance
Levels of significance are the difference that will be accepted as too large to be attributed to chance
These levels are set by the researcher at the outset of a study
Probability Samples
Probability samples are formed to ensure that each subject has an equal chance of being included so an unbiased sample can be used
Probability Samples
A sampling design explains how the subjects are chosen and should include:
Number of subjects
How they will be assessed, screened, and selected
Inclusion and exclusion criteria
Probability Samples
Random selection is accomplished by having:
Identification of all possible participants
Every potential participant is given an equal chance of being selected
Probability Samples
Variations of random sampling include:
Stratified: randomly select from each stratum
Cluster: sample groups rather than individuals
Multistage: sample from multiple sets of clusters
Nonprobability Sampling
Reasons why researchers use nonprobability samples are:
Limited resources for developing an accurate sampling frame or purchase lists of potential subjects
Information needed to identify all potential subjects is not available
Nonprobability Sampling
Reasons why researchers use nonprobability samples are:
Limited number of subjects
Subjects are difficult to find or difficult to persuade to participate in study
Subjects do not complete study
Experimental mortality
Nonprobability Sampling
Types of nonprobability samples include:
Quota sampling: select a specified number of participants from each group
Convenience sampling: enroll those who are available
Snowball network or referral sampling: begin with known individuals and ask them to refer others who meet selection criteria
Tracking and Reporting
Sample Development
In order to improve the reporting of randomized controlled trials (RCTs), the Consolidated Standards of Reporting Trials (CONSORT) were developed
A flow diagram that can be used for tracking sample development
CONSORT Flow Diagram
Source: Altman, D.G., Schulz, K.F., Moher, D., Egger, M.. Davidoff, F., Elbourne, D., Gøtzsche, P.C., & Lang, T. (2001). The revised CONSORT statement for reporting randomized trials: Explanation and elaboration. Annuals of Internal Medicine; 134(8), 663-694.
Example of Flowchart
Source: Buchbinder, R., Osborne, R.H., Ebeling, P. R., Wark, J.D., Mitchell, P.M., Wriedt, C., Graves, S.D., Staples, M.P., & Murphy, B. (2009). A randomized trial of vertebroplasty for painful osteoporotic vertebral factures. The New England Journal of Medicine, 361 ...
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
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Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Event Management System Vb Net Project Report.pdfKamal Acharya
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My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
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When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
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Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
2.
2
Problem statement, research
questions, purposes, benefits
Theory, assumptions, background
literature Variables and hypotheses
Operational definitions and measurement
Research design and methodology
Instrumentation, sampling
Data analysis
Conclusions, interpretations, recommendations
3.
A sample is “a smaller (but hopefully
representative) collection of units from a
population used to determine truths about that
population” (Field, 2005)
Why sample?
Resources (time, money) and workload
Gives results with known accuracy that can be
calculated mathematically
The sampling frame is the list from which the
potential respondents are drawn
Registrar’s office
Class rosters
Must assess sampling frame errors
5
4. What is your population of interest?
To whom do you want to generalize your
results?
All doctors
School children
Indians
Women aged 15-45 years
Other
Can you sample the entire population?
6
5.
3 factors that influence sample
representative- ness
Sampling procedure
Sample size
Participation (response)
When might you sample the entire population?
When your population is very small
When you have extensive resources
When you don’t expect a very high response
7
8. Probability (Random) Samples
Simple random sample
Systematic random sample
Stratified random sample
Multistage sample
Multiphase sample
Cluster sample
Non-Probability Samples
Convenience sample
Purposive sample
Quota 10
9.
9
The sampling process comprises several stages:
Defining the population of concern
Specifying a sampling frame, a set of items or
events possible to measure
Specifying a sampling method for selecting
items or events from the frame
Determining the sample size
Implementing the sampling plan
Sampling and data collecting
Reviewing the sampling process
10.
10
A population can be defined as
including all people or items with
the characteristic one wishes to
understand.
Because there is very rarely enough time or
money to gather information from everyone
or everything in a population, the goal
becomes finding a representative sample (or
subset) of that population.
11.
11
A probability sampling scheme is one in which every
unit in the population has a chance (greater than
zero) of being selected in the sample, and this
probability can be accurately determined.
. When every element in the population does have the
same probability of selection, this is known as an
'equal probability of selection' (EPS) design. Such
designs are also referred to as 'self-weighting'
because all sampled units are given the same weight.
13.
13
Any sampling method where some elements of population have no
chance of selection (these are sometimes referred to as 'out of
coverage'/'undercovered'), or where the probability of selection can't
be accurately determined. It involves the selection of elements based
on assumptions regarding the population of interest, which forms the
criteria for selection. Hence, because the selection of elements is
nonrandom, nonprobability sampling not allows the estimation of
sampling errors..
Example: We visit every household in a given street, and interview the
first person to answer the door. In any household with more than one
occupant, this is a nonprobability sample, because some people are
more likely to answer the door (e.g. an unemployed person who spends
most of their time at home is more likely to answer than an employed
housemate who might be at work when the interviewer calls) and it's
not practical to calculate these probabilities.
14. •
14
Nonprobability Sampling includes:
Accidental Sampling, Quota Sampling and
Purposive Sampling. In addition,
nonresponse effects may turn any
probability design into a nonprobability
design if the characteristics of
nonresponse are not well understood, since
nonresponse effectively modifies each
element's probability of being sampled.
15. •
Applicable when population is
small, homogeneous & readily
available
•
•
•
All subsets of the frame are given an equal
probability. Each element of the frame thus
has an equal probability of selection.
It provides for greatest number of possible
samples. This is done by assigning a number
to each unit in the sampling frame.
A table of random number or lottery system
is used to determine which units are to be
selected. 19
16.
16
Estimates are easy to calculate.
Simple random sampling is always
an EPS design, but not all EPS
designs are simple random
sampling.
Disadvantages
If sampling frame large, this method impracticable.
Minority subgroups of interest in population may not be
present in sample in sufficient numbers for study.
17. Optimization Concept:
The term Optimize is defined as to make perfect , effective , or as functional
as possible.
It is the process of finding the best way of using the existing resources while
taking in to the account of all the factors that influences decisions in any
experiment
Traditionally, optimization in pharmaceuticals refer to changing one variable
at a time, so to obtain solution of a problematic formulation.
Modern pharmaceutical optimization involves systematic design of
experiments (DoE) to improve formulation irregularities.
17
18. ⚫Optimization is used in pharmacy relative to
formulation and processing .
⚫It is the process of finding the best way of using the
existing resources while taking in to the account of all
the factors that influences decisions in any
experiment.
⚫Final product not only meets the requirements from
the bioavailability but also from the practical mass
production criteria. .
In development projects , one generally
experiments by a series of logical steps, carefully
controlling the variables & changing one at a
time, until a satisfactory system is obtained
18
19. ⚫Target processing parameters – ranges for each
excipients & processing factors .
Questions optimization requires:
• How we can make Formulation perfect ?
⚫What should be characteristics?
⚫ What should be the conditions?
20. Why is Optimization necessary?
OPTIMIZATION
Safety &
Reducing
error
Reproducib
ility
20
Save
Time
Primary objective may not be to optimize absolutely but to compromise
effectively & thereby produce the best formulation under a given set of
restrictions .
Reducing
cost
21. Formulation and Processing
Clinical Chemistry
Medicinal Chemistry
High Performance Liquid Chromatographic
Analysis
Formulation of Culture Medium in Virological
Studies.
Study of Pharmacokinetic Parameters.
APPLICATIONS:
21
22. Terms Used
•
22
•
o FACTOR: It is an assigned variable such as concentration , Temperature
etc..,
Quantitative: Numerical factor assigned to it
Ex- Concentration- 1%, 2%,3% etc.
Qualitative: Which are not numerical
Ex- Polymer grade, humidity condition etc.
o LEVELS: Levels of a factor are the values or designations assigned to
the factor.
o RESPONSE: It is an outcome of the experiment.
• It is the effect to evaluate.
Ex- Disintegration time.
23. Terms Used
o EFFECT: It is the change in response caused by
varying the levels
It gives the relationship between various factors
& levels.
o INTERACTION: It gives the overall effect of two
or more variables
Ex- Combined effect of lubricant and glidant on
hardness of the tablet
FACTOR LEVELS
Temperature 300 , 500
Concentration 1%, 2%
23
24. Advantages
o Yield the “Best Solution” within the domain of study.
o Require fewer experiments to achieve an optimum
formulation.
o Can trace and rectify problem in a remarkably easier
manner.
25.
26. Softwares for Optimization
⚫ Design Expert 7.1.3
⚫ SYSTAT Sigma Stat 3.11
⚫ CYTEL East 3.1
⚫ Minitab
⚫ Matrex
⚫ Omega
⚫ Compact 21-Apr-15 O
28. Problem Types
Unconstrained
• In unconstrained optimization problems there are no restrictions.
• For a given pharmaceutical system one might wish to make the hardest
tablet possible.
• The making of the hardest tablet is the unconstrained optimization problem.
Constrained
• The constrained problem involved in it, is to make the hardest tablet possible,
but it must disintegrate in less than 15 minutes.
28
29. Variables
• Independent variables : The independent variables are under the control of
the formulator. These might include the compression force or the die cavity
filling or the mixing time.
• Dependent variables : The dependent variables are the responses or the
characteristics that are developed due to the independent variables. The
more the variables that are present in the system the more the
complications that are involved in the optimization.
31. ⚫Once the relationship between the variable
and the response is known, it gives the
response surface as represented in the Fig. 1.
Surface is to be evaluated to get the
independent variables, X1 and X2, which
gave the response, Y.Any number of
variables can be considered, it is impossible
to represent graphically, but mathematically it
can be evaluated.
31
32.
33. Factorial Design (FD)
⚫ Factorial experiment is an experiment whose
design consist of two or more factor each with
different possible values or “levels”.
⚫FD technique introduced by “Fisher” in 1926.
⚫Factorial design applied in optimization
techniques.
⚫Factors : Factors can be “Quantitative” (numerical
number) or they are qualitative. They may be
names rather than numbers like Method 1, site B,
or present or absent .
34. ⚫Factorial design depends on independent
variables for development of new formulation .
⚫Factorial design also depends on Levels as well
as Coding
⚫There are three types of levels : 1) LOW
2)INTERMEDIATE 3) HIGH
⚫Simultaneously CODING takes place for Levels :
1) for LOW = (-1)
2)For intermediate = (0)
3) for HIGH =(+1)
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35. ⚫FD is for the evaluation of multiple factors
simultaneously.
⚫2 3 means 2 is level while 3 is factor .
⚫ Factorial Design is divided into two types
1. Full Factorial Design
2.Fractional factorial design
35
36. 1.Full Factorial
Design
⚫A design in which every setting of every factor
appears with setting of every other factor is full
factorial design.
⚫Simplest design to create, but extremely
inefficient.
⚫If there is k factor , each at Z level , a Full FD has
ZK
Number of runs (N)
N = y x Where, y = number of levels, x = number of
factors E.g.- 3 factors, 2 levels each, N = 23 = 8
runs
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38. TWO Levels Full FD :
⚫ 2 factors : X1 and X2 (Independent variables)
⚫ 2 levels : Low and High
⚫Coding : (-1) , (+1)
Three level Full FD :
In three level factorial design ,
• 3 factors: X1, X2 and X3
• 3 levels are use ,
1) low (-1)
2) intermediate (0)
3) high (+1)
38
39. FRACTIONAL FACTORIAL
DESIGN
⚫In Full FD , as a number of factor or level
increases , the number of experiment required
exceeds to unmanageable levels .
⚫In such cases , the number of experiments can
be reduced systemically and resulting design is
called as Fractional factorial design (FFD).
⚫Applied if no. of factor are more than 5 .
⚫Means “less than full”
⚫Levels combinations are chosen to provide
sufficient information to determine the factor
effect
⚫ More efficient
40. Types of Fractional Factorial Design
⚫Homogeneous fractional
⚫ Mixed level fractional
⚫ Plackett-Burman
Homogenous fractional
Useful when large number of factors must be
screened
Mixed level fractional
Useful when variety of factors need to be
evaluated for main effects and higher level
interactions can be assumed to be negligible.
40
41. Response surface methodology, or RSM
Collection of mathematical and statistical techniques
Useful for the modeling and analysis of problems
Response of interest is influenced by several variables
The objective is to optimize the response.
Temperature (x₁) and pressure (x₂) & yield (y)
The levels of temperature (x₁) and pressure (x₂) maximize the yield (y) of a process
The process yield is a function of the levels of temperature and pressure, say
y = f (x₁, x₂) + 𝜖
For example
Region of Interest
Region of Operability