The document describes different experimental design methods for engineering experiments, including completely randomized single-factor experiments, randomized complete block designs, and random effects models. It provides examples of setting up, analyzing, and interpreting each type of experiment. Key steps include forming a hypothesis, conducting the experiment, performing an analysis of variance to partition variability, determining significance of factors, and checking model assumptions through residual analysis.
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Branding and Product Design Portfolio - Pineapple Consultingameetmehta
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Some of the Recent works Done by Pineapple Consulting, India. Dealing into Communication, Interaction, Product & Packaging, and Visual Merchandising.
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Pineapple processing line - Equipment for Pineapple PlantGfK
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Basic Concepts of Standard Experimental Designs ( Statistics )Hasnat Israq
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This gives the basic description of Design and Analysis of Experiment . This is one of the important topic in Statistics and also for Mathematics and for Researchers - Scientists . Good Luck .
Biological screening of herbal drugs: Introduction and Need for
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
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Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
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Explore how micro-credentials are transforming Technical and Vocational Education and Training (TVET) with this comprehensive slide deck. Discover what micro-credentials are, their importance in TVET, the advantages they offer, and the insights from industry experts. Additionally, learn about the top software applications available for creating and managing micro-credentials. This presentation also includes valuable resources and a discussion on the future of these specialised certifications.
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2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
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Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
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How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
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Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
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Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
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In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
4. 13-1 Designing Engineering Experiments
Every experiment involves a sequence of activities:
1. Conjecture â the original hypothesis that motivates the
experiment.
2. Experiment â the test performed to investigate the
conjecture.
3. Analysis â the statistical analysis of the data from the
experiment.
4. Conclusion â what has been learned about the original
conjecture from the experiment. Often the experiment will
lead to a revised conjecture, and a new experiment, and so
forth.
7. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.1 An Example
⢠The levels of the factor are sometimes called
treatments.
⢠Each treatment has six observations or replicates.
⢠The runs are run in random order.
8. 13-2 The Completely Randomized Single-
Factor Experiment
Figure 13-1 (a) Box plots of hardwood concentration data.
(b) Display of the model in Equation 13-1 for the completely
randomized single-factor experiment
13-2.1 An Example
9. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.2 The Analysis of Variance
Suppose there are a different levels of a single factor
that we wish to compare. The levels are sometimes
called treatments.
10. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.2 The Analysis of Variance
We may describe the observations in Table 13-2 by
the linear statistical model:
The model could be written as
11. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.2 The Analysis of Variance
Fixed-effects Model
The treatment effects are usually defined as deviations
from the overall mean so that:
Also,
12. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.2 The Analysis of Variance
We wish to test the hypotheses:
The analysis of variance partitions the total variability
into two parts.
13. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.2 The Analysis of Variance
Definition
14. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.2 The Analysis of Variance
The ratio MSTreatments = SSTreatments/(a â 1) is called the
mean square for treatments.
15. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.2 The Analysis of Variance
The appropriate test statistic is
We would reject H0 if f0 > fÎą,a-1,a(n-1)
16. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.2 The Analysis of Variance
Definition
17. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.2 The Analysis of Variance
Analysis of Variance Table
22. 13-2 The Completely Randomized Single-
Factor Experiment
Definition
For 20% hardwood, the resulting confidence interval on the
mean is
23. 13-2 The Completely Randomized Single-
Factor Experiment
Definition
For the hardwood concentration example,
24. 13-2 The Completely Randomized Single-
Factor Experiment
An Unbalanced Experiment
25. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.3 Multiple Comparisons Following the ANOVA
The least significant difference (LSD) is
If the sample sizes are different in each treatment:
28. 13-2 The Completely Randomized Single-
Factor Experiment
Example 13-2
Figure 13-2 Results of Fisherâs LSD method in Example 13-2
29. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.5 Residual Analysis and Model Checking
30. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.5 Residual Analysis and Model Checking
Figure 13-4 Normal
probability plot of
residuals from the
hardwood concentration
experiment.
31. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.5 Residual Analysis and Model Checking
Figure 13-5 Plot of
residuals versus factor
levels (hardwood
concentration).
32. 13-2 The Completely Randomized Single-
Factor Experiment
13-2.5 Residual Analysis and Model Checking
Figure 13-6 Plot of
residuals versus iy
34. 13-3 The Random-Effects Model
13-3.2 ANOVA and Variance Components
The linear statistical model is
The variance of the response is
Where each term on the right hand side is called a
variance component.
35. 13-3 The Random-Effects Model
13-3.2 ANOVA and Variance Components
For a random-effects model, the appropriate
hypotheses to test are:
The ANOVA decomposition of total variability is
still valid:
36. 13-3 The Random-Effects Model
13-3.2 ANOVA and Variance Components
The expected values of the mean squares are
37. 13-3 The Random-Effects Model
13-3.2 ANOVA and Variance Components
The estimators of the variance components are
40. 13-3 The Random-Effects Model
Figure 13-8 The distribution of fabric strength. (a) Current
process, (b) improved process.
41. 13-4 Randomized Complete Block Designs
13-4.1 Design and Statistical Analyses
The randomized block design is an extension of the
paired t-test to situations where the factor of interest has
more than two levels.
Figure 13-9 A randomized complete block design.
42. 13-4 Randomized Complete Block Designs
13-4.1 Design and Statistical Analyses
For example, consider the situation of Example 10-9,
where two different methods were used to predict the
shear strength of steel plate girders. Say we use four
girders as the experimental units.
43. 13-4 Randomized Complete Block Designs
13-4.1 Design and Statistical Analyses
General procedure for a randomized complete block
design:
44. 13-4 Randomized Complete Block Designs
13-4.1 Design and Statistical Analyses
The appropriate linear statistical model:
We assume
⢠treatments and blocks are initially fixed effects
⢠blocks do not interact
â˘
45. 13-4 Randomized Complete Block Designs
13-4.1 Design and Statistical Analyses
We are interested in testing:
46. 13-4 Randomized Complete Block Designs
13-4.1 Design and Statistical Analyses
The mean squares are:
47. 13-4 Randomized Complete Block Designs
13-4.1 Design and Statistical Analyses
The expected values of these mean squares are:
55. 13-4 Randomized Complete Block Designs
13-4.2 Multiple Comparisons
Fisherâs Least Significant Difference for Example 13-5
Figure 13-10 Results of Fisherâs LSD method.
56. 13-4 Randomized Complete Block Designs
13-4.3 Residual Analysis and Model Checking
Figure 13-11 Normal
probability plot of
residuals from the
randomized complete
block design.