This gives the basic description of Analysis of Experiment . This is one of the most important topic in Statistics and also for Mathematics and for Researchers-Scientists .
Randomized complete block design - Dr. Manu Melwin Joy - School of Management...manumelwin
A completely randomized design (CRD) is one where the treatments are assigned completely at random so that each experimental unit has the same chance of receiving any one treatment.
For the CRD, any difference among experimental units receiving the same treatment is considered as experimental error.
Stability analysis and G*E interactions in plantsRachana Bagudam
Gene–environment interaction is when two different genotypes respond to environmental variation in different ways. Stability refers to the performance with respective to environmental factors overtime within given location. Selection for stability is not possible until a biometrical model with suitable parameters is available to provide criteria necessary to rank varieties / breeds for stability. Different models of stability are discussed.
Basic Concepts of Experimental Design & Standard Design ( Statistics )Hasnat Israq
This gives the basic description of Design and Analysis of Experiment . This is one of the most important topic in Statistics and also for Mathematics and for Researchers-Scientists
LATIN SQUARE DESIGN RESEARCH DESIGN: DESCRIPTION OF LATIN SQUARE DESIGN, PROCEDURE, TABLES, LINEAR MODEL, ANALYSIS, ADVANTAGES AND DISADVANTAGES OF LATIN SQUARE DESIGN
Ducan’s multiple range test - - Dr. Manu Melwin Joy - School of Management St...manumelwin
In 1955, Duncan devised a method to compare each treatment mean with every other treatment mean. The procedure is simple and powerful and has become very popular among researchers, especially in the plant science area.
Non Parametric Test
1. Wilcoxon Signed Rank Test: (WSRT)
In this test the difference in positive and negative value is taken into consideration without assigning any weightage to the magnitude of the differences as a result, the sign test is often used in practice.
The Wilcoxon Sign Rank test can be used to overcome this limitation.
2. Wilcoxon Rank Sum test: (WRST)
This is also called as Mann- Whitney U test.
WRST is used to compare two independent sample while WSRT compare two related or two dependent samples.
This test is applicable if the data are at least ordinal {i.e. the observation can be ordered}
3. MANN-WHITNEY U-TEST
It is a non-parametric method used to determine whether two independent samples have been drawn from populations with same distribution. This test is also known as U-Test.
This test enables us to test the null hypothesis that both population medians are equal(or that the two samples are drawn from a single population).
4. KRUSKAL WALLIS TEST
This test is employed when more then 2 population are involved where as Man Whitney test is used when there are 2 populations. The use of this test will enable us to determine weather independent samples have been drawn from the sample population (or) different populations have the same distribution.
5. FRIEDMAN TEST
It is a non-parametric test applied to a data i.e. at least ranked and it is in the form of a 2 way ANOVA design. This test which may be applied to ranked or Interval or Ratio type of data is used when more than 2 treatment, group are included in the experiment.
The test used to ascertain whether the difference between estimator & parameter or between two estimator are real or due to chance are called test of hypothesis.
T-test.
Chi-square (휒^2)- test.
F-Test.
ANOVA.
Randomized complete block design - Dr. Manu Melwin Joy - School of Management...manumelwin
A completely randomized design (CRD) is one where the treatments are assigned completely at random so that each experimental unit has the same chance of receiving any one treatment.
For the CRD, any difference among experimental units receiving the same treatment is considered as experimental error.
Stability analysis and G*E interactions in plantsRachana Bagudam
Gene–environment interaction is when two different genotypes respond to environmental variation in different ways. Stability refers to the performance with respective to environmental factors overtime within given location. Selection for stability is not possible until a biometrical model with suitable parameters is available to provide criteria necessary to rank varieties / breeds for stability. Different models of stability are discussed.
Basic Concepts of Experimental Design & Standard Design ( Statistics )Hasnat Israq
This gives the basic description of Design and Analysis of Experiment . This is one of the most important topic in Statistics and also for Mathematics and for Researchers-Scientists
LATIN SQUARE DESIGN RESEARCH DESIGN: DESCRIPTION OF LATIN SQUARE DESIGN, PROCEDURE, TABLES, LINEAR MODEL, ANALYSIS, ADVANTAGES AND DISADVANTAGES OF LATIN SQUARE DESIGN
Ducan’s multiple range test - - Dr. Manu Melwin Joy - School of Management St...manumelwin
In 1955, Duncan devised a method to compare each treatment mean with every other treatment mean. The procedure is simple and powerful and has become very popular among researchers, especially in the plant science area.
Non Parametric Test
1. Wilcoxon Signed Rank Test: (WSRT)
In this test the difference in positive and negative value is taken into consideration without assigning any weightage to the magnitude of the differences as a result, the sign test is often used in practice.
The Wilcoxon Sign Rank test can be used to overcome this limitation.
2. Wilcoxon Rank Sum test: (WRST)
This is also called as Mann- Whitney U test.
WRST is used to compare two independent sample while WSRT compare two related or two dependent samples.
This test is applicable if the data are at least ordinal {i.e. the observation can be ordered}
3. MANN-WHITNEY U-TEST
It is a non-parametric method used to determine whether two independent samples have been drawn from populations with same distribution. This test is also known as U-Test.
This test enables us to test the null hypothesis that both population medians are equal(or that the two samples are drawn from a single population).
4. KRUSKAL WALLIS TEST
This test is employed when more then 2 population are involved where as Man Whitney test is used when there are 2 populations. The use of this test will enable us to determine weather independent samples have been drawn from the sample population (or) different populations have the same distribution.
5. FRIEDMAN TEST
It is a non-parametric test applied to a data i.e. at least ranked and it is in the form of a 2 way ANOVA design. This test which may be applied to ranked or Interval or Ratio type of data is used when more than 2 treatment, group are included in the experiment.
The test used to ascertain whether the difference between estimator & parameter or between two estimator are real or due to chance are called test of hypothesis.
T-test.
Chi-square (휒^2)- test.
F-Test.
ANOVA.
A Mathematical Model for the Hormonal Responses During Neurally Mediated Sync...IJRES Journal
The purpose of this study is to find a Mathematical model for the participation of central serotonergic activity in neurocardiogenic syncope by comparing cortisol and prolactin plasma levels in patients with positive and negative tilt test by using Multivariate Normal Distribution.
A Mathematical Model for the Hormonal Responses During Neurally Mediated Sync...irjes
The purpose of this study is to find a Mathematical model for the participation of central serotonergic activity in neurocardiogenic syncope by comparing cortisol and prolactin plasma levels in patients with positive and negative tilt test by using Multivariate Normal Distribution.
Basic Concepts of Standard Experimental Designs ( Statistics )Hasnat Israq
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 .
Opendatabay - Open Data Marketplace.pptxOpendatabay
Opendatabay.com unlocks the power of data for everyone. Open Data Marketplace fosters a collaborative hub for data enthusiasts to explore, share, and contribute to a vast collection of datasets.
First ever open hub for data enthusiasts to collaborate and innovate. A platform to explore, share, and contribute to a vast collection of datasets. Through robust quality control and innovative technologies like blockchain verification, opendatabay ensures the authenticity and reliability of datasets, empowering users to make data-driven decisions with confidence. Leverage cutting-edge AI technologies to enhance the data exploration, analysis, and discovery experience.
From intelligent search and recommendations to automated data productisation and quotation, Opendatabay AI-driven features streamline the data workflow. Finding the data you need shouldn't be a complex. Opendatabay simplifies the data acquisition process with an intuitive interface and robust search tools. Effortlessly explore, discover, and access the data you need, allowing you to focus on extracting valuable insights. Opendatabay breaks new ground with a dedicated, AI-generated, synthetic datasets.
Leverage these privacy-preserving datasets for training and testing AI models without compromising sensitive information. Opendatabay prioritizes transparency by providing detailed metadata, provenance information, and usage guidelines for each dataset, ensuring users have a comprehensive understanding of the data they're working with. By leveraging a powerful combination of distributed ledger technology and rigorous third-party audits Opendatabay ensures the authenticity and reliability of every dataset. Security is at the core of Opendatabay. Marketplace implements stringent security measures, including encryption, access controls, and regular vulnerability assessments, to safeguard your data and protect your privacy.
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Data and AI
Discussion on Vector Databases, Unstructured Data and AI
https://www.meetup.com/unstructured-data-meetup-new-york/
This meetup is for people working in unstructured data. Speakers will come present about related topics such as vector databases, LLMs, and managing data at scale. The intended audience of this group includes roles like machine learning engineers, data scientists, data engineers, software engineers, and PMs.This meetup was formerly Milvus Meetup, and is sponsored by Zilliz maintainers of Milvus.
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Data and AI
Round table discussion of vector databases, unstructured data, ai, big data, real-time, robots and Milvus.
A lively discussion with NJ Gen AI Meetup Lead, Prasad and Procure.FYI's Co-Found
3. Split plot design are needed when the levels of some factors
more difficult to change during the experiment than those of
others .SPD is a mixture of hard to change and easy to
change factors . The hard to change factors are implemented
first , followed by easier to change factors.
Real life application of SPD:
SPD are commonly seen in agriculture designs and industries
they can also be used across a wide variety of disciplines.
EXAMPLE:
Basically a split plot design consists of two experiments with
different experimental units of different “size”. Experimental
units, whereas other factors can be easily applied to
“smaller” plots of land.
4. Advantage:
1. Estimates of subplot treatments and its interaction with
whole plot treatments are obtained in SPD than in RBD.
2.Two or more factors needing relatively large and small units
can be combined in the same experiment of SPD.
Disadvantage:
1.Main plot treatments are measured with less precision in SPD
than in comparable RBD.
2.Analysis of data is relatively complicated in SPD.
5. The model is,
𝑦𝑖𝑗𝑘 = 𝜇 + ρ𝑖 + α𝑗 + δ𝑖𝑗 + β 𝑘 + αβ 𝑗𝑘 + Ԑ𝑖𝑗𝑘 𝑖 = 1,2 … 𝑟
𝑗 = 1,2 … 𝑝
𝑘 = 1,2 … . 𝑞
here,
𝜇=General mean.
α𝑗=Effect of 𝑗𝑡ℎ whole plot treatment.
δ𝑖𝑗=Whole plot error.
β 𝑘=Effect of 𝑘 𝑡ℎ
subplot treatment.
αβ 𝑗𝑘=interaction between 𝑗 𝑡ℎ
whole plot treatment and 𝑘 𝑡ℎ
subplot treatment
Ԑ𝑖𝑗𝑘 = Random error term occurring in the split plot.
6. Analysis Of Covariance is the process of analysis of variance
on the observations of response variable y after adjusting for
the effects of uncontrolled concomitant variables.
Example: In animal feeding experiment , the
initial weight of animals under
investigation can be used as covariate.
1.Increased precision and
error control.
2.Estimation of missing
values.
Uses of ANCOVA:
7. ANOVA ANCOVA
1.Both linear and non linear
models are used in ANOVA.
1.Only linear model is used in
ANCOVA.
2.ANOVA includes only categorical
variables.
2.ANCOVA includes categorical
and interval variable.
3.Covariate is ignored in ANOVA. 3.Covariate is considered in
ANCOVA.
4.ANOVA attributes Between Group
variation to treatment.
4.ANCOVA divides Between Group
variation into treatment and
covariate.
Analysis of variance is the process of partitioning and decomposing
total variation in data into various independent components.
Difference between ANOVA and ANCOVA:
8. The variable representing yield is called main variable
denoted by y the additional variables representing
heterogeneity of experimental units are called concomitant
variables.
Example:
In an experiment involving various teaching methods,
the results of students can be adjusted for I.Q. before the
experiment starts.
9. The Model is-
𝑦𝑖𝑗 = 𝜇 + τ𝑖 + 𝛽 𝑥𝑖𝑗 − 𝒙 + Ԑ𝑖𝑗 𝑖 = 1,2, … , 𝑘
𝑗 = 1,2, … , 𝑟𝑖
Where ,
𝑦𝑖𝑗=𝑖 𝑡ℎ
observation on response variable under 𝑖 𝑡ℎ
treatment.
𝑥𝑖𝑗= value of the covariate x corresponding to 𝑦𝑖𝑗.
𝜇=Grand mean of response variable y
τ𝑖= 𝑖 𝑡ℎ
treatment effect after allowance for the relationship of y to x
β=regression coefficient of y on x
x̅ =grand mean of x
Ԑ𝑖𝑗 = Random error component in the (𝑖. 𝑗) 𝑡ℎ
unit
1.Covariate 𝑋 is a fixed non random variable whose values are measured
without error and is not affected by the treatments.
2.Regression effect is independent of treatment.
Assumptions of Analysis of Covariance in CRD:
11. For test of 𝐻0:β=0.
Test statistic is , F=(𝑏. 𝐸 𝑥𝑦/1)/(𝑆 𝐸/n-k-1)∼𝐹1,𝑛−𝑘−1under Hₒ.
CR is 𝐹𝑐𝑎𝑙>=𝐹𝑡𝑎𝑏;1,𝑛−𝑘−1.
If this hypothesis is accepted then concomitant 𝑥 is rejected and
need to be carried out. Then we test the hypothesis,
𝐻0=adjusted treatment means are equal.
𝐻1=At least two adjusted treatment means are unequal.
Test statistics is F=Adjusted treatment M.S/Residual SS in the
error.
=((𝑆 𝑇+𝐸 −𝑆 𝐸)/𝑘 − 1)/(𝑆 𝐸/𝑛 − 𝑘 − 1)
CR is given by 𝐹𝐶𝑎𝑙>𝐹𝑡𝑎𝑏.
12. The equation is,
𝑦𝑖𝑗 = 𝜇 + α𝑖 + τ𝑗 + 𝛽 𝑥𝑖𝑗 − 𝒙 + Ԑ𝑖𝑗 𝑖 = 1,2, … , 𝑟
𝑗 = 1,2, … , 𝑘
here,
𝑦𝑖𝑗=Observation on response variable 𝑦 in the 𝑖 𝑡ℎ
block under 𝑗 𝑡ℎ
treatment.
𝑥𝑖𝑗 = Corresponding observation on covariate 𝑥.
𝜇=Overall mean of response variable 𝑦.
α𝑖=Effect of 𝑖 𝑡ℎ
block after allowing for regression effect.
τ𝑗= Effect of 𝑗 𝑡ℎ
treatment after adjusting for regression effect.
𝛽=regression coefficient of 𝑦 on 𝑥 .
𝒙 ̅ =grand mean of covariate 𝑥.
Ԑ𝑖𝑗 = Random error term.
1.Covariate x is a fixed non random variable whose values are measured without
error.
2.Concomitant variable x is not influenced by the treatment.
3.Block effect, treatment effects and regression effects are additive.
Assumption of Analysis of Covariance in RBD:
14. For test of 𝐻ₒ: 𝛽=0.
Test statistic is , F=[{(𝐸 𝑥𝑦)²/𝐸 𝑥𝑥}/1]/[𝑆 𝐸/{(𝑟 − 1)(𝑘 − 1) − 1}] under 𝐻ₒ.
CR is 𝐹𝑐𝑎𝑙>=𝐹𝑡𝑎𝑏;1, (𝑟 − 1)(𝑘 − 1) − 1.
If this hypothesis is accepted then concomitant 𝑥 is rejected and need
to be carried out . Then we test the hypothesis,
𝐻0=adjusted treatment means are equal.
𝐻1=At least two adjusted treatment means are unequal.
Test statistics is F=Adjusted treatment M.S/residual SS in the error.
=[(𝑆 𝑇+𝐸-𝑆 𝐸)/(𝑘 − 1)]/[𝑆 𝐸/(𝑟 − 1)(𝑘 − 1) − 1]
CR is given by 𝐹𝑐𝑎𝑙>𝐹𝑡𝑎𝑏.
15. The model is,
𝑦𝑖𝑗𝑘= 𝜇 + α𝑖 + γ 𝑗 + τ 𝑘 + 𝛽(𝑥𝑖𝑗𝑘 − 𝒙 ̅ ) + Ԑ𝑖𝑗𝑘
here,
𝑦𝑖𝑗𝑘=Observation on response variable 𝑦 in the 𝑖 𝑡ℎ
row, 𝑗 𝑡ℎ
column under
𝑘 𝑡ℎ
treatment.
𝜇=General mean of response variable 𝑦.
α𝑖=Fixed effect of 𝑖 𝑡ℎ
row after adjusting for the effect of covariate 𝑥.
γ 𝑗= Fixed effect of 𝑗 𝑡ℎ
column after adjusting for the effect of covariate 𝑥.
τ 𝑘=Fixed effect of 𝑘 𝑡ℎ
treatment after adjusting for the effect of covariate 𝑥.
β=regression coefficient of 𝑦 on 𝑥 .
Ԑ𝑖𝑗𝑘= Random error component.
1.Covariate 𝑥 is not affected by the treatment.
2.Regression of y on 𝑋 is linear.
3.Regression coefficient for various classes are identical.
Assumption of Analysis of Covariance in LSD:
17. For test of 𝐻ₒ: 𝛽=0.
Test statistic is,F=[{(𝐸 𝑥𝑥)²/𝐸 𝑥𝑥}/1]/[𝑆 𝐸/{(𝑟 − 1)(𝑟 − 2) − 1}] under 𝐻ₒ.
CR is 𝐹𝑐𝑎𝑙>=𝐹𝑡𝑎𝑏;1, (𝑟 − 1)(𝑟 − 2) − 1.
,.If this hypothesis is accepted then concomitant 𝑥 is rejected and
need to be carried out . Then we test the hypothesis,
𝐻ₒ=adjusted treatment means are equal.
𝐻1=At least two adjusted treatment means are unequal.
Test statistics is F=Adjusted treatment M.S/residual SS in the
error.
=[(𝑆 𝑇+𝐸-𝑆 𝐸)/(𝑟 − 1)]/[𝑆 𝐸/(𝑟 − 1)(𝑟 − 2) − 1]
CR is given by 𝐹𝑐𝑎𝑙>𝐹𝑡𝑎𝑏.
18. Response Surface:
The surface represented by E(y)=f(𝑥1,𝑥2,…,𝑥 𝑛) is called Response
Surface.
Factor Space:
The set of points (𝑥1,𝑥2,…,𝑥 𝑛) at which observation can be made on
response is called factor space.
Response Surface Design:
The design for fitting response surface are termed as response
surface designs.
RSM is a collection of mathematical and statistical technique that are
useful for modeling and analysis of problems in which a response of
interest is influenced by several variable and the objective is to optimize
the response.
Response Surface Methodology(RSM):
19. Assumption:
First order model,
y=βₒ+β₁X₁+β₂X₂+…+βκXκ+Ԑ
Here,Ԑ is random error term.
Second Order model,
y=βₒ+β₁X₁²+β₂X₂+…+βκXκ+Ԑ
Here, independent variable’s power 2.And so on higher order models.
Models Of Response Surface Design:
1.Response variable y is a random variable.
2.Ԑ𝑗 is a random error component in the 𝑗 𝑡ℎ
observation.