Designs of Experiment Terminology (2023)

by

Planning an experiment to obtain appropriate data and drawing inferences from the data concerning any problem under investigation is known as the design and analysis of the experiment or simply the designs of experiment (DOE).

Important Designs of Experiment Terminology are:

EXPERIMENT: An experiment deliberately imposes a treatment on a group of objects or subjects in the interest of observing the response.

EXPERIMENTAL UNIT: The experimental unit is the basic entity or unit on which the experiment is performed. It is an object to which the treatment is applied and in which the variable under investigation is measured and analyzed. For example, the experimental unit may be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied.

Designs of Experiment

Identify the Experimental Units

  • A teacher practices the different teaching methods on different groups in her class to see which yields the best results.
  • A doctor treats a patient with a skin condition with different creams to see which is most effective.

The experimental unit is the physical entity or subject exposed to the treatment independently of other units. In other words, it is the basic unit on which the experiment is performed (smallest division of experimental material).

TREATMENTS: In experiments, a treatment is something that researchers administer to experimental units. For example, a corn field is divided into four, each part is ‘treated’ with a different fertilizer to see which produces the most corn.

Treatment is an experimental condition whose effect is to be measured and compared. For example, animal diets, temperature, soil types, and brands of tires.

FACTOR: A factor of an experiment is a controlled independent variable; a variable whose levels are set by the experimenter. A factor is a general type or category of treatments. Different treatments constitute different levels of a factor.

Designs of Experiment

EXPERIMENTAL ERROR

It describes the variation among identically and independently treated experimental units. In the designs of experiments, various origins of experimental error include:

  • The natural variation among the experimental units.
  • Inability to reproduce the treatment conditions exactly from one unit to another.
  • Interaction of treatments and experimental units.
  • Any other extraneous factors that influence the measured characteristics.

There are two types of errors:

  1. Systematic Errors
    Systematic Errors are caused by a consistent bias in one direction, consistently pushing your results away from the true value. Systematic errors can be caused by a variety of factors, such as a faulty instrument, an incorrect calibration, or an error in the experimental design. Systematic errors will cause data points to shift all in the same direction, away from the true value.
  2. Random Error
    The random error is caused by small and unpredictable variations that occur in every experiment. Random errors can come from a variety of sources, such as slight differences in how a measurement is made, or fluctuations in environmental conditions. Random errors tend to cause data points to scatter randomly around the true value.

The experimental error can be controlled by

  • Blocking
  • Proper plot technique
  • Data Analysis

EXPERIMENTAL DESIGN

An experimental design is a plan to collect the data relevant to the problem under investigation. In such a way as to provide a basis for valid and objective inferences about the stated problem.

The plan usually consists of the selection of the treatments, specifications of the experimental layouts, allocation of the treatments, and collection of observations for analysis.

Hence designs of Experiments are simply a sequence of steps taken ahead of time to ensure that the appropriate data will be obtained in a way that permits an objective analysis leading to a valid analysis concerning the problem.

R Language Frequently Asked Questions

Online MCQs Tests Website with Answers

Learn more about Designs of Experiments

Important Online Multivariate MCQ

by

Multivariate Analysis term includes all statistics for more than two simultaneously analyzed variables. The post contains a Multivariate Quiz.

Online Multivariate MCQs

MCQs Cluster Analysis 6Multivariate Quiz 5Multivariate MCQs 4
Multivariate MCQs 3Multivariate MCQs 2Multivariate MCQs 1

Multivariate analysis is based upon an underlying probability model known as the Multivariate Normal Distribution (MND). The objective of scientific investigations to which multivariate methods most naturally lend themselves includes. Multivariate analysis is a powerful technique for analyzing data that goes beyond the limitations of simpler, single-variable methods.

Online Multivariate MCQ
  • Data reduction or structural simplification
    The phenomenon being studied is represented as simply as possible without sacrificing valuable information. It is hoped that this will make interpretation easier.
  • Sorting and Grouping
    Graphs of similar objects or variables are created, based on measured characteristics. Alternatively, rules for classifying objects into well-defined groups may be required.
  • Investigation of the dependence among variables
    The nature of the relationships among variables is of interest. Are all the variables mutually independent or are one or more variables depend on the observation of the other variables?
  • Prediction
    Relationships between variables must be determined for predicting the values of one or more variables based on observation of the other variables.
  • Hypothesis Construction and testing
    Specific statistical hypotheses, formulated in terms of the parameter of the multivariate population, are tested. This may be done to validate assumptions or to reinforce prior convictions.
https://itfeature.com

Multivariate analysis provides a comprehensive and robust way to analyze the data. It leads to better decision-making across various fields. Multivariate analysis is a vital tool for researchers and data scientists seeking to extract deeper insights from complex datasets.

Online MCQs Test With Answers Website

R Language Programming

Easy Multivariate Analysis MCQs – 1

by

Multivariate Analysis term includes all statistics for more than two simultaneously analyzed variables. The post contains Multivariate Analysis MCQs. Let us start with the Online Multivariate Analysis MCQs test.

Multiple Choice Questions about Multivariate and Multivariate Analysis

1. If $A$ is a square matrix, then $det(A – \lambda)=0$ is known as

 
 
 
 

2. The pdf of multivariate normal distribution exists only when $\sigma$ is

 
 
 
 

3. Let $x$ be distributed as $N_p(\mu, \sigma)$ with $|\sigma | > 0$, then $(x-\mu)’ \sigma^{-1} (x-\mu)$ is distributed as:

 
 
 
 

4. The eigenvalue is the factor by which the Eigenvector is

 
 
 
 

5. Eigenvalues and Eigenvectors are only for the matrices

 
 
 
 

6. Let $x_1, x_2, \cdots, x_n$ be a random sample of size $n$ from a p-variate normal distribution with mean $\mu$ and covariance matrix $\sigma$, then

 
 
 
 

7. Let $A$ be a $k\times k$ symmetric matrix and $X$ be a $k\times 1$ vector. Then

 
 
 
 

8. The set of all linear combination of $X_1, X_2, \cdots, X_k$ is called

 
 
 
 

9. Eigenvalue is often introduced in the context of

 
 
 
 

10. A matrix in which the number of rows and columns are equal is called

 
 
 
 

11. If $A$ is a square matrix of order ($m \times m$) then the sum of diagonal elements is called

 
 
 
 

12. A square matrix $A$ and its transpose have the Eigenvalues

 
 
 
 

13. A matrix $A_{m\times n}$ is defined to be orthogonal if

 
 
 
 

14. How many Eigenvalues does a 2 by 2 matrix have?

 
 
 
 

15. Let $x_1, x_2, \cdots, x_n$ be a random sample from a joint distribution with mean vector $\mu$ and covariance $\sigma$. Then $\overline{x}$ is an unbiased estimator of $\mu$ and its covariance matrix is:

 
 
 
 

16. The rank of a matrix $\begin{bmatrix}1 & 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 1 & 2 \\ 1 & 1 & 0 & 0 & 2 \\ 0 & 1 & 1 & 1 & 3\end{bmatrix}$ is

 
 
 
 

17. If $A$ and $B$ are two $n \times n$ matrices, which of the following is not always true?

 
 
 
 

18. What are Eigenvalues?

 
 
 
 

19. Length of vector $\underline{X}$ is calculated as

 
 
 
 

20. A set of vectors $X_1, X_2, \cdots, X_n$ are linearly independent if

 
 
 
 

Multivariate Analysis MCQs

Multivariate Analysis MCQs

  • If $A$ and $B$ are two $n \times n$ matrices, which of the following is not always true?
  • Let $x_1, x_2, \cdots, x_n$ be a random sample from a joint distribution with mean vector $\mu$ and covariance $\sigma$. Then $\overline{x}$ is an unbiased estimator of $\mu$ and its covariance matrix is:
  • Let $x$ be distributed as $N_p(\mu, \sigma)$ with $|\sigma | > 0$, then $(x-\mu)’ \sigma^{-1} (x-\mu)$ is distributed as:
  • Let $A$ be a $k\times k$ symmetric matrix and $X$ be a $k\times 1$ vector. Then
  • Let $x_1, x_2, \cdots, x_n$ be a random sample of size $n$ from a p-variate normal distribution with mean $\mu$ and covariance matrix $\sigma$, then
  • The set of all linear combination of $X_1, X_2, \cdots, X_k$ is called
  • A set of vectors $X_1, X_2, \cdots, X_n$ are linearly independent if
  • Length of vector $\underline{X}$ is calculated as
  • A matrix in which the number of rows and columns are equal is called
  • A matrix $A_{m\times n}$ is defined to be orthogonal if
  • If $A$ is a square matrix of order ($m \times m$) then the sum of diagonal elements is called
  • The rank of a matrix $\begin{bmatrix}1 & 0 & 1 & 0 & 2 \ 0 & 0 & 1 & 1 & 2 \ 1 & 1 & 0 & 0 & 2 \ 0 & 1 & 1 & 1 & 3\end{bmatrix}$ is
  • If $A$ is a square matrix, then $det(A – \lambda)=0$ is known as
  • The pdf of multivariate normal distribution exists only when $\sigma$ is
  • The eigenvalue is the factor by which the Eigenvector is
  • Eigenvalue is often introduced in the context of
  • How many Eigenvalues does a 2 by 2 matrix have?
  • What are Eigenvalues?
  • Eigenvalues and Eigenvectors are only for the matrices
  • A square matrix $A$ and its transpose have the Eigenvalues

R Frequently Asked Questions and Interview Questions