## Multivariate Quiz 3

Multivariate Analysis term includes all statistics for more than two variables analyzed simultaneously. The post is about Multivariate Quiz. Let us start with the Online Multivariate Quiz with Answers.

The quiz contains Multivariate related multiple choice questions with answers.

1. It can be defined as the correlation coefficient between the variable and the factor.

2. The most common method of rotation is called

3. Factor analysis is a:

4. To determine which variables relate to which factors, a researcher would use:

5. An empirically based hypothetical variable consisting of items that are strongly associated with each other and upon which individuals differ is known as what?

6. Variables are not always measured in the same units so using the correlation matrix in factor analysis is equivalent to standardizing the data so that they are comparable.

7. Rotation usually involves _____ high correlations and _____ low ones.

8. In factor analysis, there are two common rotation techniques:

9. Some steps for Conducting factor analysis are:

10. Determination of a number of factors:

11. If a researcher wanted to determine which variables were associated with which factors they would look at:

12. ——— was known for his seminal work on testing and measuring “Human Intelligence” by using “Factor Analysis” during World War I.

13. If a researcher uses factor rotation in a factor analysis, what will be the likely outcome:

14. A technique for the study of interrelationships among variables, usually for data reduction and the discovery of underlying constructors or latent dimensions is known as:

15. Principle component analysis is one of the methods of:

16. Assumptions to be fulfilled for running factor analysis:

17. Look at the steps below. Is there anything else a researcher could d0?

The correlation matrix is produced → factors are then retained based on eigenvalues over 1 and theoretical considerations → then the rotated factor loadings (whatever their loading) are used to name factors.

18. In factor analysis ———— is the amount of variance explained by a factor.

19. You cannot retain factors that have an eigenvalue value of less than 1 as only factors with an eigenvalue over 1 should be kept.

20. Identify the correct statement from the following

An application of different statistical methods applied to the economic data used to find empirical relationships between economic data is called Econometrics. In other words, Econometrics is “the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference”.

#### Multivariate Quiz Questions

• An empirically based hypothetical variable consisting of items that are strongly associated with each other and upon which individuals differ is known as what?
• Identify the correct statement from the following
• Look at the steps below. Is there anything else a researcher could do? The correlation matrix is produced → factors are then retained based on eigenvalues over 1 and theoretical considerations → then the rotated factor loadings (whatever their loading) are used to name factors.
• Rotation usually involves __________ high correlations and _________ low ones.
• The most common method of rotation is called
• Variables are not always measured in the same units so using the correlation matrix in factor analysis is equivalent to standardizing the data so that they are comparable.
• You cannot retain factors that have an eigenvalue value of less than 1 as only factors with an eigenvalue over 1 should be kept.
• ——— was known for his seminal work on testing and measuring “Human Intelligence” by using “Factor Analysis” during World War I.
• Factor analysis is a:
• Assumptions to be fulfilled for running factor analysis:
• Principle component analysis is one of the methods of:
• Determination of a number of factors:
• In factor analysis ———— is the amount of variance explained by a factor.
• In factor analysis, there are two common rotation techniques:
• It can be defined as the correlation coefficient between the variable and the factor.
• Some steps for Conducting factor analysis are:
• A technique for the study of interrelationships among variables, usually for data reduction and the discovery of underlying constructors or latent dimensions is known as:
• To determine which variables relate to which factors, a researcher would use:
• If a researcher wanted to determine which variables were associated with which factors they would look at:
• If a researcher uses factor rotation in a factor analysis, what will be the likely outcome:
• Partial Least Squares (PLS) Regression is an example of multivariate analysis (MVA).
• Multivariate Multiple Regression is a method of modeling multiple dependent variables, with a single set of predictor variables.
• Testing text and visual elements on a webpage together.
• An example of multivariate data is Vital signs recorded for a newborn baby: This includes multiple variables such as heart rate, respiratory rate, blood pressure, and temperature.

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## Design of Experiments Objective Questions 3

MCQs about the Design of Experiments Objective Questions for the preparation of PPSC, FPSC Lecturer Statistics job, and BS, M.Phil, Ph.D. Statistics Degree Programs. Let us start with the Design of Experiments Objective Questions quiz.

Please go to Design of Experiments Objective Questions 3 to view the test

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.

An experiment deliberately imposes a treatment on a group of objects or subjects to observe the response. 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 the variable under investigation is measured and analyzed.

Single-Factor Design: In a single-factor experiment only a single factor varies while all others are kept constant. The CRD, RCBD, and LSD are examples of single-factor designs.

Multi-Factor Design: Multi-factor designs are also known as factorial experiments. When several factors are investigated simultaneously in a single experiment, such experiments are known as factorial experiments.

Systematic Designs: In systematic designs treatments are applied to the experimental units by some systematic pattern, i.e., by the choice of the experimenter. For example, the experimenter wishes to test three treatments and he decides to have four repetitions of each treatment.

Randomized Designs: In randomized designs, as the treatments are applied randomly, therefore the conclusions drawn are supported by statistical tests. In this way, inferences are applicable in a wider range and the random process minimizes the systematic error. The analysis of variance techniques is also suitable for randomized designs only.

The purpose of the Design of Experiments is:

• Get maximum information for minimum expenditure in the minimum possible time.
• Helps to reduce the experimental error.
• To ignore spurious effects, if any.
• To evaluate and examine the outcomes critically and logically.

### Design of Experiments Objective Questions

• Which one provides the estimate of experimental error in the design of the experiment
• There are – – – – – – – – basic principles of sound statistical design.
• If the experimental material is not homogenous and there is one source of variation in the experiment then we use
• An experiment is performed in CRD with 3 replications to compare four treatments. Then, the total experimental units will be
• An experiment is performed in CRD with 3 replications to compare four treatments, then what will be the degrees of freedom for error?
• An experiment is performed in CRE with 3 replications to compare four treatments. The treatment sum of squares = 8. If the error sum of square = 12 then what will be the total sum of square?
• An experiment is performed in CRD with 3 replications to compare four treatments. The treatment sum of squares = 9. If the error sum of squares = 12 then what will be the mean sum of squares for treatment?
• What will be the F ratio if an experiment is performed in CRD with 3 replications to compare four treatments? The treatment mean sum of squares = 96, error mean sum of squares = 12.
• Analysis of variance is a statistical method of comparing the – – – – – – – – of several populations.
• To test the hypothesis about one population variance, the test statistic will be – – – – – – -.
• Under one-way variability in environmental conditions, the appropriate design for experimenting will be – – – – – – – -.
• The scientific method for the construction of a statistical layout plan for an experiment is – – – – – -?
• Manova stands for
• For a $7 \times 7$ Latin Square Design, there will be ___________ observations.
• The experiment is performed on
• The random process of assigning treatments to the experimental units can be done by
• In systematic designs, the treatments are applied to the experimental units by some
• Planning an experiment to obtain appropriate data and drawing inferences out of the data for any problem under investigation is known as ___________
• One of the purposes of experimental design is to
• What will be a degree of freedom (df) for column-wise blocking in $5 \times 5$ Latin Square Design?

## Classification of Randomized Designs

The post is about the classification of Randomized Designs.

### Randomized Designs

In randomized designs, the treatments are applied randomly, therefore the conclusions drawn are supported by statistical tests. The classification of randomized designs for single-factor are:

Example: A market gardener wants to test three types of peas, $A$, $B$, and $C$, on his land. He divides a square plot into nine equal squares, three to be planted with each type of pea. The problem which he then faces is which square to plant with which type.

One method is a Completely Randomized Design (CRD) which might,

This would be all right if all the plots were equally desirable. If however, there were prevailing north wind so that the northernmost plots were exposed, he might decide to use, a Randomize Complete Block Design (RCBD).

Randomized Complete Block Design, where each of the types $A$, $B$, and $C$ is planted once in each west-east block.

If the gardener also felt that the soil to the east was rather better than that to the west, he would use, a Latin Square Design (LSD).

A Latin Square design, where each type of pea is planted once in each row (west-east), and once in each column (north-south).

For Randomized Designs, Note that

• Completely Randomized Desing (CRD) is a statistical experimental design where the treatments are assigned completely at random so that each treatment unit has the same chance (equal chance) of receiving any one treatment.
• In CRD any difference among experimental units receiving the same treatment is considered as an experimental error.
• CRD is applicable only when the experimental material is homogeneous (eg., homogeneous soil conditions in the field).
• Since soil is heterogeneous in the field, the CRD is not a preferable method in field experiments. Therefore, CRD generally applies to the lab experimental conditions, as in labs, the environmental conditions can be easily controlled.
• The concept of “local control” is not used in CRD.
• CRD is best suited for experiments with a small number of treatments.

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