Design of Experiments (DOE)

Lecture notes and quizzes related to the Design of Experiments (DOE).

Design of Experiments MCQs 6

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The post is about the Design of Experiments MCQs with Answers. There are 20 multiple-choice questions. The quiz is related to the Basics of the Design of Experiments, Analysis of variation, assumptions of ANOVA, and Principles of DOE. Let us start with the Design of Experiments Design MCQs.

Online Multiple-Choice Questions about Design of Experiments

1. What is the first step of designing an experiment?

 
 
 
 

2. The sampling distribution of the sample from the population approaches normal distribution if the sample size is large enough.

 
 
 
 

3. What is the test for testing population mean(s) when the sample size is small?

 
 
 
 

4. Name the test(s) of equality of two population means.

 
 
 
 

5. Repeating the same experiment more than once is called

 
 
 
 

6. Tests of population mean(s) include.

 
 
 
 

7. How power of a design can be improved?

 
 
 
 

8. What should be the final step of the design of an experiment?

 
 
 
 

9. What is the first step in testing of hypothesis?

 
 
 
 

10. Analysis of the experimental data is usually performed using

 
 
 
 

11. Blocking reduces

 
 
 
 

12. To control the variation of extraneous sources of variation we do

 
 
 
 

13. The hypothesis is constructed about?

 
 
 
 

14. What is the last step of testing of hypothesis?

 
 
 
 

15. When population variance is unknown but the sample size is large, for testing population mean we use:

 
 
 
 

16. When fractionalizing, which resolution should be preferred?

 
 
 
 

17. Pure error is estimated through

 
 
 
 

18. The arrangement of experimental units in groups that are homogeneous internally and different externally is called

 
 
 
 

19. To check the reliability of results under the same environment we do

 
 
 
 

20. Measuring a quantitative response will improve the power of your experiment with

 
 
 
 

Online Design of Experiments MCQs with Answers

  • Repeating the same experiment more than once is called
  • Pure error is estimated through
  • To check the reliability of results under the same environment we do
  • The arrangement of experimental units in groups that are homogeneous internally and different externally is called
  • To control the variation of extraneous sources of variation we do
  • Blocking reduces
  • What is the first step of designing an experiment?
  • Analysis of the experimental data is usually performed using
  • What should be the final step of the design of an experiment?
  • When fractionalizing, which resolution should be preferred?
  • How power of a design can be improved?
  • Measuring a quantitative response will improve the power of your experiment with
  • What is the first step in testing of hypothesis?
  • The hypothesis is constructed about?
  • What is the last step of testing of hypothesis?
  • Tests of population mean(s) include.
  • The sampling distribution of the sample from the population approaches normal distribution if the sample size is large enough.
  • What is the test for testing population mean(s) when the sample size is small?
  • Name the test(s) of equality of two population means.
  • When population variance is unknown but the sample size is large, for testing population mean we use:
Design of Experiments MCQs Quiz

General Knowledge Quiz

Incomplete Block Design: A Quick Guide

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When the block size is less than the number of treatments to be tested is known as an incomplete block design (IBD). Yates introduced incomplete block designs to eliminate the heterogeneity when the number of treatments becomes very large.

It is known that the precision of the estimate of a treatment effect depends on the number of replications of the treatment, that is, the larger the number of replications, the more the precision. A similar criterion holds for the precision of estimating the difference between two treatment effects. If two treatments occur together in a block, then we say that these are replicated once in that block.

Different patterns of values of the numbers of replications or different pairs of treatments in a design have given rise to different types of incomplete block designs.

The randomized block designs in which every treatment is not present in every block then these designs are known as randomized incomplete block designs. The choice of incomplete block designs depends on factors such as the number of treatments.

Examples of Incomplete Block Designs

Example 1: When the set of treatments is larger than the block size, we use incomplete block designs. Suppose, we want to test the quality of six tires on a given car only 4 tires can be tested, such a block would be incomplete, as it is not possible to test all 6 tires on a given car at once.

Example 2: Consider a study comparing the effectiveness of three fertilizers ($A$, $B$, and $C$) on crop yield. If there are 12 experimental plots, a BIBD with 4 blocks of 3 plots each could be used. Each fertilizer would appear in 4 blocks, and each pair of fertilizers would appear together in 2 blocks.

Example 3: A pharmaceutical company wants to compare the effectiveness of four new drugs for treating a disease. Due to ethical considerations, patients cannot receive all four drugs. An IBD can be used to assign the drugs to different groups of patients, ensuring that each drug is tested against a variety of patient characteristics.

Incomplete block design

Using an IBD, the experimenter can control for variability between plots while still comparing the effects of the fertilizers.

Types of Incomplete Block Designs

The following are types of incomplete block design:

  • Balanced Incomplete Block Designs (BIBDs):
    • Each treatment appears in an equal number of blocks.
    • Each block contains an equal number of experimental units.
    • Every pair of treatments appears together in an equal number of blocks.
  • Partially Balanced Incomplete Block Designs (PBIBDs):
    • Similar to BIBDs but with a more relaxed constraint on the number of times pairs of treatments appear together.
  • Cyclic Designs:
    • A special type of BIBD where the treatments are arranged in a cyclic order within each block.

    Advantages and Disadvantages of IBDs

    • Advantages:
      • Reduced Experiment Size: IBD can require fewer experimental units compared to complete block designs.
      • Feasibility: IBD can be more practical when it is difficult or impossible to apply all treatments to every experimental unit.
    • Disadvantages:
      • Increased Complexity: Analysis can be more complex compared to complete block designs.
      • Reduced Efficiency: May not be as efficient as complete block designs in terms of precision.

    Applications of IBD

    • Agricultural Experiments: Testing different crop varieties or fertilizer treatments.
    • Industrial Experiments: Evaluating different manufacturing processes or materials.
    • Medical Research: Comparing the effectiveness of different treatments for a disease.

    Analysis of IBD

    • Hypothesis Testing: Testing hypotheses about the effects of treatments.
    • Estimation of Treatment Effects: Estimating the differences between treatment effects.
    • Analysis of Variance (ANOVA): IBD Can be used to assess the effects of treatments and blocks.
    • Least Squares Estimation: IBD is used to estimate treatment effects and block effects.
    • Tukey’s HSD: IBD can be used for multiple comparisons to identify significant differences between treatments.

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    Important MCQs on Experimental Design 1

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    The post is about MCQs on Experimental Design with Answers. There are 20 multiple-choice questions. The quiz is related to the Basics of the Design of Experiments, Analysis of variation, assumptions of ANOVA, One-Way ANOVA, Single-factor designs, and Two-Way ANOVA. Let us start with the MCQs on the Experimental Design Quiz.

    Please go to Important MCQs on Experimental Design 1 to view the test

    Online MCQs on Experimental Design

    MCQs on Experimental Design Quiz
    • Analysis of variance is used to test
    • The assumption used in ANOVA is
    • In ANOVA we use
    • Consider $k$ independent samples each containing $n_1, n_2, \cdots, n_k$ items such that $n_1+n_2+\cdots+ n_k=n$. In ANOVA we use F-distribution with a degree of freedom
    • In one-way ANOVA, with the usual notation, the error degree of freedom is
    • In one-way ANOVA, given $SSB = 2580, SSE =1656, k = 4, n = 20$ then the value of F is
    • In two-way ANOVA with $m$ rows and $n$ columns, the error degrees of freedom is
    • In one-way ANOVA, the calculated F value is less than the table F value then
    • In two-way ANOVA with $m=5$, $n=4$, then the total degrees of freedom is
    • In one-way ANOVA with the total number of observations is 15 with 5 treatments then the total degrees of freedom is
    • If the treatments consist of all combinations that can be formed from the different factors then the experiment is
    • Consider an experiment to investigate the efficacy of different insecticides in controlling pests and their effects on subsequent yield. What is the best reason for randomly assigning treatment levels (spraying or not spraying) to the experimental units (farms)?
    • Which of the following are important in designing an experiment?
    • Analysis of variance
    • A Mean Square is
    • For a single-factor ANOVA involving five populations, which of the following statements is true about the alternative hypothesis?
    • An experiment is performed in CRD with 10 replications to compare two treatments. The total experimental units will be
    • A teacher uses different teaching ways for different groups in his class to see which yields the best results. In this example a treatment is
    • If the total degrees of freedom between treatments in a CRD are 15 and 4 respectively, the degrees of freedom for error will be
    • If there are 6 treatments with 3 blocks in a RCBD then the degrees of freedom for error are
    Statistics Help MCQs on Experimental Design

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