Design of Experiments (DOE)

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

Design of Experiments Quiz Questions 7

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Online Quiz about Design of Experiments Quiz Questions with Answers. There are 20 MCQs in this DOE Quiz covers the basics of the design of experiments, hypothesis testing, basic principles, and single-factor experiments. Let us start with “Design of Experiments MCQs with Answer”. Let us start with the Design of Experiments Quiz Questions with Answers now.

Online Design of Experiments Quiz Questions with Answers

1. In ANOVA we use

 
 
 
 

2. A paired samples t-test is also called:

 
 
 
 

3. Paired samples are:

 
 
 
 

4. Paired samples t-test utilizes degree of freedom:

 
 
 
 

5. In a single-factor random effects experiment we assume that the levels of the factor are selected at random from an infinitely large population of possible levels.

 
 

6. In case of pairing, samples are usually taken from:

 
 
 
 

7. For the validity of different inferential tools we assume that errors have:

 
 
 
 

8. ANOVA is suitable to compare —————- means

 
 
 
 

9. To apply the t-test, two samples must be:

 
 
 
 

10. The Fisher LSD procedure used to compare pairs of treatment means following an ANOVA is extremely conservative.

 
 

11. When population variance is unknown and sample sizes are small we can estimate the variance by

 
 
 
 

12. The t-test is used when:

 
 
 
 

13. When comparing more than two population means at the same time we should not use:

 
 
 
 

14. In an independent samples t-test two samples:

 
 
 
 

15. Why would an agricultural field trial require a different experimental strategy than a typical industrial experiment?

 
 
 
 

16. The analysis of variance treats the factor as if it were qualitative even if it is a continuous variable such as temperature.

 
 

17. Why is randomization an important aspect of conducting a designed experiment?

 
 
 
 

18. Basic ANOVA measures ————— source/s of variation

 
 
 
 

19. If a single-factor experiment has a continuous factor with $a$ levels and a polynomial of degree $a – 1$ is fit to the data the error sum of squares for the polynomial model will be identical to the error sum of squares that resulted from the standard ANOVA.

 
 

20. Sir Ronald A. Fisher is regarded as the modern pioneer of designed experiments because

 
 
 
 

Question 1 of 20

Design of Experiments Quiz Questions with Answers

Design of Experiments Quiz Questions with Answers

  • Why is randomization an important aspect of conducting a designed experiment?
  • Why would an agricultural field trial require a different experimental strategy than a typical industrial experiment?
  • Sir Ronald A. Fisher is regarded as the modern pioneer of designed experiments because
  • The analysis of variance treats the factor as if it were qualitative even if it is a continuous variable such as temperature.
  • The Fisher LSD procedure used to compare pairs of treatment means following an ANOVA is extremely conservative.
  • If a single-factor experiment has a continuous factor with $a$ levels and a polynomial of degree $a – 1$ is fit to the data the error sum of squares for the polynomial model will be identical to the error sum of squares that resulted from the standard ANOVA.
  • In a single-factor random effects experiment we assume that the levels of the factor are selected at random from an infinitely large population of possible levels.
  • When comparing more than two population means at the same time we should not use:
  • In an independent samples t-test two samples:
  • When population variance is unknown and sample sizes are small we can estimate the variance by
  • To apply the t-test, two samples must be:
  • The t-test is used when:
  • Paired samples are:
  • A paired samples t-test is also called:
  • Paired samples t-test utilizes degree of freedom:
  • In case of pairing, samples are usually taken from:
  • Basic ANOVA measures ————— source/s of variation
  • ANOVA is suitable to compare —————- means
  • In ANOVA we use
  • For the validity of different inferential tools we assume that errors have:

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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.

Please go to Design of Experiments MCQs 6 to view the test

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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