Important MCQs DOE Quiz 4

The quiz contains MCQs on the Design of Experiments DOE Quiz. Most MCQs on the DOE Quiz are from Basics of Design of Experiments.

Online Multiple Choice Questions about Design of Experiments with Answers

1. Probability theory is based on the paradigm of:

 
 
 
 

2. The important use of DOE in life sciences is?

 
 
 
 

3. The most simple blocked design is:

 
 
 
 

4. Conducting Bayesian experimentation we use:

 
 
 
 

5. Robustness against missing observations means?

 
 
 
 

6. Randomized complete block design is used in agriculture when?

 
 
 
 

7. Robustness against outliers means?

 
 
 
 

8. What is the main characteristic of a designed experiment?

 
 
 
 

9. What is the design of the experiment?

 
 
 
 

10. What is a random experiment?

 
 
 
 

11. What is the purpose of the experiment?

 
 
 
 

12. When the experiment is to be repeated a large number of times under similar conditions, this is called?

 
 
 
 

13. The important use of DOE in engineering is?

 
 
 
 

14. Evaluation and comparison of basic design configuration is important applications in:

 
 
 
 

15. When prior knowledge of variables is available we should use?

 
 
 
 

16. When treatments are continuous quantitative variables we use?

 
 
 
 

17. The first step in the random experiment is:

 
 
 
 

18. What treatments are continuous quantitative variables we should use?

 
 
 
 

19. Common types of DOE for environmental sciences include.

 
 
 
 

20. One of the main objectives of an experiment?

 
 
 
 

Design of experiments (DOE) is a systematic method used to plan, conduct, analyze, and interpret controlled tests to study the relationship between factors and outcomes. Design of Experiment is a powerful tool used in various fields, including science, engineering, and business, to gain insights and optimize processes.

Design of Experiments DOE Quiz

By following the principles of DOE, one can conduct more efficient and informative experiments, ultimately leading to better decision-making and improved outcomes in various fields.

DOE Quiz with Answers

  • What is the purpose of the experiment?
  • What is a random experiment?
  • Probability theory is based on the paradigm of:
  • What is the design of the experiment?
  • What is the main characteristic of a designed experiment?
  • The first step in the random experiment is:
  • One of the main objectives of an experiment?
  • Robustness against missing observations means?
  • Robustness against outliers means?
  • Randomized complete block design is used in agriculture when?
  • When treatments are continuous quantitative variables we use?
  • The most simple blocked design is:
  • The important use of DOE in engineering is?
  • What treatments are continuous quantitative variables we should use?
  • Evaluation and comparison of basic design configuration is important applications in:
  • The important use of DOE in life sciences is?
  • When prior knowledge of variables is available we should use?
  • Conducting Bayesian experimentation we use:
  • Common types of DOE for environmental sciences include.
  • When the experiment is to be repeated a large number of times under similar conditions, this is called?

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Split Plot Design

The design in which the levels of one factor can be applied to large experimental units and the levels of other factors to the sub-units are known as “split plot design“.

A split plot experiment is a blocked experiment in which blocks serve as experimental units. After blocking the levels of other factors are randomly applied to large units within blocks, often called whole plots or main plots.

The split plot design are specifically suited for two factors designs that have more treatment to be accommodated by a complete block designs. In split plot design all the factors are not of equal importance. For example, in an experiment of varieties and fertilizers, the variety is less important and the fertilizer is more important.

In these design, the experimental units are divided into two parts, (i) Main plot and (ii) sub-plot. The levels of one factor are assigned at random to large experimental units (main plot) and the levels of the other (second) factor are applied at random the the sub-units (sub-plot) within the large experimental units. The sub-units are obtained by dividing the large experimental units.

Note that the assignment of a particular factor to either the main plot or to the subplot is extremely important, it is because the plot size and precision of measurement of the effects are not the same for both factors.

The sub-plot treatments are the combination of the levels of different factors.

The split plot design involves assigning the levels of one factor to main plots which may be arranged in a “CRD”, “RCBD” or “LSD”. The levels of the other factor are assigned to subplots within each main plot.

Split Plot Design Layout Example

If there are 3 varieties and 3 fertilizers and we want more precision for fertilizers then with the RCBD with 3 replication, the varieties are assigned randomly to the main plots within 3 blocks using a separate randomization for each. Then the levels of the fertilizers are randomly assigned to the subplots within the main plots using a separate randomization in each main plot. The layout is

Split Plot Design

Another Split Plot Design Example

Suppose we want to study the effects of two irrigation methods (factor 1) and two different fertilizer types (factor 2) on four different fields (“whole plots”). While a field can easily be split into two for the two different fertilizers, the field cannot easily be split into two for irrigation: One irrigation system normally covers a whole field and the systems are expensive to replace.

Split Plot Design Example

Advantages and Disadvantages of Split Plot Design

Advantages of Split Plot Design

  • More Practical
    Randomizing hard-to-change factors in groups, rather, than randomizing every run, is much less labor and time intensive.
  • Pliable
    Factors that naturally have large experimental units can be easily combined with factors having smaller experimental units.
  • More powerful
    Tests for the subplot effects from the easy-to-change factors generally have higher power due to partitioning the variance sources.
  • Adaptable
    New treatments can be introduced to experiments that are already in progress.
  • Cheaper to Run
    In case of a CRD, implementing a new irrigation method for each subplot would be extremely expensive.
  • More Efficient
    Changing the hard-to-change factors causes more error (increased variance) than changing the easy-to-change factors a split-plot design is more precise (than a completely randomized run order) for the subplot factors, subplot by subplot interactions and subplot by whole-plot interactions.
  • Efficient
    More efficient statistically, with increased precision. It permits efficient application of factors that would be difficult to apply to small plots.
  • Reduced Cost
    They can reduce the cost and complexity of manipulating factors that are difficult or expensive to change.
  • Precision
    The overall precision of split-plot design relative to the randomized complete block design may be increased by designing the main plot treatment in a Latin square design or in an incomplete Latin square design.

Disadvantages of Split Plot Design

  • Less powerful
    Tests for the hard-to-change factors are less powerful, having a larger variance to test against and fewer changes to help overcome the larger error.
  • Unfamiliar
    Analysis requires specialized methods to cope with partitioned variance sources.
  • Different
    Hard-to-change (whole-plot) and easy-to-change (subplot) factor effects are tested against different estimated noise. This can result in large whole-plot effects not being statistically significant, whereas small subplot effects are significant even though they may not be practically important.
  • Precision
    Differential in the estimation of interaction and the main effects.
  • Statistical Analysis
    Complicated statistical analysis.
  • Sources of Variation
    They involve different sources of variation ad error for each factor.
  • Missing Data
    When missing data occurs, the analysis is more complex than for a randomized complete block design.
  • Different treatment comparisons have different basic error variances which make the analysis more complex than with the randomized complete block design, especially if some unusual type of comparison is being made.
Design of Experiment

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Layout of the Factorial Design: Two Factor $2^2$ (2024)

The layout of a factorial design is typically organized in a table format. Each row of the table represents an experimental run, while each column represents a factor or the response variable. The levels of factors are indicated by symbols such as + and – for high and low levels, respectively. The response variable values corresponding to each experimental condition are recorded in the form of a sign table.

Consider a simple example layout for a two-factor factorial design with factors $A$ and $B$.

RunFactor AFactor BResponse
1$Y_1$
2+$Y_2$
3+$Y_3$
4++$Y_4$

Layout of the Factorial Design: Two Factor in $n$ Replicates

Consider there are two factors and each factor has two levels in $n$ replicates. The layout of the factorial design will be as described below for $n$ replicates.

Layout for the factorial design Two Factor Two Level

$y_{111}$ is the response from the first factor at the low level, the second factor at the low level, and the first replicate of the trial. Similarly, $y_{112}$ represents the second replicate of the same trial, and up to $n$th observation is $n$th trial at the same level of $A$ and $B$.

Geometrical Structure of Two-Factor Factorial Design

The geometrical structure of two factors (Factor $A$ and $B$), each factor has two levels, low ($-$) and high (+). Response 1 is at the low level of $A$ and a low level of $B$, similarly, response 2 is produced at a high level of $A$ and a low level of $B$. The third response is at a low level of $A$ and a high level of $B$, similarly, the 4th response is at a high level of $A$ and a high level of $B$.

Geometrical Structure of two Factor Layout of Factorial Experiment

Real Life Example

The concentration of reactant vs the amount of the catalyst produces some response, the experiment has three replicates.

Layout of Two Factors Real Life Example

Geometrical Structure of the Example

Layout of the Factorial Design: Two Factor $2^2$ (2024)

Factor Effects

\begin{align} A &=\frac{(a+ab)-((I) +b)}{2} = \frac{100+90-80-60}{2} = 25\\
B &= \frac{(b+ab) – ((I) +a) }{2} = \frac{60+90-80-100}{2} = -15\\
AB&=\frac{((I)+ab)-(a+b)}{2} = \frac{80+90-100-60}{2}=5
\end{align}

Minus 15 ($-15$) is the effect of $B$, which shows the change in factor level from low to high bringing on the average $-15$ decrease in the response.

Reference

Montgomery, D. C. (2017). Design and Analysis of Experiments. 9th ed, John Wiley & Sons.

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