Best Design of Experiments MCQS with Answers 5

Online Quiz about Design of Experiments MCQs with Answers. There are 20 MCQs in this test. Let us start with “Design of Experiments MCQs with Answer”.

Online Multiple Choice Questions about Design of Experiments with Answers

1. What is the most common one-factor-at-a-time design in social sciences?

 
 
 
 

2. Common applications of DOE in management sciences include.

 
 
 
 

3. An important application of DOE in social sciences is to:

 
 
 
 

4. Initial applications of DOE are in?

 
 
 
 

5. An important application of DOE in management sciences is to?

 
 
 
 

6. A phenomenon whose effect on the experimental unit is observed is called.

 
 
 
 

7. Taguchi designs were presented ———- Plackett-Burman designs.

 
 
 
 

8. Physical science is the systematic study of the inorganic world, consisting of astronomy, physics, chemistry, and:

 
 
 
 

9. The process of choosing experimental units randomly is called

 
 
 
 

10. Laboratory experiments are usually performed under:

 
 
 
 

11. Which term is estimated through replication?

 
 
 
 

12. Accidental bias (where chance imbalances happen) is minimized through

 
 
 
 

13. Common applications of DOE in physical sciences include.

 
 
 
 

14. The different states of a factor are called.

 
 
 
 

15. A single performance of an experiment is called?

 
 
 
 

16. When do experimental factors include the proportions of ingredients we use?

 
 
 
 

17. Selection bias (where some groups are underrepresented) is eliminated

 
 
 
 

18. Changes in mean scores over three or more time points are compared under the:

 
 
 
 

19. With the passage of time, Statisticians moved from?

 
 
 
 

20. DOE can be used in management sciences to organize:

 
 
 
 

Design of Experiments MCQs with Answers

Design of Experiments MCQs with Answers

  • Laboratory experiments are usually performed under:
  • Common applications of DOE in physical sciences include.
  • When do experimental factors include the proportions of ingredients we use?
  • Physical science is the systematic study of the inorganic world, consisting of astronomy, physics, chemistry, and:
  • Common applications of DOE in management sciences include.
  • An important application of DOE in management sciences is to?
  • DOE can be used in management sciences to organize:
  • What is the most common one-factor-at-a-time design in social sciences?
  • An important application of DOE in social sciences is to:
  • Changes in mean scores over three or more time points are compared under the:
  • Initial applications of DOE are in?
  • With the passage of time, Statisticians moved from?
  • Taguchi designs were presented ———- Plackett-Burman designs.
  • Which term is estimated through replication?
  • A single performance of an experiment is called?
  • The different states of a factor are called.
  • A phenomenon whose effect on the experimental unit is observed is called.
  • The process of choosing experimental units randomly is called
  • Accidental bias (where chance imbalances happen) is minimized through
  • Selection bias (where some groups are underrepresented) is eliminated

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One Way Analysis of Variance: Made Easy

The article is about one way Analysis of Variance. In the analysis of variance, the total variation in the data of the sample is split up into meaningful components that measure different sources of variation. Each component yields an estimate of the population variance, and these estimates are tested for homogeneity by using the F-distribution.

One Way Classification (Single Factor Experiments)

The classification of observations based on a single criterion or factor is called a one-way classification.

In single factor experiments, independent samples are selected from $k$ populations, each with $n$ observations. For samples, the word treatment is used and each treatment has $n$ repetitions or replications. By treatment, we mean the fertilizers applied to the fields, the varieties of a crop sown, or the temperature and humidity to which an item is subjected in a production process. The collected data consisting of $kn$ observations ($k$ samples of $n$ observations each) can be presented as.

One way analysis of variance

where

$X_{ij}$ is the $i$th observation receiving the $j$th treatment

$X_{\cdot j}=\sum\limits_{i=1}^n X_{ij}$ is the total observations receiving the $j$th treatment

$\overline{X}_{\cdot j}=\frac{X_{\cdot j}}{n}$ is the mean of the observations receiving the $j$th treatment

$X_{\cdot \cdot}=\sum\limits_{i=j}^n X_{\cdot j} = \sum\limits_{j=1}^k \sum\limits_{i=1}^n X_{ij}$ is the total of all observations

$\overline{\overline{X}} = \frac{X_{\cdot \cdot}}{kn}$ is the mean of all observations.

The $k$ treatments are assumed to be homogeneous, and the random samples taken from the same parent population are approximately normal with mean $\mu$ and variance $\sigma^2$.

Design of Experiments

One Way Analysis of Variance Model

The linear model on which the one way analysis of variance is based is

$$X_{ij} = \mu + \alpha_j + e_{ij}, \quad\quad i=1,2,\cdots, n; \quad j=1,2,\cdots, k$$

Where $X_{ij}$ is the $i$th observation in the $j$th treatment, $\mu$ is the overall mean for all treatments, $\alpha_j$ is the effect of the $j$th treatment, and $e_{ij}$ is the random error associated with the $i$th observation in the $j$th treatment.

The One Way Analysis of Variance model is based on the following assumptions:

  • The model assumes that each observation $X_{ij}$ is the sum of three linear components
    • The true mean effect $\mu$
    • The true effect of the $j$th treatment $\alpha_j$
    • The random error associated with the $j$th observation $e_{ij}$
  • The observations to which the $k$ treatments are applied are homogeneous.
  • Each of the $k$ samples is selected randomly and independently from a normal population with mean $\mu$ and variance $\sigma^2_e$.
  • The random error $e_{ij}$ is a normally distributed random variable with $E(e_{ij})=0$ and $Var(e_{ij})=\sigma^2_{ij}$.
  • The sum of all $k$ treatments effects must be zero $(\sum\limits_{j=1}^k \alpha_j =0)$.

Suppose you are comparing crop yields that were fertilized with different mixtures. The yield (numerical) is the dependent variable, and fertilizer type (categorical with 3 levels) is the independent variable. ANOVA helps you determine if the fertilizer mixtures have a statistically significant effect on the average yield.

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Split Plot Design in Agriculture

The article is about the use and application of split plot design in Agriculture, here we will discuss the conditions in which split plot design should be used in agriculture, the related real-life examples of split plot design, and the model of the design. In factorial experiments, there are certain situations where it becomes difficult to handle all the combinations of different levels of the factors. This may be because of the following reasons:

  • The nature of the factors may be such that levels of one factor require large experimental units as compared to the levels of other factors. For example, If the two factors are Rowing Methods and Nitrogen Levels”, then in the two-factor experiment the rowing methods require machinery, so they require large experimental units, and the nitrogen levels can be applied to the smaller units.
  • Greater precision may be required for levels of one factor as compared to the levels of other factors. For example, If we want to compare two factors, varieties, and fertilizers, and more precision is required for fertilizers, then varieties would be in the larger units and the fertilizers would be in the smaller units.
  • It may be that new treatments have to be introduced into an experiment that is already in progress.

Conditions in which Split Plot Design Used

The split plot design (and a variation, the split block) is frequently used for factorial experiments in which the nature of the experimental material or the operations involved makes it difficult to handle all factor combinations in the same manner.

  • If irrigation is more difficult to vary on a small scale and fields are large enough to be split, a split-plot design becomes appropriate.
  • Usually used with factorial sets when the assignment of treatments at random can cause difficulties, large-scale machinery can required for one factor but not another irrigation and tillage.
  • Plots that receive the same treatment must be grouped.
  • Degree of Precision: For greater precision for Factor $B$ than for factor $A$, the factor $B$ should be assigned to the subplot and factor $A$ to the main plot.
  • Relative Size of the Main Effects: If the main effect of (say factor $B$) is much larger and easier to detect than that of the other factor (factor $A$), the factor $B$ can be assigned to the main plot, and factor $A$ to the subplot. This increases the chance of detecting the difference among levels of factor $A$ which has a smaller effect.
  • Management Practices: The cultural practices required by a factor may dictate the use of large plots. For example, in an experiment to evaluate water management and variety, it may be desirable to assign water management to the main plot to minimize water movement between adjacent plots, facilitate the simulation of the water level required, and reduce border effects.

Split Plot Design in Agriculture: Irrigation and Fertilizer (Example 1)

In agricultural experiments involving two factors “irrigation” and “nitrogen” fertilizer. Sometimes, it is very convenient to apply different levels of irrigation to small neighbouring plots but there is no such difficulty for the application of different levels of nitrogen fertilizer. To meet such situations, it is desirable to have different sizes of the experimental units in the same experiment. For this purpose, we have two sizes of the experimental units. First, a design with bigger plots is taken to accommodate the factors that require bigger plots. Next, each of the bigger plots is split into as many plots as the number of treatments coming from the other factors.

The bigger plots are called main plots. The treatments allotted to them are called main plot treatments or simply main treatments. The consequent parts of the main plots are called sub-plots or split plots and the treatments allotted to them are called sub-plot treatments. The different types of treatments are allotted at random to their respective plot. Such a design is called split-plot design.

Split Plot design in Agriculture

Split Plot Design in Agriculture: Irrigation and Fertilizer (Example 2)

Let there be 3 levels of irrigation prescribing 3 different amounts of water per plot and 4 doses of nitrogen fertilizer.

First, a randomized block design with a suitable plot is taken with 3 levels of irrigation as treatments say with 5 replications of the design. The irrigation treatments are then allotted at random to each five blocks, each consisting of 4 sub-plots.

Next, each of these main plots is split into 4 sub-plots to accommodate the 4 levels of nitrogen. The main 15 plots serve as 15 replications of the subplot treatments. Treatments are allotted at random to sub-plots of each of the main plots. The split-plot design is the combination of two or more randomized designs depending on several factors, such as the plots of one design from the block of another design. The main plot treatment or the levels of one factor or different factors each of which requires a similar plot size.

Model of Split Plot Design

\begin{align} y_{ijk} &= \mu + \tau_i + \beta_j + (\tau \beta){ij} + \gamma_k + (\tau \gamma){ik} + (\beta\gamma){jk}+(\tau \beta\gamma){ijk} + \varepsilon_{ijk}\\
i &= 1,2,\cdots, a \text{ levels of factor } A\\
j &= 1,2,\cdots, b \text{ levels of factor } B\\
k &= 1,2,\cdots, c \text{ levels of factor } C
\end{align}

Model Terms

  • Linear Terms
    • $\mu$: Overall mean
    • $\tau_i$: Effect of $i$th level of $A$
    • $\beta_j$: Effect of $j$th level of $B$
    • $\gamma_k$: Effect of $k$th level of $C$
  • Interactions Terms
    • $(\tau \beta){ij}$: Interaction effect of $A$ and $B$\ $(\tau \gamma){ik}$: Interaction effect of $A$ and $C$\
    • $(\beta\gamma){jk}$: Interaction effect of $B$ and $C$\ $(\tau\beta\gamma){ijk}$:Interaction effect of $A$, $B$ and $C$ \item \textbf{Error} $\varepsilon{ijk}$: Random error at $i$th level of $A$, $j$th level of $B$ and $k$th level of $C$\
    • $\varepsilon_{ijk} \sim NID(0,\sigma_{\varepsilon}^2)$
  • Response
    • $y_{ijk}$: Response of $i$th level of $A$, $j$th level of $B$ and $k$th level of $C$

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