Online Design of Experiments Quiz Test Questions with Answers. There are 20 MCQs in this DOE Quiz that cover the basics of the design of experiments, hypothesis testing, basic principles, single-factor experiments, sums of squares and means squares. Let us start with the “Design of Experiments Quiz Test with Answer”. Let us start with the Design of Experiments Quiz Test Questions with Answers now.
Online Design of Experiments Quiz Test with Answers
Design of Experiments Quiz Test
A market analyst is interested in examining a particular brand of machines, he draws a random sample of the brand and examines the working of machines. We choose:
To study how a particular group of antibiotics acts on the body, an experimenter takes a random sample from such antibiotics and observes their working. The model used is called:
The sum of squares of the total can be partitioned into ——————–
The error sum of squares can be computed by ———————-.
Error degree of freedom is computed by subtracting treatment degree of freedom from:
The Theorem which tells us about the distributions of partitioned sums of squares of normally distributed random variables is called:
Cochran’s theorem concludes that, under the assumption of normality, the various quadratic forms are independent and have:
The chi-square distribution is the ratio of two —————— variables.
Within treatments or error sum of squares is also called:
Between the sum of squares is also called:
The sum of observations from their mean is equal to:
The mean square of error is computed by dividing the sum of the squares of error by:
The expected value of the mean square of error is equal to:
For $a$ treatments the degree of freedom of treatment is:
The mean square of treatment is computed by dividing the sum of the squares of error by:
The expected value of the mean square of treatment is equal to:
The expected value of the mean square of treatment is always ————– to/than the expected value of the mean square of error.
The Latin Square Designs is an effective tool that can simultaneously handle two sources of variation among the treatments, which are treated as two independent blocking criteria. These blocks are known as row-block and column-block, also called double-block. Both sources of variations (blocks) are perpendicular to each other. Latin Square Designs are used to simultaneously eliminate (or control) the two sources of nuisance variability (Rows and Columns).
Table of Contents
Introduction
In a Latin square, treatments are arranged in a square matrix such that each treatment appears exactly once in each row and once in each column. This structure helps mitigate the influence of extraneous variables, allowing researchers to focus on the effects of the treatments themselves.
Latin square designs are widely used in agriculture (field experiments), psychology, and many fields where controlled experiments are necessary. The Latin Square Designs are applied in field trials, where
the experimental area has two fertility gradients running perpendicular to each other
in the greenhouse experiments in which the experimental pots are arranged in straight lines perpendicular to the sheets or walls of the greenhouse such that the difference between rows and the distance from the wall is expected to be two major extraneous sources of variation,
in laboratory experiments where the trials are replicated over time such that the difference between the experimental units conducted at the same time and those conducted over different time period constitute the two known sources of variations
Rows of Tree
Water Channel
A
B
C
B
C
A
C
A
B
Key Features of Latin Square Designs
The Latin square designs have the following key features:
Control for Two Variables: The design simultaneously accounts for variability in two factors (e.g., time and location).
Efficient Use of Resources: These designs allow for the evaluation of multiple treatments without requiring a full factorial design, which can be resource-intensive.
Simple Analysis: The data collected can be analyzed using standard statistical techniques such as ANOVA.
Randomization and Layout Plan for Latin Square Designs
Suppose, there are five treatments (A, B, C, D, E) for this we need $5 \times 5$ LS-Designs, which means we should layout the experiment with five rows and five columns:
A
B
C
D
E
B
C
D
E
A
C
D
E
A
B
D
E
A
B
C
E
A
B
C
D
First of all, randomize the row arrangement by using random numbers then randomize the column arrangement by using random numbers. One can generate five random numbers on your calculator or computer. For example,
Random Numbers
Sequence
Rank
628
1
3
846
2
4
475
3
2
902
4
5
452
5
1
The first rank is 3, treatment c is allocated to cell-1 in column-1, then treatment D is allocated to cell-2 of column-1, and so on.
C
D
A
E
B
D
E
B
A
C
B
A
E
C
D
E
C
D
B
A
A
B
C
D
E
Now, generate random numbers for the columns
Random Numbers
Sequence
Rank
792
1
4
032
2
1
947
3
5
293
4
3
196
5
2
For the layout of LS-Designs, the 4th column from the first random generation is used as the 1st column of LS-Designs, then the 1st column as the 2nd of LS-Design, and so on. The complete Design is:
ANOVA Table for Latin Square Designs
For a statistical analysis, the ANOVA table for LS-Designs is used given as follows:
SOV
df
SS
MS
Fcal
F tab/P-value
Rows
$r-1 = 4$
Columns
$c-1 = 4$
Treatments
$t-1 = 4$
Error
$12$
Total
$rc-1 = 24$
Example: An experiment was conducted with three maize varieties and a check variety, the experiment was laid out under Latin Square Designs, Analyse the data given below
$C$-1
$C$-2
$C$-3
$C$-4
$Total$
$R$-1
1640(B)
1210(D)
1425(C)
1345(A)
$R$-2
1475(C)
1185(A)
1400(D)
1290(B)
$R$-3
1670(A)
710(C)
1665(B)
1180(D)
$R$-4
1565(D)
1290(B)
1655(A)
660(C)
$Total$
Solution:
A
B
C
D
1670
1640
1475
1565
1185
1290
710
1210
1655
1665
1425
1400
1345
1290
660
1180
The following formulas may be used for the computation of Latin Square Design’s ANOVA Table.
In summary, the Latin square design is an effective tool for researchers looking to control for variability and conduct efficient, straightforward analyses in their experiments.
Online Quiz about Design of Experiments Quiz Questions with Answers. There are 20 MCQs in this DOE Quiz cover the basics of the design of experiments, hypothesis testing, basic principles, and single-factor experiments, fixed effect models, random effect models. Let us start with “Design of Experiments MCQs with Answer”. Let us start with the Design of Experiments Quiz Questions with Answers now.
If an interaction effect in a factorial design is significant the main effects of the factors involved in that interaction may be difficult to interpret.
Factorial experiments cannot be used to detect the presence of interaction.
An interaction term in a factorial model with quantitative factors introduces curvature in the response surface representation of the results.
A factorial experiment can be run as an RCBD by assigning the runs from each replicate to separate blocks.
One of the ANOVA assumptions is that treatments have:
For ANOVA we assume that treatments are applied to the experimental units:
One factor ANOVA means, there is only:
For one factor ANOVA, the model contains:
Single-factor ANOVA is also called:
In a fixed effect model:
In a random effect model:
The treatment effect is associated with:
If the experiment were to be repeated and the same set of treatments would be included, we choose:
The experimenter is interested in treatment means only. The model used is called:
A fixed effect model is used when the effect of —————– is assumed to be fixed during the experiment.
A researcher is interested in measuring the rate of production of five particular machines. The model will be a:
To compare the IQ level of five students a series of tests is planned and IQ is computed based on their results. The model will be:
If the treatments in a particular experiment are a random sample from a large population of similar treatments. we choose:
If the experimenter is interested in the variation among treatment means not the treatment means themselves. The model used is called:
In a random effects model ————- are randomly chosen from a large population.
