Statistics for Data Analyst

The post contains MCQs on the Design of Experiments Quiz (DOE). Most of the MCQs on the Design of Experiments Quiz are from factorial Experiments. Let us start with Online MCQs on the Design of Experiments Quiz.

Multiple Choice Questions about the Design of Experiments for preparation of examinations related to PPSC, FPSC, NTS, and Statistics job- and education-related examinations

1. The number of aliases of two-factor interactions in a $2^6$-factorial experiment (1/4 replicate) would be

 20

 23

 21

 9

2. An experiment was designed to investigate the effect of the amount of water and seed variety on the subsequent growth of plants. Each plant was potted in a clay plot, and a measured amount of water was given weekly. The height of the plant at the end of the experiment was measured. Which of the following is not correct?

 Randomization was used to eliminate the effect of other possible upon the growth of the plants

 A possible uncontrollable factor in this experiment is any nutrients that might be present in the clay pots

 The explanatory variables are the amount of water and seed variety

 The response variable is the plant height

3. The parameter $\lambda$ for a balanced incomplete block design with $a=4, b=4, k=3, r=3$ as usual notation is

 3

 2

 4

 1

4. An experiment was conducted where you analyzed the results of the plant growth experiment after you manipulated the amount of water and seed variety. Which of the following is correct?

 We could determine the best combination of water and seed variety by examining the difference in plant height in the final week of the experiment.

 The growth of the plants was linear over time.

 The variability in growth among plants of the same variety who received the same amount of water was constant over time.

 The growth of a particular plant in week 3 is likely to be independent (unrelated) of the growth of the same plant in week 2.

5. The designs in which the number of treatments must be an exact square, the size of a block is the square root of this form separate replications are called

 Split-Plot designs

 Balanced Lattices

 Rectangular Lattices

 Youden Square designs

6. Which of the following is NOT CORRECT about a randomized complete block experiment?

 Blocks should contain experimental units that are as different as possible from each other

 Every treatment must appear at least once in every block

 Blocking is used to remove the effects of another factor (not of interest) from the comparison of levels of the primary factor

 Every block is randomized separately from every other block

7. In a $2^3$ factorial experiment with partial confounding in three replications of 6 blocks, the error degrees of freedom would be

 13

 11

 8

 6

8. In a randomized complete block design, the block should be constructed so that

 The blocks are heterogenous internally and one treatment is used in a complete block

 The block is not homogenous internally and all the treatments could be used in a block

 The block is homogeneous internally and all the treatments could be used in a block

 The block is homogeneous internally and one treatment is used in a complete block

9. An important relationship between the coefficient of determination $R^2$ and the F-ratio used in ANOVA is

 There is no relation between $F$ and $R^2$

 $F=\frac{(1-R^2)/(n-K)}{R^2/(K-1)}$

 $F=\frac{R^2}{(1-R^2}$

 $F=\frac{R^2/(K-1)}{(1-R^2)/(n-K)}$

10. A design with $v$ treatment labels, each occurring $r$ times, and with $bk$ experimental units grouped into $b=v$ blocks of size $k<v$ in such a way that the units within a block are alike and units in different blocks are substantially different is

 All Cyclic, BIB and PBIB designs

 BIBD

 Cyclic design

 PBIBD

11. When a number of confounded arrangements for factorial designs are made in Latin Squares, the designs are called

 Rectangular designs

 Quasi-Latin square designs

 Cyclic designs

 Randomized complete block designs

12. For a two-factor factorial design, if there are ‘$a$’ levels of Factor-A and ‘$b$’ levels of Factor-B, then $df$ of interaction are:

 $ab-a-1$

 $(a-1)(b-1)$

 $ab-1$

 $ab-b+1$

13. The models in which the levels of treatment factors are specifically chosen are known as

 Fixed Effect Models

 Linear Models

 Mixed Effect Models

 Random Effect Models

14. In a factorial experiment, if $r$ is the number of replicates then each factorial effect has the same variance, that is

 $\frac{\sigma^2}{4r}$

 $\frac{\sigma^2}{2r}$

 $\frac{\sigma^2}{2r^2}$

 $\frac{\sigma^2}{4r^2}$

15. When all pairs of treatments are compared with approximately the same precision, even though the differences among blocks may be large, called

 Latin Square design

 Cyclic design

 $\alpha$-Block design

 Balanced Lattice design

16. Let ADE and BCE be two effects confounded in blocks. Then generalized interaction is

 ABC

 ABCDE

 ABCD

 BCDE

17. When a factorial experiment is performed in fractional replication, the two factorial effects that are represented by the same comparisons are called

 orthogonal Effects

 Defining Contrast

 Confounding Effects

 Aliases

18. In $3^k$ factorial design with $n$ replicates in the experiment, the $df$ of error are

 $3^k n-1$

 $3^k(n-1)$

 $3^k-1$

 $1-n-3^k$

19. For a Latin Square design

 Only the number of rows and columns should be the same

 The number of columns and treatments should be the same which may be different from the number of rows

 The number of rows and columns should be the same, which may be different from the number of treatments

 The number of rows, columns, and treatments should be the same

20. If ABC is confounded in replicate I,
AB is confounded in replicated II,
BC is confounded in replicate III,
then the design technique is called

 Moderate Counding

 Partial Confounding

 Complete Confounding

 Fractional Factorial

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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 Quiz

• The parameter $\lambda$ for a balanced incomplete block design with $a=4, b=4, k=3, r=3$ as usual notation is
• For a two-factor factorial design, if there are ‘$a$’ levels of Factor-A and ‘$b$’ levels of Factor-B, then $df$ of interaction are:
• In $3^k$ factorial design with $n$ replicates in the experiment, the $df$ of error are
• Let ADE and BCE be two effects confounded in blocks. Then generalized interaction is
• If ABC is confounded in replicate I, AB is confounded in replicated II, BC is confounded in replicate III, then the design technique is called
• An important relationship between the coefficient of determination $R^2$ and the F-ratio used in ANOVA is
• In a randomized complete block design, the block should be constructed so that
• For a Latin Square design
• In a factorial experiment, if $r$ is the number of replicates then each factorial effect has the same variance, that is
• When all pairs of treatments are compared with approximately the same precision, even though the differences among blocks may be large, called
• In a $2^3$ factorial experiment with partial confounding in three replications of 6 blocks, the error degrees of freedom would be
• When a factorial experiment is performed in fractional replication, the two factorial effects that are represented by the same comparisons are called
• When a number of confounded arrangements for factorial designs are made in Latin Squares, the designs are called
• The number of aliases of two-factor interactions in a $2^6$-factorial experiment (1/4 replicate) would be
• The designs in which the number of treatments must be an exact square, the size of a block is the square root of this form, and separate replications are called
• A design with $v$ treatment labels, each occurring $r$ times, and with $bk$ experimental units grouped into $b=v$ blocks of size $k<v$ in such a way that the units within a block are alike and units in different blocks are substantially different is
• An experiment was designed to investigate the effect of the amount of water and seed variety on the subsequent growth of plants. Each plant was potted in a clay plot, and a measured amount of water was given weekly. The height of the plant at the end of the experiment was measured. Which of the following is not correct?
• The models in which the levels of treatment factors are specifically chosen are known as
• Which of the following is NOT CORRECT about a randomized complete block experiment?
• An experiment was conducted where you analyzed the results of the plant growth experiment after you manipulated the amount of water and seed variety. Which of the following is correct?

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