Basic Statistics and Data Analysis

Statistics Lecture Notes, Online MCQs

Author: Muhammad Imdad Ullah

Basic Statistics

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MCQs DOE 2

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

 
 
 
 

2. 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:

 
 
 
 

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

 
 
 
 

4. Let ADE and BCE be two effects confounded in blocks. Then generalzed interaction is

 
 
 
 

5. 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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

8. For a Latin Square design

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

16. 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

 
 
 
 

17. An experiment was designed to investigate the effect of the amount of water and seed variety upon 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?

 
 
 
 

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

 
 
 
 

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

 
 
 
 

20. 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?

 
 
 
 

Random Variables

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MCQs Random Variable

The following are online quizzes containing MCQs about Random variable.

Start any of the online quizzes/exams/tests by clicking the links below.

MCQs Random Variable 6MCQs Random Variable 5MCQs Random Variable 4
MCQs Random Variable 3MCQs Random Variable 2MCQs Random Variable 1

A Random Variable (random quantity or stochastic variable) is a set of possible values from a random experiment. The domain of a random variable is called sample space. For example, in the case of a coin toss experiment, there are only two possible outcomes, namely heads or tails. A random variable can be either discrete or continuous. The discrete random variable takes only certain values such as 1, 2, 3, etc., and a continuous random variable can take any value within a range such as the height of persons.

MCQs Random Variable

Non-Parametric Tests

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Wilcoxon Signed Rank Test

The Wilcoxon Signed Rank test assumes that the population of interest is both continuous and symmetric (not necessarily normal). Since the mean and median are the same (for symmetrical distribution), the hypothesis tests on the median are the same as the hypothesis test on the mean.

The Wilcoxon test is performed by ranking the non-zero deviations in order of increasing magnitude (that is, the smallest non-zero deviation has a rank of 1 and the largest deviation has a rank of $n$). The ranks of the deviations with positive and negative values are summed.

These sums are used to determine whether or not the deviations are significantly different from zero. Wilcoxon Signed Rank Test is an alternative to the Paired Sample t-test.

One-Tailed Test

$H_0: \mu = \mu_0\quad $ vs $\quad H_1: \mu < \mu_0$

Test Statistics: $T^-$: an absolute value of the sum of the negative ranks

Two-tailed Test

$H_0: \mu = \mu_0 \quad$ vs $\quad H_1:\mu \ne \mu_0$

Test Statistics: $min(T^+, T^-)$

Because the underlying population is assumed to be continuous, ties are theoretically impossible, however, in practice ties can exist, especially if the data has only a couple of significant digits.

Two or more deviations having the same magnitude are all given the same average rank. The deviations of zero are theoretically impossible but practically possible. Any deviations of exactly zero are simply thrown out and the value of $n$ is reduced accordingly.

Wilcoxon Signed Rank Test
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