Factorial Designs

 

Sampling Techniques and Design of Experiments (2020-21 admitted batch Syllabus)

 

GAYATRI VIDYA PARISHAD COLLEGE FOR DEGREE AND P.G. COURSES (A)

DEPARTMENT OF STATISTICS

PROPOSED SYLLABUS FOR FOURTH SEMESTER

For the Admitted Batch of  2020-21

Paper-IV: SAMPLING TECHNIQUES AND DESIGN OF EXPERIMENTS

 

Assessment	Internal	External	Total	No. of Hrs per Week	Credits
Theory (Marks)	25	75	100	4	4
Practical (Marks)	Internal & External		50	2	1

 

·         Course Objectives:

·         The sampling techniques deals with the ways and methods that should be used to draw samples to obtain the optimum results, i.e., the maximum information about the characteristics of the population with the available sources at our disposal in terms of time, money and manpower to obtain the best possible estimates of the population parameters

·         This paper throw light on understanding the variability between group and within group through Analysis of Variance

·         This gives an idea of logical construction of Experimental Design and applications of these designs now days in various research areas.

·         Factorial designs allow researchers to look at how multiple factors affect a dependent variable, both independently and together.

 

Unit-I  (11 hours) [CO1]

Simple Random Sampling (with and without replacement): Notations and terminology, various probabilities of selection. Random numbers tables and its uses. Methods of selecting simple random sample, lottery method, method based on random numbers. Estimates of population total, mean and their variances and standard errors, determination of sample size, simple random sampling of attributes.

Unit-II (12 hours)[CO2]

Stratified random sampling: Stratified random sampling, Advantages and Disadvantages of Stratified Random sampling, Estimation of population mean, and its variance. Stratified random sampling with proportional and optimum allocations. Comparison between proportional and optimum allocations with SRSWOR.

Systematic sampling: Systematic sampling definition when N = nk and merits and demerits of systematic sampling - estimate of mean and its variance. Comparison of systematic sampling with Stratified and SRSWOR.

 

Unit-III (12 hours)[CO3]

Analysis of variance :Analysis of variance(ANOVA) –Definition and assumptions. One-way with equal and unequal classification, Two way classification.

Design of Experiments: Definition, Principles of design of experiments, CRD: Layout, advantages and disadvantage and Statistical analysis of Completely Randomized Design(C.R.D).

 

Unit-IV (12 hours)[CO4]

Randomized Block Design (R.B.D) and Latin Square Design (L.S.D) with their layouts and Analysis, Missing plot technique in RBD and LSD . Efficiency RBD over CRD, Efficiency of LSD over RBD and CRD.

Unit – V (11 hours) [CO5]

Factorial experiments – Main effects and interaction effects of 22 and 23 factorial experiments and their Statistical analysis. Yates procedure to find factorial effect totals.

Text Books:

1.      Telugu AcademyBA/BSc III year paper - III Statistics - applied statistics - Telugu academy by Prof.K.Srinivasa Rao, Dr D.Giri. Dr A.Anand, Dr V.Papaiah Sastry.

2.      K.V.S. Sarma: Statistics Made Simple: Do it yourself on PC.PHI.

Reference books:                

1.      Fundamentals of applied statistics : VK Kapoor and SCGupta.

2.      Indian Official statistics - MR aluja.

3.      Anuvarthita  Sankyaka Sastram -  Telugu Academy.

Practicals - Semester – IV

 

Sampling Techniques:

Estimation of population mean and its variance by

1.  Simple random sampling with and without replacement. Comparison between SRSWR and SRSWOR.

2.    Stratified random sampling with proportional and optimum allocations. Comparison between proportional and optimum allocations with SRSWOR.

3.  Systematic sampling with N=nk. Comparison of systematic sampling with Stratified and SRSWOR.

Design of Experiments:

4.      ANOVA - one - way classification with equal and unequal number of observations

5.      ANOVA Two-way classification with equal number of observations.

6.      Analysis of CRD.

7.      Analysis of RBD Comparison of relative efficiency of CRD with RBD

8.      Estimation of single missing observation in RBD and its analysis

9.      Analysis of LSD and efficiency of LSD over CRD and RBD

10.  Estimation of single missing observation in LSD and its analysis

11.  Analysis of 2² with RBD layout

12.  Analysis of 23 with RBD layout

 Note: Training shall be on establishing formulae in Excel cells and deriving the results. The excel output shall be exported to MS Word for writing inferences.

 Course Learning Outcomes :

The Student shall get

1. Introduced to various statistical sampling schemes such as Simple Random      Sampling and related concepts

2. An idea about stratified, systematic sampling and its related concepts

3. Carry out one way and two way Analysis of Variance and Understand the basic     terms used in design of experiments and Completely randomized design

4. Understand the RBD and LSD experiments and its analysis,

5. Understand the basic terms used in Factorial experiments and their statistical     analysis.

Sampling Techniques and Design of Experiments (New Model Paper)

 

5.4. Latin Square Design

 

Latin Square Design (LSD):

The entire experimental area is divided into relative homogeneous groups / blocks with respect to two sources of variation rows and columns, treatments are now allocated to all experimental units in rows and columns in a such a way that every treatment occurs once and only once in each row and column, such design is called Latin Square Design.

Lay out of LSD:

In LSD, the number of treatments and number of replications are equal i.e., the number of rows is equal to number of columns. Suppose we consider m treatments, then there is mxm = m² experimental units. So the whole experimental area is divided into m² experimental units and arranged in a square so that each row and column consists of m units. Then the m treatments are allocated at random to these rows and columns in such a way that every treatment occurs once and only in each row and in each column. This lay out is known as mxm LSD.

For example:

A	B	C
B	C	A
C	A	B

 

A	B	C	D
B	C	D	A
C	D	A	B
D	A	B	C

Advantages:

1. LSD controls variation in three ways i.e., row, column and treatment

2. The statistical analysis is simple even with missing value

3. More than one factor can be studied simultaneously and with fewer trials than more complicated designs.

Dis advantages:

1. The number of treatments is equal to the number of replications in LSD, this restricts the use of this design.

2. If several units are missing in LSD, the statistical analysis is more complex

3. LSD, performs only on a square field but RBD or CRD can perform rectangular fields also

4. The fundamental assumption that there is no interaction between different factors may not be true in general.

Syllabus and Modal Paper

 GAYATRI VIDYA PARISHAD COLLEGE FOR DEGREE AND P.G. COURSES (A)

DEPARTMENT OF STATISTICS

SYLLABUS FOR FIFTH SEMESTER.

w.e.f 2015-16

 

Paper – V: SAMPLING TECHNIQUES AND DESIGN OF EXPERIMENTS

 

 

Course Objectives:

The objective of the course is to understand an overview of the concepts of how to plan, design and conduct sampling technique efficiently and effectively, theory and applications of various sampling procedures in survey research methods. To understand the procedure of testing of hypothesis, analysis and interpretation of ANOVA technique. To understand the concepts of design of experiments, various designs and statistical analysis issues.

 

Unit-I (10 hours) [CO1]

Sampling Theory: Principle steps in a sample survey, Censes versus sample survey, sampling and Non-sampling errors. Types of sampling - subjective, probability and mixed sampling methods.

Unit-II (10 hours) [CO2]

Simple Random Sampling: Meaning of Samples and methods to draw, estimation of population mean, variances in SRSWR& SRSWOR.

Unit-III (11 hours) [CO3]

Stratified random sampling: Proportional and optimum allocation of sample sizes in stratification. Variances in these methods. Systematic sampling: Systematic sampling when N = nk comparison of their relative efficiencies. Advantages and Disadvantages of above methods of sampling.

Unit-IV (11 hours) [CO4]

Analysis of Variance:  One way with equal and unequal classifications and two way classifications.

Unit – V (13 hours) [CO5]

 

Design of Experiments: Principles of experimentation in Designs, analysis of completely randomised design (CRD), and Randomised block design (RBD) and Latin square design (LSD) including one missing observation. Efficiency of these designs and concept of factorial Experiment.

 Practical’s Semester – V:

1.              Estimation of population Mean, variance by SRSWOR.

2.              Estimation of population Mean, variance by SRSWR.

3.              Comparison of proportional, optimum allocations with SRSWOR.

4.              Systematic Sampling.

5.              ANOVA-CRD.

6.              ANOVA - RBD with one missing observation.

7.              ANOVA - LSD withone missing observation.

8.              Practical’s are to be conducted using MS-Excel.

Course Objectives:

1.       Student can learn an overview of the concepts of how to plan, design and different sampling techniques

2.       Student able to conduct sampling technique efficiently and effectively, understand the theory and applications of Simple Random sampling method.

3.       Student able to conduct sampling technique efficiently and effectively, understand the theory and applications of Stratified and Systematic sampling methods.

4.       Student can enhance the procedure of testing of hypothesis, analysis and interpretation of ANOVA technique.

5.        Student acquires knowledge about the concepts of design of experiments, various designs and applies ANOVA technique for analysis of designs.

Text Books:

1.             Telugu AcademyBA/BSc III year paper - III Statistics - applied statistics - Telugu academy by Prof.K.SrinivasaRao, Dr D.Giri. Dr A.Anand, Dr V.PapaiahSastry.

2.             Statistics Made Simple: Do it yourself on PC, K.V.S. Sarma,PHI.

Reference Books:

1.             Fundamentals of applied statistics: VK Kapoor and SC Gupta.

2.             AnuvarthitaSankyakaSastram- Telugu Academy, V L Narasimham.

 

e-Source: (Sampling Techniques and Design of Experiments)

https://www.youtube.com/watch?v=bQ5_PPRPjG4

https://www.youtube.com/watch?v=mlQRIoBErso

https://www.youtube.com/watch?v=yx5KZi5QArQ

https://www.youtube.com/watch?v=rsNCCQhkKN8

https://www.youtube.com/watch?v=sYRUYJYOpG0

https://www.youtube.com/watch?v=q48uKU_KWas

https://www.youtube.com/watch?v=5eGHZsGi4ZE

https://www.youtube.com/watch?v=82GOJMqKd2Y

https://www.youtube.com/watch?v=95ZMKW75zvg

https://www.youtube.com/watch?v=THMQZTFa4ow

GAYATRI VIDYA PARISHAD COLLEGE FOR DEGREE AND P.G COURSES (A)
III Year B.Sc. (STATISTICS)
Semester – V, MODEL PAPER
PAPER-V: SAMPLING TECHNIQUES AND DESIGN OF EXPERIMENTS
(With effect from 2017-18)
Date:				Max. Marks: 75
TIME:
SECTION – A
		I. Answer the following questions			4× 10 = 50 M
1. (a)		Explain in detail various steps in sample survey.(CO1)
OR
(b)		Explain sampling and non-sampling errors.(CO1)
2.(a)	Define Simple Random Sampling. In Simple Random Sampling without replacement, show that Var () = .                                                                       (CO2)
OR
(b)		How do you allocate the sample sizes from different strata in stratified random sampling? Also show that Var ( ≥ Var (.                                                                                             (CO2)
3. (a)		Write advantages and disadvantages of systematic sampling.(CO3)
OR
(b)		Describe the statistical analysis of two-way ANOVA.(CO4)
4. (a)		Explain the principles of experimentation.(CO5)
OR
(b)		Analyse the Randomized Block Design.(CO5) SECTION-B
		II. Answer any Five of the following questions					5 ´ 3 = 15 M
5.		Explain the subjective sampling method.(CO1)
6.		Describe various probability sampling methods.(CO2)
7.		What is Simple Random Sampling with replacement and without replacement?(CO3)
8.		What are the advantages and disadvantages of stratified random sampling?(CO3)
9.		Describe the statistical analysis of one-way ANOVA.(CO4)
10.		State the assumptions of two-way ANOVA. (CO4)
11.		Write a note on Factorial experiment. (CO5)
12.		Define the experimental error.(CO5)
SECTION – C
		III. Answer All the following questions				10 ´ 2 = 20 M
13.		Distinguish between census survey and sample survey.(CO1)
14.		State the limitations of sampling.(CO1)
15.		What is the estimate of population total in simple random sampling?(CO2)
16.		Describe the method of Random Numbers.(CO2)
17.		Describe the disadvantages of stratified random sampling.(CO3)
18.		Define stratified random sampling.(CO3)
19.		State the assumptions of one-way ANOVA. (CO4)
20.		Define Least Significant Difference.(CO4)
21.		State the advantages of CRD.(CO5)
22.		State the formula for finding missing value in LSD.(CO5)         GAYATRI VIDYA PARISHAD COLLEGE FOR DEGREE & P.G. COURSES (A) III Year B.Sc. (STATISTICS) SEMESTER-V, (BLUE PRINT) Paper-V: SAMPLING TECHNIQUES AND DESIGN OF EXPERIMENTS Time: 3hours                                                                                          Max.Marks:75   UNIT ESSAY QUESTIONS SHORT QUESTIONS VERY SHORT QUESTIONS I 2 1 2 II 2 1 2 III 1 2 2 IV 1 2 2 V 2 2 2