6. SRSWOR Vs SRSWR

 

 Source: Telugu Academy, Govt. of AP, Applied Statistics V.K.Kapoor & S.C.Gupta, Fundamentals of  Mathematical Statistics, G Gupta & D Gupta, Sampling Techniques, W.G. Cochran

5. SRS of Attributes

 

 Source: Telugu Academy, Govt. of AP, Applied Statistics V.K.Kapoor & S.C.Gupta, Fundamentals of  Mathematical Statistics, G Gupta & D Gupta, Sampling Techniques, W.G. Cochran

4. SRSWR

 

 Source: Telugu Academy, Govt. of AP, Applied Statistics V.K.Kapoor & S.C.Gupta, Fundamentals of  Mathematical Statistics, G Gupta & D Gupta, Sampling Techniques, W.G. Cochran

3. SRS Theorems

 

        Source: Telugu Academy, Govt. of AP, Applied Statistics V.K.Kapoor & S.C.Gupta, Fundamentals of  Mathematical Statistics, G Gupta & D Gupta

2. SRS

 Simple Random Sampling

It is a technique of drawing a sample in such a way that each unit of population has an equal and independent chance of being included in the sample. In this method, an equal probability of selection is assigned to each unit of the population at the first draw. It also implies an equal probability of selecting any unit from the available units at subsequent draws. There are two simple random sampling plans that is Simple Random sampling Without Replacement (SRSWOR) and Simple Random sampling With Replacement (SRSWR).

If the unit selected in any draw is not replaced in the population before making the next draw, then it is known as Simple Random sampling Without Replacement (SRSWOR)

If the unit selected in any draw is replaced in the population before making the next draw, then the sampling plan is known as Simple Random sampling With Replacement (SRSWR).

Simple Random Sampling has an important and interesting feature is that, “the probability of selecting a specified unit of population at any given draw is equal to the probability of its being selected at the first draw”. This implies that in this case from a population of size N, the probability that any sampling unit is included in the sample is 1/N and this probability remains constant throughout the drawing.

Selection methods of Simple Random Samples:

Random sample reefers to that method of sample selection in which every item has an equal chance of being selected. But random sample does not depend upon the method of selection but also on the size and nature of population. Some procedures which are simple and good for small population and is not so for large population. In general the method of selection should be independent of the properties of sampled population. If the selected sample should be random, one can take proper care. Human is inherent in nature and especially is more in sampling schemes. Hence random samples can be obtained by any one of the following methods.

                (i). Lottery Method

                (ii). Mechanical randomization or Random Numbers method.

(i).   Lottery Method: It is the simplest method of selecting random sample from the population under study.  The procedure of lottery method described as: Suppose we want to select n units out of N units.

Let assign the numbers 1 to N (i.e., one number to one unit) to all population units in the Universe and write these numbers on n slips, which are made as homogeneous with respect to shape, size, colour, etc. Then, these slips are put in a big bag and thoroughly shuffled and then n slips are drawn one by one. The n slips units are constitute as random sample of size n.

Merit: 1. It is simplest method of drawing random samples from the Universe.

Demerit:1. If the population is sufficiently large, then it is time consuming and cumbersome to use.

(ii). Mechanical randomization or Random Numbers method: It is the most practical and inexpensive method of selecting a random sample consists in the use of Random Number Tables. The procedure of selecting Random samples through this method described as;

Step 1: Identify or note N units in the population with the numbers 1 to N

Step 2: Select at random, any page of the random number table and pickup the numbers in any row or column or diagonal at random

Step 3: The population units corresponding to the numbers selected in step (2) constitutes the random sample.

 Notations and Terminology:

Let us consider finite units of population of size N and the requires sample size is n. Let Y_i (i=1, 2, 3, ……N) be considered as the value of the character for the i^th unit of the population and corresponding small letters considered as the value of the character for the i^th unit of sample. Generally population parameters will be usually be denoted by either the capital letters of the English alphabet or by Greek letters and their estimates which are functions of the sample observation, are denoted by either small letters or putting the symbol caps on the corresponding parameters. Thus  Y hat indicates the estimate of the population mean.

Source: Telugu Academy, Govt. of AP, Applied Statistics V.K.Kapoor & S.C.Gupta

Unit-2: 1. Simple Random Sampling: Introduction

 

Sources: Fundamentals of Applied Statistics, S.C.Gupta & V.K.Kapoor, Fundamentals of Mathematical Statistics, S.C.Gupta & V.K.Kapoor, Sampling Techniques, W.G.Cochran

Non-Probability Sampling Methods

 

Non-Probability/ Non-random sampling Methods

1.         Convenience Sampling: In this sampling, the sample units are selected with the convenience of Investigator. Convenient samples are selected neither by probability nor by judgment.

Merit: Useful in pilot survey

Demerit: 1. Results usually biased and

2. Unsatisfactory

 2.   Quota Sampling: Most commonly used in non-probability sampling. The population is first segmented into mutually exclusive sub-groups, then judgment is used to select subjects or units from each segment based on a specific proportion.

Eg: 1. In a radio-listening survey, the organization told to interview persons, out of every 100 persons, 60 are to be housewives, 25 farmers and 15 are children under age 15 years.

2. Public opinion studies.

3. Judgment Sampling: In this method of sampling the choice of sample items depends exclusively on the judgment of the investigator. It is used when the investigator thinks to be most typical to select samples from the Universe.

eg: 1. 10 students are to be selected from a class of 60 for analyzing the spending habits of students, the investigator would select 10 students who, in his opinion, are representative of the class.

Merits: 1.When only a small number of units are in the universe, SRS may miss the more important elements, where judgment selection would certainly include them in the sample.

2. When we want to study some unknown traits of population, some of whose characteristics are known, we may then stratify the population according to these known properties and select sampling units from each stratum on the basis of judgment. This method is used to obtain a more representative sample.

Limitations: 1.This method is not scientific because the population units to be sampled may be affected by personal bias of the investigator.

2. There is no objective way of evaluating the reliability of sample results. The success of this method depends on the excellence in judgment.

4.  Snowball Sampling/C0ld-calling/Chain sampling/ Chain referral sampling:  

It is used where potential participants are hard to find. Snowball literally means once you have the ball rolling, it picks up more “snow” along the way and becomes larger and larger. A special non probability method used when the desired sample characteristic is rare.  The research starts with a key person and introduces the next on to become a chain.

 

Merits: 1. When the lack of desired sample/ participants

2. It may help to discover characteristics about a population that weren’t aware existed.

Limitations: 1.It is not possible to determine sampling errors or make inference about population based on the obtained sample.

 

 

 

 

 

Sources: Fundamentals of Applied Statistics, S.C.Gupta & V.K.Kapoor, Fundamentals of Mathematical Statistics, S.C.Gupta & V.K.Kapoor, Sampling Techniques, W.G.Cochran