PROBABILITY SAMPLING TECHNIQUES

Maneesh pMpil economicsDepartment of economics

INTRODUCTION

A population can be defined as including all people or items with the characteristic one wishes to understand. Because there is very rarely enough time or money to gather information from everyone or everything in a population, the goal becomes finding a representative sample (or subset) of that population.

Research comprises "creative work undertaken on a systematic basis in order to increase the stock of knowledge, including knowledge of humans, culture and society, and the use of this stock of knowledge to devise new applications. (Kerlinger, 1986)

In every research work the data could be collected through two approaches namely census (in where all units of a population are studied) and sample (in where a part of a population are studied).

A single member of the population is called as element. Element, or members of population are selected from a sampling frame, which is a listing of all elements of a population.

sampling is concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. 

Sampling: examining less than 100% of items in a population

Sample: The selected respondents of the total population.

Population - total group of respondents that the researcher wants to study. Populations are too costly and time consuming to study in entirety.

Sample - selecting and surveying respondents (research participants) from the population.

Sample size The number of items to be selected from the universe or population constitute ‘sample size’

Sample design It is a definite plan for obtaining a sample from a given population

Sampling error Sampling errors are the random variations in the sample estimates around the true population parameters

Characteristics of a good sample

•Results in a truly representative sample•Small sampling error•Viable in the context of funds •Systematic bias to be controlled •Results of the sample study can be applied for the universe with a reasonable level of confidence.Need to reduce… •Inappropriate sampling frame•Defective measuring device •Non-respondents •Indeterminacy principle•Natural bias in the reporting of data

Need for Sampling

•Saves money and time – relatively produces results at a

faster speed

•May enable accurate measurements

•If the population is infinite…

•When test involves destruction of the items

•Enables to estimate the sampling errors

Limitations •May not ensure representation

•Without thorough knowledge – it may mislead

•Complicated sampling may not give accurate results

The sampling technique is divided into two techniques namely probability and non-probability.

Sampling Techniques

Classification of Sampling Techniques

Non-probabilitySampling Techniques

ConvenienceSampling

ProbabilitySampling Techniques

JudgmentSamples

QuotaSampling

SnowballSampling

SystematicSampling

StratifiedSampling

ClusterSampling

Simple randomSampling

PROBABILITY SAMPLING

The probability sampling techniques is the techniques that every units of universe has the equal chance to be as a member of sample.

Probability sampling: elements in the population have a known and non-zero chance of being chosen

Eliminates bias in the selection process

Probability sampling includes:

Simple Random Sampling, Systematic Sampling,Stratified Random Sampling, Cluster Sampling

CHARACTERISTICS OF PROBABILITY SAMPLING

The following are the main characteristics of probability

sampling:

1. In probability sampling we refer from the sample as well as the population.

2. . In probability sampling every individual of the population has equal probability to be taken into the sample.

3. Probability sample may be representative of the population.

4. The observations (data) of the probability sample are used for the inferential purpose.

5. Probability sample has not from distribution for any variable.

6. Inferential or parametric statistics are used for probability sample.

7. There is a risk for drawing conclusions from probability sample. 8. The probability is comprehensive. Representativeness refers to characteristic. Comprehensiveness refers to size and area.

Simple Random Sampling

A simple random sample is one in which each element of the population has

an equal and independent chance of being included in the sample i.e. a sample

selected by randomization method is known as simple-random sample and this

technique is simple random-sampling.

Randomization is a method and is done by using a number of techniques as :

(a) Tossing a coin.

(b) Throwing a dice.

(c) Lottery method.

(d) Blind folded method.

(e) By using random table of ‘Tippett’s Table’.

The probability of a member of the population being selected is unaffected by the selection of other members of the population, i.e. each selection is entirely independent of the next.

Advantages

(a) It requires a minimum knowledge of population. (b) It is free from subjectivity and free from personal error. (c) It provides appropriate data for our purpose. (d) The observations of the sample can be used for inferential purpose.

Disadvantages

(b) The representativeness of a sample cannot be ensured by this method. (b) This method does not use the knowledge about the population. (c) The inferential accuracy of the finding depends upon the size of the

sample.

Population elements are an ordered sequence (at least,

conceptually).

The first sample element is selected randomly from the

first k population elements.

Thereafter, sample elements are selected at a constant

interval, k, from the ordered sequence frame.

SYSTEMATIC SAMPLING

To find the frequency use the formula:

snNf

where f = frequency interval;

N = the total number of the wider population;

sn = the required number in the sample.

• In a company of 1,500 employees a sample size of 306 is required (from tables of sample size for random samples). The formula is:

f = 1500 = 4.9 306This rounds to 5, i.e. every 5th person.

A simple example would be to select every 10th name from the telephone directory (an 'every 10th' sample, also referred to as 'sampling with a skip of 10').

Example…..

Purchase orders for the previous fiscal year are serialized 1 to 10,000 (N =

10,000).

A sample of fifty (n = 50) purchases orders is needed for an audit.

k = 10,000/50 = 200

First sample element randomly selected from the first 200 purchase orders.

Assume the 45th purchase order was selected.

Subsequent sample elements: 245, 445, 645, . . .

ADVANTAGES:

•Sample easy to select

•Suitable sampling frame can be identified easily

•Sample evenly spread over entire reference population

DISADVANTAGES:

•Sample may be biased if hidden periodicity in population

coincides with that of selection.

•Difficult to assess precision of estimate from one survey.

Stratified random sampling

• Stratified random sampling is a modification of random sampling in which you divide the population into two or more relevant and significant strata based in a one or a number of attributes (age, sex, educational background)

• In effect, your sampling frame is divided into a number of subsets.

• A random sample (simple or systematic) is then drown from each of the strata.

• Consequently stratified sampling shares many of the advantages and disadvantages of simple random or systematic sampling

Advantages

Increase probability of sample being representative.

Assures adequate number of cases for subgroups

Dis advantages

Requires adequate knowledge of population

May be costly to prepare stratified lists

Statistics are more complicated

• Sampling within a particular cluster (e.g. geographical cluster);

• Useful where population is large and widely dispersed.

CLUSTER SAMPLING

Population is divided into non overlapping clusters or areas

Each cluster is a miniature, or microcosm, of the population.

A subset of the clusters is selected randomly for the sample.

If the number of elements in the subset of clusters is larger than the desired value of n, these clusters may be subdivided to form a new set of clusters and subjected to a random selection process.

For cluster sampling your sampling frame is the complete list of clusters rather than complete list of individual cases within population, you then select a few cluster normally using simple random sampling,. Data are then collected from every case within the selected clusters

Advantages• More convenient for geographically dispersed

populations• Reduced travel costs to contact sample elements• Simplified administration of the survey• Unavailability of sampling frame prohibits using other

random sampling methods

Disadvantages• Statistically less efficient when the cluster elements are

similar• Costs and problems of statistical analysis are greater than

for simple random sampling

Advantages of probability samples

Disadvantages of probability samples

- The researcher can be sure of obtaining information from a representative cross section of the population of interest.

- Sampling error can be computed.

-The survey results are projectable to the total population.

- They are more expensive than non-probability samples of the sample size in most cases. The rules for selection increase interviewing costs and professional time must be spent in developing the sample design.

- Probability samples take more time to design and execute than non- probability samples.

Sampling: the process of selecting a sufficient number of elements from the population, so that results from analyzing the sample are generalizable to the population.

With probability samples the chance , or probability, of each case being selected from the population is known And usually equal to all cases. This means that it is possible to answer research questions and to achieve objectives that require you to estimate statistically the characteristics of the population from the sample. Consequently, probability sampling is often associated with survey and experimental research strategies.

CONCLUSION

Probability sampling is applicable only if we have complete list of information or Sample frame.

If sample frame is un available, we can prefer non probability sampling techniques

THANK YOU FOR YOUR ATTENTION!!!