Parameter & Statistics

The statistical constants used for further analysis of Data collected such as Mean (μ), Variance (σ²), Skewness (β1), Kurtosis (β2), Correlation (γ) can be computed for the sample drawn from the population.

Sampling is the important part of any research before data collection. So the sampling process should be done in a careful way to obtain the exact samples and sample size of the population on which the research is to be done.

Example: A researcher who would like to study the customer satisfaction for a health drink namely Horlicks should identify the population who are consuming Horlicks. If the consumers are varying in age, genders all over the state or country, he should be able to decide to particular consumers are going to be focused. Again, if the number is more to survey he has to decide on how many individuals he targets for his study.

Hence the effecting sampling process should have the following steps:

Define the population

(Elements, units, extent, and time)

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Specify the sample frame

(The mean of representing the elements of population map, city directory)

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Specifying the sampling unit

(Sampling unit containing more population elements)

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Specifying the sampling method

(The method by which sampling units are to be selected)

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Determine the sample size

(The no. of elements of the population to decided)

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Sampling plan

(Procedure for selected sampling unit)

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Select the sample

(The effective and field work revision for section of samples)

Hence a sample design is a definite plan for obtaining a sample from a given population.

So whenever samples have to be decided for the study, the following can be considered:

- Outline the universe - Define a sampling unit - Sampling frame

- Size of the sample Sampling Techniques

Sampling techniques can be divided into two types:

1. Probability or representative sampling a. Simple random sampling b. Stratified random sampling c. Systematic sampling

d. Cluster sampling e. Multistage sampling

2. Non probability or judgmental sampling a. Quota sampling

b. Purposive sampling Other methods

· Snow ball sampling

· Spatial sampling

· Saturation sampling 1. Probability Sampling

This is a scientific technique of drawing samples form the population according to some laws of change according to which each unit in the universe has some definite pre-assigned probability of being selected in the sample.

Simple Random Sampling

In this technique, sample is drawn in such a way that every elements or unit in the population has an equal and independent chance of being included in the sample.

The unit selected in any draw from the population is not preplanned in population before making the next draw is known as simple random sampling without replacement.

If the unit is replaced back before making the next draw the sampling plan is called as simple random sampling with replacement.

Stratified Random Sampling

When the population is heterogeneous with respect to the variable or characteristics under the study this sampling method is used. Stratification means division into

homogenous layers or groups. Stratified random sampling involves stratifying the given population into a number of sub-groups or sub-population known as strata.

The characteristics of stratified samples are as follows:

· The units within each stratum are as homogenous as possible.

· The differences between various strata are as marked as possible.

· Each and every unit in the population belongs to one and only one stratum.

The population can be stratified according to geographical, sociological or economic characteristics. Some of the commonly used stratifying factors are age, sex, income, occupation, education level, geographic area, economic status etc. To decide on the no.

of samples or items drawn from the different strata, will be wept proportional to the sizes of the strata.

Example: If pi represents the proportion of the population included in stratum 'i', and n represents the total sample size, then the number of elements selected from stratum i is (n - pi)

Example: Suppose we need a sample size of n = 30 to be drawn from a population of size N= 6000 which is divided into three strata of sizes N1 = 3000, N2 = 1800, N3= 1200.

Total population = 3000+1800+1200 = 6000

Hence using the proportional allocation, the sample size for different strata are 15, 9, and 6, which are proportionate to the strata sizes of 3000, 1800, and 1200.

Systematic Sampling

This sampling is a slight variation of simple random sampling in which only the first sample unit is selected at random while remaining units are selected automatically in a definite sequence at equal spacing from one another. This kind of sampling is

recommended only when if a complete and up to date list of sampling units is available and the units are arranged in a systematic order as alphabetical, chronological,

geographical etc.

Systematic sampling can be taken as an improvement over a simple random sampling since it spreads more evenly over the entire population. This method is one of the easier and less costly methods of sampling and can be conveniently used in case of large

population.

Cluster Sampling

If the total area of interest happens to be a big one, a convenient way in which a sample can be taken is to divide the area into a number of smaller non-overlapping areas and then to randomly select a number of these smaller areas.

In cluster sampling, the total population is divided into a number of relatively small sub divisions which are themselves clusters of still smaller units and some of these clusters are randomly selected for inclusion in overall sample. Cluster sampling reduces the cost

by concentrating surveys in clusters. But this type of sampling is less accurate than random sampling.

Multistage Sampling

It is a further development of the principle of cluster sampling. In case of investigating the working efficiency of nationalized banks in India, a sample of few banks may be taken for the purpose of investigation.

Here to select the banks as a first step, the main states in a country are selected from the states from which the banks to be included for the study will be selected. This represents the two stage sampling. Even further, from the district certain towns may be selected, from where the banks will be selected. This may represent three stages sampling.

Even thereafter, instead of taking census from all the banks in all the towns we have selected, once again banks may be selected randomly for the survey. Hence the random selection at all levels (various levels) is known as multistage random sampling design.

Sequential Sampling

This is one of the complex sampling designs. The ultimate size of sample in this technique is not fixed in advance but it is determined according to the mathematical decision rules on the basis of information yielded in the survey.

This method is adopted when sampling plan is accepted in context of Statistical Quality Control.

Example: When a lot is to be accepted or rejected on the basis of single sample, it is known as single sampling; when the decision is to be taken on the basis of two samples it is known as double sampling, and in case the decision is based on the more than two samples but the number of samples is certain and decided in advance, the sampling is known as multi sampling. In case when the number of samples is more than two but it is neither certain nor decided in advance, this type of system is often referred to as Sequential Sampling. So in case of Sequential Sampling, one can go on taking samples one after another as long as one desires to do so.

2. Non-probability Sampling