4th Chapter Sampling

SamplingStatistical-method-of obtainingrepresentativedataor observations from agroup(lot,batch,population, oruniverse).

Definition of 'Sampling

A process used in statistical analysis in which a predetermined number of observations will be taken from a larger population. The methodology used to sample from a larger population will depend on the type of analysis being performed, but will include simple random sampling, systematic sampling and observational sampling. The sample should be a representation of the general population.

Meaning Of Sampling:-

Sampling methods are used to select a sample from within a general population. Proper sampling methods are important for eliminating bias in the selection process. They can also allow for the reduction of cost or effort in gathering samples. Common methods of sampling include simple random sampling (completely random selection from the population), systematic sampling (ordering the population and selecting at regular intervals),

Contd. stratified sampling (splitting the population into categories and randomly selecting from within each category), matched random sampling (population is divided into pairs based on a criterion and then randomly assigned to groups), and panel sampling (applying the same test over time to randomly selected groups).

Needs for SamplingIn order to carryout primary research it is necessary to use sampling.This is because it would be impossible to ask every single customer or prospective customer.Sampling involves selecting a few peoples to interview, and so it is important that they are representative of the market being looked atThe Normal Distribution is a statistical model which is often used to show why sampling is necessary.

Aims of SamplingWe usually sample because we have neither the time nor the money to collect information about the entire population in which we are interested. Before continuing it will help to define samples and populations more carefully.Population:-A group that includes all the cases (individuals, objects, or groups) in which the researcher is interested. SampleSampling:-A relatively small subset from a population.

Aims of samplingReduces cost of research (e.g. political polls)Generalize about a larger population (e.g., benefits of sampling city r/t neighbourhood)In some cases (e.g. industrial production) analysis may be destructive, so sampling is needed

ProbabilityProbability: what is the chance that a given event will occur? Probability is expressed in numbers between 0 and 1. Probability = 0 means the event never happens; probability = 1 means it always happens.The total probability of all possible event always sums to 1.

Sample or PopulationWe give different names to statistical measures depending on whether they refer to a sample or a population.ParameterA measure (for example, mean or standard deviation) used to describe a population distribution. StatisticSamplingA measure (for example, mean or standard deviation) used to describe a sample distribution. This distinction is easy to remember if you keep the initial letter of each word in mind:Population:ParameterSample:StatisticThe following figure (which is also Figure 7.1 on page 198 in the textbook) graphically conveys the distinction between samples and populations.

What is a census (complete enumeration)?Acensusis a study of everyunit, everyone or everything, in a population.It is known as acomplete enumeration, which means a complete count.

Census v/s Sampling1.Each and every unit of the population is studied.2.Requires large amount of finance, time and labour.3.Results are quite reliable.4.It is more suitable if population is heterogeneous in nature.5.It cannot be used when part of the population is missing.

1.Only few units of the population studied.2.Relatively less amount of finance, till labour is required.3.Results are less reliable.4.It is more suitable if population homogeneous in nature.5.It can be used, if part of the population is missing.

Characteristics of a Good SampleIn a field study due to time and cost involved, generally, only a section of the population is studied. These respondents are known as the sample and are representative of the general population or universe. A sample design is a definite plan for obtaining a sample from a population. It refers to the technique or the procedure for obtaining a sample from a given population.

Following are the characteristics of good sample design:1.Sample design should be a representative sample: A researcher selects a relatively small number for a sample from an entire population. This sample needs to closely match all the characteristics of the entire population. If the sample used in an experiment is a representative sample then it will help generalize the results from a small group to large universe being studied.2.Sample design should have small sampling error: Sampling error is the error caused by taking a small sample instead of the whole population for study. Sampling error refers to the discrepancy that may result from judging all on the basis of a small number. Sampling error is reduced by selecting a large sample and by using efficient sample design and estimation strategies.

3.Sample design should be economically viable:Studies have a limited budget called the research budget. The sampling should be done in such a way that it is within the research budget and not too expensive to be replicated.4.Sample design should have marginal systematic bias: Systematic bias results from errors in the sampling procedures which cannot be reduced or eliminated by increasing the sample size. The best bet for researchers is to detect the causes and correct them.5. Results obtained from the sample should be generalized and applicable to the whole universe: The sampling design should be created keeping in mind that samples that it covers the whole universe of the study and is not limited to a part.

Principles of SamplingSampling is a process of taking a few units from a target population, analyzing the sample data and making conclusion about the population. with the help of probability sampling estimate of population mean or other parameter can be made with considerable precision.the branch of statistics dealing with this activity is called sampling theory.there are two important principles on which the theory of sampling is based1.principle of statistical regularity; and2.principle of inertia of large numbers

Principles of Statistical Regularity

The principle of statistical regularity is bases on the statistical theory of probability. King writes the law of statistical regularity lays down that a moderately large number of items chosen at random form a large group are almost sure on the average to possess the characteristic of the large group.

Contd...This principle states that when a sample is chosen at random, it is likely to possess almost the same characteristics and qualities to the universe. The term random means that each and every unit should have an equal chance of being included in the made by deliberate exercise of ones discretion. A sample selected at random would represent the unversed, if this method is followed, then it is possible to depict the attributes of the whole by studying a part of it.

Principle of Inertia of Large NumbersIt is actually derived from the principle of statistical regularity. According to it as sample size increases, results would be more reliable.

Large numbers are relatively more stable in their characteristics than small numbers. It does not mean the variation in large numbers is not much. It is there; but it is much less than what it is in small numbers.

*Contd....For example, if we toss a coin ten times it is quite likely that we may get 7 heads and 3 tails; but if we toss it 100 times, results would be more dependable and we may get say 60 heads and 40 tails. If the coin is tossed 1000 times, the likelihood is that the number of heads and tails would be very close to each other. Thus, larger the sample size, the more dependable are the results.

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*Simple RandomA randomly selected sample from a larger sample or population, giving all the individuals in the sample an equal chance to be chosen. In a simple random sample, individuals are chosen at random and not more than once to prevent a bias that would negatively affect the validity of the result of the experiment.

*Systematic samplingA method of choosing a random sample from among a larger population. The process of systematic sampling typically involves first selecting a fixed starting point in the larger population and then obtaining subsequent observations by using a constant interval between samples taken. Hence, if the total population was 1,000, a random systematic sampling of 100 data points within that population would involve observing every 10th data point.

*stratified random sampling,A method of sampling that involves the division of a population into smaller groups known as strata. In stratified random sampling, the strata are formed based on members' shared attributes or characteristics. A random sample from each stratum is taken in a number proportional to the stratum's size when compared to the population. These subsets of the strata are then pooled to form a random sample.

*Cluster samplingMultistage sampling is a complex form of cluster sampling. Cluster sampling is a type of sampling which involves dividing the population into groups (or clusters). Then, one or more clusters are chosen at random and everyone within the chosen cluster is sampled.

*Convenience samplingA statistical method of drawing representative data by selecting people because of the ease of their volunteering or selecting units because of their availability or easy access. The advantages of this type of sampling are the availability and the quickness with which data can be gathered. The disadvantages are the risk that the sample might not represent the population as a whole, and it might be biased by volunteers.

Convenience sampling is a non-probability sampling technique where subjects are selected because of their convenient accessibility and proximity to the researcher.

*Snoball samplingIn sociology and statistics research, snowball sampling is a technique for developing a research sample where existing study subjects.

*Quota samplingA sampling method of gathering representative data from a group. As opposed to random sampling, quota sampling requires that representative individuals are chosen out of a specific subgroup. For example, a researcher might ask for a sample of 100 females, or 100 individuals between the ages of 20-30.