# Sampling and Estimation

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Sampling Methods

Sampling method refers to the way that observations are selected from a population to be in the sample for a sample survey. Various types of sampling method are discussed

• Population Parameter vs. Sample Statistic – The reason for conducting a sample survey is to estimate the value of some attribute of a population. A population parameter is the true value of a population attribute.
• Probability vs. Non-Probability Samples – As a group, sampling methods fall into one of two categories – probability and non-probability samples. With probability sampling methods, each population element has a known (non-zero) chance of being chosen for the sample.

Probability Sampling Methods

The main types of probability sampling methods are simple random sampling, stratified sampling, cluster sampling, multistage sampling, and systematic random sampling. The key benefit of probability sampling methods is that they guarantee that the sample chosen is representative of the population. This ensures that the statistical conclusions will be valid.

Simple random sampling. Simple random sampling refers to any sampling method that has the following properties.

• The population consists of N objects.
• The sample consists of n objects.
• If all possible samples of n objects are equally likely to occur, the sampling method is called simple random sampling.

There are many ways to obtain a simple random sample. One way would be the lottery method. Each of the N population members is assigned a unique number.

Stratified sampling. With stratified sampling, the population is divided into groups, based on some characteristic. Then, within each group, a probability sample (often a simple random sample) is selected. In stratified sampling, the groups are called strata.

As an example, suppose we conduct a national survey. We might divide the population into groups or strata, based on geography – north, east, south, and west. Then, within each stratum, we might randomly select survey respondents.

Cluster sampling. With cluster sampling, every member of the population is assigned to one, and only one, group. Each group is called a cluster. A sample of clusters is chosen, using a probability method (often simple random sampling). Only individuals within sampled clusters are surveyed.

Note the difference between cluster sampling and stratified sampling. With stratified sampling, the sample includes elements from each stratum. With cluster sampling, in contrast, the sample includes elements only from sampled clusters.

Multistage sampling. With multistage sampling, we select a sample by using combinations of different sampling methods.

For example, in Stage 1, we might use cluster sampling to choose clusters from a population. Then, in Stage 2, we might use simple random sampling to select a subset of elements from each chosen cluster for the final sample.

Systematic random sampling. With systematic random sampling, we create a list of every member of the population. From the list, we randomly select the first sample element from the first k elements on the population list. Thereafter, we select every kth element on the list.

This method is different from simple random sampling since every possible sample of the elements is not equally likely.

Statistical Sampling

Statistical sampling techniques are the strategies applied by researchers during the statistical sampling process.

Concerns in Statistical Sampling

Representativeness – This is the primary concern in statistical sampling. The sample obtained from the population must be the representative of the same populations.

This can be accomplished by using randomized statistical sampling techniques or probability sampling like cluster sampling and stratified sampling.

Practicability – Practicability of statistical sampling techniques allows the researchers to estimate the possible number of subjects that can be included in the sample, the type of sampling technique, the duration of the study, the number of materials, ethical concerns, availability of the subjects/samples, the need for the study and the amount of workforce that the study demands.

All these factors contribute to the decisions of the researcher regarding to the study design.

Sampling Risks – There are two types of sampling risks, first is the risk of incorrect acceptance of the research hypothesis and the second is the risk for incorrect rejection. These risks pertain to the possibility that when a test is conducted to a sample, the results and conclusions may be different from the results and conclusions when the test is conducted to the entire population.

The risk of incorrect acceptance pertains to the risk that the sample can yield a conclusion that supports a theory about the population when it is actually not existent in the population. On the other hand, the risk of incorrect rejection pertains to the risk that the sample can yield a conclusion that rejects a theory about the population when in fact, the theory holds true in the population.

Random Sampling

A random sample is obtained by using methods such as random numbers, which can be generated from calculators, computers, or tables. In random sampling, the basic requirement is that, for a sample of size n, all possible samples of this size have an equal chance of being selected from the population.

• The first method is to number each element of the population and then place the numbers on cards. Place the cards in a hat or fishbowl, mix them, and then select the sample by drawing the cards.
• The second and preferred way of selecting a random sample is to use random numbers.

The theory behind random numbers is that each digit, 0 through 9, has an equal probability of occurring. That is, in every sequence of 10 digits, each digit has a probability of occurring. This does not mean that in every sequence of 10 digits, you will find each digit. Rather, it means that on the average, each digit will occur once. For example, the digit 2 may occur 3 times in a sequence of 10 digits, but in later sequences, it may not occur at all, thus averaging to a probability of.

To obtain a sample by using random numbers, number the elements of the population sequentially and then select each person by using random numbers.

Sampling Bias

Bias in sampling is the tendency for samples to differ from the corresponding population in some systematic way. Bias can result from the way in which the sample is selected or from the way in which information is obtained once the sample has been chosen. The most common types of bias encountered in sampling situations are selection bias, measurement or response bias, and non-response bias.

Selection bias (sometimes also called undercoverage) is introduced when the way the sample is selected systematically excludes some part of the population of interest.

Measurement or response bias occurs when the method of observation tends to produce values that systematically differ from the true value in some way. This might happen if an improperly calibrated scale is used to weigh items or if questions on a survey are worded in a way that tends to influence the response.

Other things that might contribute to response bias are the appearance or behavior of the person asking the question, the group or organization conducting the study, and the tendency for people not to be completely honest when asked about illegal behavior or unpopular beliefs.

Non-response bias occurs when responses are not obtained from all individuals selected for inclusion in the sample. As with selection bias, non-response bias can distort results if those who respond differ in important ways from those who do not respond. Although some level of non-response is unavoidable in most surveys, the biasing effect on the resulting sample is lowest when the response rate is high. To minimize non-response bias, it is critical that a serious effort be made to follow up with individuals who do not respond to an initial request for information.

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