Sampling and Sampling distributions

Sampling is a technique to draw samples from a population, that is, Sampling is a process. The sampling distribution is a probability distribution of a statistic (such as mean, variance, proportion, etc.). This category contains posts about sampling and sampling distribution.

Probability and Non-Probability Sampling

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The fundamental methods of Probability and non-probability sampling are used for selecting a sample from a population in research studies. They differ in how they approach the selection process and the resulting generalizability of the findings. The non-probability sampling methods are valuable for initial research stages or specific situations, but for strong statistical inferences and generalizability, probability sampling is preferred.

In probability sampling, each unit of the population has a known (non-zero) probability of being included in the sample, and samples are selected randomly by using some random selection method. That’s why probability sampling may also be called random sampling. In probability sampling, the reliability of the estimates can be determined. In probability sampling, samples are selected without any interest. The advantage of probability sampling is that it provides a valid estimate of sampling error. Probability sampling is widely used in various areas such as industry, agriculture, business sciences, etc.

Types of Probability Sampling

Important types of probability sampling are

  • Simple Random Sampling
  • Stratified Random Sampling
  • Systematic Sampling
  • Cluster Sampling
Sample and Sampling

These sampling methods are capable of

  • Generalizability: Results can be statistically projected to the entire population.
  • Accuracy: Reduces bias, ensuring a representative sample.
  • Statistical Analysis: Allows for confidence intervals and hypothesis testing.

and are used in

  • Opinion polls
  • Market research
  • Government surveys (e.g., census)
  • Medical trials

Types of Non-Probability Sampling

In this sampling technique, samples are selected by personal judgment; due to this personal judgment in the selection of the sample, bias may be introduced, which makes the result unrepresentative. This sampling technique may also be called non-random sampling. The disadvantage of non-probability is that the reliability of the estimates cannot be determined.

The Non-Probability Samplings are:

  • Purposive sampling
  • Quota sampling
  • Judgment sampling
  • Snowball sampling
  • Convenience sampling

These sampling methods are:

  • Cost & Time Efficiency: Quicker and cheaper than probability sampling.
  • Exploratory Research: Useful for preliminary insights.
  • Hard-to-Reach Populations: Helps study niche or hidden groups.

and are widely used in

  • Pilot studies
  • Qualitative research (e.g., interviews)
  • Case studies
  • Social media surveys

Differences between Probability and Non-Probability Sampling

The difference between these two is that non-probability sampling does not involve random selection of objects, while in probability sampling, objects are selected by using some random selection method. In other words, it means that non-probability samples aren’t representative of the population, but it is not necessary. However, it may mean that non-probability samples cannot depend upon the rationale of probability theory.

In general, researchers may prefer probabilistic or random sampling methods over non-probabilistic sampling methods and consider them to be more accurate and rigorous.  However, in applied social sciences, for researchers, there may be circumstances where it is not possible to obtain sampling using some probability sampling methods. Even practical or theoretical, it may not be sensible to do random sampling. Therefore, a wide range of non-probability sampling methods may be considered in these circumstances.

FeatureProbability SamplingNon-Probability Sampling
SelectionRandomNon-random
BiasLowHigh
GeneralizabilityHigh (if done correctly)Low
Cost & EffortHighLow
Best ForQuantitative researchQualitative/exploratory research
Probability and Non-Probability Sampling

The choice between probability and non-probability sampling depends on the research question, resources available, and the desired level of generalizability.

  • Use probability sampling when the generalizability of findings to the population is crucial, and resources allow for random selection.
  • Use non-probability sampling when: You need a quick and easy way to gather initial insights, explore a topic, or a complete sampling frame is unavailable. However, be cautious about generalizing the results.
ApplicationNon-Probability SamplingProbability Sampling
GoalInitial insights, specific situationsGeneralizable Finding
Selection MethodConvenience, judgement basedRandom
GeneralizabilityLimitedHigh
ExamplePilot studies, focus groups, market research, case studiesPublic opinion polls, medical research

In summary, use probability sampling when you need statistically valid, generalizable results. Use non-probability sampling when quick, cost-effective insights are needed, or when studying specific groups.

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Sampling Basics and Objectives (2021)

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In this article, we will discuss the Sampling Basics. It is often required to collect information from the data. These two methods are used for collecting the required information.

  • Complete information
  • Sampling

Complete Information

This method collects the required information from every individual in the population. This method is used when it is difficult to draw some conclusion (inference) about the population based on sample information. This method is costly and time-consuming. This method of getting data is also called Complete Enumeration or Population Census.

Sampling Basics

What is Sampling?

Sampling is the most common and widely used method of collecting information. Instead of studying the whole population only a small part of the population is selected and studied and the result is applied to the whole population. For example, a cotton dealer picked up a small quantity of cotton from the different bales to know the quality of the cotton.

Sampling and Sampling Distribution

Purpose or objective of sampling

Two basic purposes of sampling are

  1. To obtain the maximum information about the population without examining every unit of the population.
  2. To find the reliability of the estimates derived from the sample, which can be done by computing the standard error of the statistic.

Advantages of sampling over Complete Enumeration

  1. It is a much cheaper method to collect the required information from the sample as compared to complete enumeration as fewer units are studied in the sample rather than the population.
  2. From a sample, the data can be collected more quickly and greatly save time.
  3. Planning for sample surveys can be done more carefully and easily as compared to complete enumeration.
  4. Sampling is the only available method of collecting the required information when the population object/ subject or individual in the population is destructive.
  5. Sampling is the only available method of collecting the required information when the population is infinite or large enough.
  6. The most important advantage of sampling is that it provides the reliability of the estimates.
  7. Sampling is extensively used to obtain some of the census information.
Sampling Basics and Objectives

This is all about Sampling Basics.

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For further reading visit: 

Sampling Theory and Reasons to Sample
Sampling Basics

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Standard Error 2: A Quick Guide

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Introduction to Standard Errors (SE)

Standard error (SE) is a statistical term used to measure the accuracy within a sample taken from a population of interest. The standard error of the mean measures the variation in the sampling distribution of the sample mean, usually denoted by $\sigma_\overline{x}$ is calculated as

\[\sigma_\overline{x}=\frac{\sigma}{\sqrt{n}}\]

Drawing (obtaining) different samples from the same population of interest usually results in different values of sample means, indicating that there is a distribution of sampled means having its mean (average values) and variance. The standard error of the mean is considered the standard deviation of all those possible samples drawn from the same population.

Size of the Standard Error

The size of the standard error is affected by the standard deviation of the population and the number of observations in a sample called the sample size. The larger the population’s standard deviation ($\sigma$), the larger the standard error will be, indicating more variability in the sample means. However, the larger the number of observations in a sample, the smaller the estimate’s SE, indicating less variability in the sample means. In contrast, by less variability, we mean that the sample is more representative of the population of interest.

Adjustments in Computing SE of Sample Means

If the sampled population is not very large, we need to make some adjustments in computing the SE of the sample means. For a finite population, in which the total number of objects (observations) is $N$ and the number of objects (observations) in a sample is $n$, then the adjustment will be $\sqrt{\frac{N-n}{N-1}}$. This adjustment is called the finite population correction factor. Then the adjusted standard error will be

\[\frac{\sigma}{\sqrt{n}} \sqrt{\frac{N-n}{N-1}}\]

Uses of Standard Error

  1. It measures the spread of values of statistics about the expected value of that statistic. It helps us understand how well a sample represents the entire population.
  2. It is used to construct confidence intervals, which provide a range of values likely to contain the true population parameter.
  3. It helps to test the null hypothesis about population parameter(s), such as t-tests and z-tests. It helps determine the significance of differences between sample means or between a sample mean and a population mean.
  4. It helps in determining the required sample size for a study to achieve the desired level of precision.
  5. By comparing standard errors of different samples or estimates, one can assess the relative variability and reliability of those estimates.
Standard Error

The SE is computed from sample statistic. To compute SE for simple random samples, assuming that the size of the population ($N$) is at least 20 times larger than that of the sample size ($n$).
\begin{align*}
Sample\, mean, \overline{x} & \Rightarrow SE_{\overline{x}} = \frac{n}{\sqrt{n}}\\
Sample\, proportion, p &\Rightarrow SE_{p} \sqrt{\frac{p(1-p)}{n}}\\
Difference\, b/w \, means, \overline{x}_1 – \overline{x}_2 &\Rightarrow SE_{\overline{x}_1-\overline{x}_2}=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}\\
Difference\, b/w\, proportions, \overline{p}_1-\overline{p}_2 &\Rightarrow SE_{p_1-p_2}=\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}
\end{align*}

Summary

The SE provides valuable insights about the reliability and precision of sample-based estimates. By understanding SE, a researcher can make more informed decisions and draw more accurate conclusions from the data under study. The SE is identical to the standard deviation, except that it uses statistics whereas the standard deviation uses the parameter.

FAQS about SE

  1. What is the SE, and how it is computed?
  2. What are the uses of SE?
  3. From which is the size of the SE affected?
  4. When will the SE be large?
  5. When will the SE be small?
  6. What will be the standard error for proportion?

For more about SE follow the link Standard Error of Estimate

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