# Application of Sampling Distribution Methods in Psychology

When conducting research, an important step is to ensure that the sample of the population is selected randomly and is representative of the entire population. However, the population is often very large. Therefore, statistics employ sampling techniques so that a reliable sample can be chosen. However, how do we eliminate variability from the sample? What is it called if we have picked more than one sample from a population to study different statistics? This article aims to explore these questions and others.

## What is Sampling Distribution?

Statistics employs various methods when it comes to sampling. The main aim of the sampling distribution is to decide something about the chosen population. We know that the size of the population is very large. Therefore, in order to study the population, we pick a subset of that population. We decide the size of the population, and it is selected randomly to eliminate bias in sampling. A statistical sample is, therefore, of size n. The probability distribution of a particular statistic procured from several samples is called a "sampling distribution." It could also be understood in terms of the distribution of frequencies of different statistical outcomes that could probably come from a population's statistics (such as the mean, median, or mode).

## How did Sampling Distribution Originate?

A sampling distribution occurs when a researcher gathers more than one random sample of a similar size from the desired population. The researcher makes sure that these samples are independent of each other. So if a particular individual is part of one sample, then it is optional that he cannot be part of the next sample drawn, and they have the same likelihood of appearing in the next sample.

The researcher calculates a statistic for each sample. For instance, if the researcher wants to find out the weight of bananas, he will pick five samples of 10 bananas each. He will calculate each group's mean (statistic) in the second step. Each sample will mostly produce a varying value or mean of bananas. The range that the researcher obtains is called the sampling distribution. In summary, a sampling distribution can be defined as a statistical distribution we get when we repeatedly draw samples from a larger population. In a larger population, sampling distribution gives us a range of likely outcomes for a particular statistic, such as the mean or median of a particular variable.

## What are the steps involved in Sampling Distribution?

Major steps are

• A researcher chooses a random sample from a larger population. For example, if the researcher wants to study height in adolescents, they select a random sample from a larger group of adolescents.

• The researcher calculates the mean height of adolescents.

• The researcher then collects another random sample from the group of adolescents and calculates the mean.

• This way, the average height from all the samples is plotted on a graph. This gives the researcher a sample distribution of the mean height of adolescents from a particular group. In this way, sample distributions for different statistics can be obtained.

Understanding how far or how to spread apart the statistics (mean in the above example) are from one another, and the given population gives us knowledge about how close the sample mean is to the population mean. When the sample size increases, the possibility of a standard error in the sampling distribution reduces.

## What are the types of Sampling Distributions?

Here are the types of sampling distribution in inferential statistics Here are the types of sampling distribution in inferential statistics

### Sampling distribution of mean

It is possible to calculate the average or mean of every sample chosen from the population. The researcher can then plot all the results as data points. The graph that comes out will be a normal distribution, and the center of this distribution will be the mean of the sampling distribution. This can be considered the average or mean of the entire population.

### Sampling distribution of proportion

When we want to know more about the proportions in a population, we use the sampling distribution of a proportion. The researcher would choose samples from the desired population to get a sample proportion. The average of all sample proportions calculated for each sample group becomes the proportion of the whole population.

### T-distribution

T-distribution is used when the researcher needs to become more acquainted with the chosen population or when the sample size needs to be bigger. This distribution helps estimate the population's average or mean through linear regressions or other statistical differences.

## Why is Sampling Distribution Important?

The sampling distribution is very helpful because the populations are mostly very large. It is not possible to conduct tests on the entire population, and sampling distribution helps in randomly selecting a subset from the entire population. In inferential statistics, sampling distribution helps manage large chunks of data easily. It helps in making inferences about the entire population. Understanding statistical inference is crucial because it allows people to comprehend the distribution of frequencies and what different outcomes look like inside a dataset.

## What is the Central Limit Theorem?

Apart from the center of the distribution and the spread of data points, it is challenging to comment on the shape of the sampling distribution. The central limit theorem can be applied to learn more about the shape of a sampling distribution. The central limit theorem aids in plotting the mean of the sample distribution. This theorem tells us that the more sample groups we use for our study, the closer we get to the bell-shaped curve for our distribution. In other words, having more sample groups reduces the distance between two points on a graph. The more sample groups you utilize, the less varied the sample group mean will be. The standard error decreases as the sample size grows. As a result, the sample distribution's center is near the population's real mean.

## Conclusion

In inferential statistics, it is not easy to study an entire population, and it is too large to study all at once. To resolve this issue, a researcher can draw a random sample or several sample groups to study a phenomenon. A process known as sampling distribution helps to study the variability among these samples. It is a probability distribution procured from larger samples taken from a specific population. The sampling distribution of a particular population is the spread of frequencies of various possible outcomes for a certain statistic regarding that population.

Updated on: 30-Dec-2022

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