What is Sampling Distribution and its Types in Statistics?

Sampling Distribution

 

Sampling Distribution in the field of statistics is a subtype of proportion distribution wherein a statistic is calculated by randomly analyzing samples from a given population. It is the distribution of samples in a population that leads to the revelation of data in numerous fields. 

 

Even though the sampling distribution does not include any sample that deviates far off from the population's mean value, the frequency distribution of sampling distribution often generates a normal distribution with maximum samples close to the population's mean value. 

 

(Must Read - 10 Types of Statistical Data Distribution Models) 

 

Let us find out more about this concept in the following segments and discover various aspects as well.

 

Understanding the concept

 

Ever heard about probability? Ever conjectured the possibility of an event? In statistics, probability is a major concept that has things like these covered. In this blog, we are going to understand Sampling Distribution, a concept of probability distribution in statistics. 

 

Sampling Distribution is a statistic that aims to conjecture a large number of samples obtained from a specific group of subjects repeatedly. In statistics, the probability is used for calculating the likely occurrence of a phenomenon. 

 

This is done by collecting samples from populations. While samples (value of the focus) are the main focus, in this case, populations (subjects) help us to procure them, and thus, both samples and populations are considered to be equally essential. 

 

A lot of data that is collected over time is included in studies that aim to calculate the probabilities of an event. This data is collected with utmost precision and care so that it leads to an effective result and does not hamper the statistics involved. 

 

(Also Read - Importance of Statistics and Probability in Data Science) 

 

Sampling Distribution can be concerned with almost any subject. Be it the weight of population or traits of animals, sampling distribution can cover almost anything and everything. Another dimension of this concept is the binomial distribution. 

 

The binomial distribution is defined as the calculation of the probability of success in a given population. For this, the population size is required to be large (almost 20 times the size of a sample) so that the successor can be conjectured by using a large number of samples. 

 

Defined as a concept that focuses on a statistic of sample statistics, sampling distribution involves more than one statistical value of a sample. Let us understand this with the help of a sampling distribution example. 

 

Example of Sampling Distribution

 

Suppose a researcher wishes to identify the average age of babies when they begin to walk. Instead of keeping a track of all the babies around the world, the researcher will select a total of 500 babies. 

 

The number of babies constitutes the population for this particular research. Now, the researcher will identify the age of babies when they begin to walk. Let us assume that 25% of the babies began to walk at the age of 1.5 years old. Another 30% of the babies began to walk at the age of 2 years old. 

 

This way, the researcher will calculate the actual mean of the sampling distribution of babies by picking a handful of samples. The sample mean (average of a sample) will be further calculated along with other sample means obtained from the same population. 

 

This is how Sampling Distribution is calculated. In sampling distribution, the standard deviation of the sampling distribution is regarded as the standard error that keeps decreasing with the increase of the sample size. 

 

Here is a step-by-step guide for you to create your own sampling distribution. Let's get started!

 

1. Choose a population and sample for this experiment.

2. Select a sample randomly out of the given population. 

3. Calculate the sample mean of this group. 

4. Follow the above steps for obtaining a number of sample means out of the same population.

5. Generate frequency distribution: Plot the sample means of the statistic on a graph sheet or tabulate the data. The final graph will demarcate your sample distribution. 

 

(Also read: Different types of Statistical techniques)

 

 

Significance of Sampling Distribution

 

The primary purpose of Sampling Distribution is to establish representative results of small samples of a comparatively larger population. 

 

This helps researchers and analysts to dig deep into the population, get a closer look into small groups of the population, and create generalized results based on the same. The significance of sampling distribution is immense in the field of statistics. 

 

1. Firstly, the concept of sampling distribution provides accuracy. For any population being studied, it is important for a researcher to collect all possible samples to generate an inclusive and effective result. 

 

Sampling Distribution allows one to do that by collecting all possible samples and developing the sample means to give the best possible result.

 

2. Secondly, the repeated collection of samples from the same set of subjects leads to consistency. What's more, the standard error also allows a researcher to reflect on the deviation and thus identify the unbiased nature of the sampling distribution altogether. 

 

3. Thirdly, the variability of the sampling distribution is immensely significant as it reflects the inclusion of numerous samples from the same set of subjects. This leads to an almost symmetric graph. The variability also ensures that all possible samples are collected from the population. 

 

(Must read: Statistical data analysis)

 

 

Types of Sampling Distribution

 

As we have already discovered about Sampling Distribution, we will now learn about the various types of Sampling Distribution in statistics. To begin with, there are 3 types of Sampling Distribution. They are as follows-

---

Types of Sampling Distribution

---

1. Sampling Distribution of Mean

 

The first and foremost type of sampling distribution is of the mean. This type focuses on calculating the mean average of all sample means which then lead to sampling distribution. 

 

The average of every sample is put together and a sampling distribution mean is calculated which reflects the nature of the whole population.

 

 With more samples, the standard deviation decreases which leads to a normal frequency distribution or a bell-shaped curve on the graph. 

 

 

2. Sampling Distribution of Proportion

 

When it comes to the second type of Sampling Distribution, the population's samples are calculated to obtain the proportions of a population. Herein, the mean of all sample proportions is calculated, and thereby the sampling distribution of proportion is generated. 

 

As the proportion of a population is defined by a part of the population that possesses a certain attribute, the sampling distribution of proportion aims to achieve a mean of all sample proportions that involve the whole population. 

 

(Related blog: Types of data in statistics)

 

 

3. T-Distribution

 

Third of all, T-Sampling Distribution is considered to involve a small size of the population that gives about no information about standard deviation. Under this type of sampling distribution, the population size is very small that, in turn, leads to a normal distribution. 

 

The frequent distribution in this type is the most near to the mean of the sampling distribution. Only a handful of samples are far off from the mean value of the whole population. 

---

T-Distribution curve

---

One of the characteristics of this T-distribution is that it cannot work well with a population that is large in size. Therefore, this type works well with only a small-sized population. 

 

 

Related Terminologies

 

• Probability Distribution - In statistics, probability distribution generates the probable occurrences of different outcomes by calculating statistics in a given population. 

 

It is a mathematical representation of a probable phenomenon among a set of random events. Sampling Distribution is a type of Probability Distribution. 

 

• Frequency Distribution - Sampling Distribution results in frequency distribution which is either a graphical representation or a tabular representation of sample outcomes obtained from a given population. 

 

• Binomial Distribution - Binomial Distribution indicates the distribution of total successes that are probable in a given population. It is used in order to label an outcome as either a failure or a success. One of the parameters of binomial distribution is that it best works with a large-sized population. 

 

• Data Distribution - In statistics, data Distribution refers to the listing of data of a given population. It simply represents the distribution of data that helps in further analysis. Some of the Data Distribution types are Binomial Distribution and Normal Distribution 

 

• Standard Error - A statistical concept, standard error demarcates the standard deviation or variance of sample mean from the actual mean in the sampling distribution. It represents the accuracy of a sample mean as compared to the actual mean. Frequency distribution is helpful for standard error calculation. 

 

(Must catch: T-test vs Z-test)

 

Wrapping Up

 

To wrap up, Sampling Distribution is a statistical concept that defines the distribution of a sample statistic throughout a given population. A type of probability distribution, this concept is often used to obtain accurate data from a large population that is divided into a number of samples that are randomly selected. 

 

(Recommended blog: Types of statistical analysis)

 

This concept is further classified into 3 types - Sampling Distribution of mean, proportion, and T-Sampling. Sampling Distribution is immensely significant for generating accurate data that can otherwise be hampered if repeated sampling does not take place. Perhaps this concept helps in randomly selecting samples and calculating a statistic from there on since it helps one to try out the highest possible sample outcomes.