Category : Sampling

In life, you can’t always get what you want, but if you try sometimes, you get what you need. In what concerns to statistics, this is also true. After all, while you may want to know everything about a population or group, in most cases, you will need to deal with approximations of a smaller group. In the end, you need to hope that the answer you get is not that far from the truth. 

The difference between the truth of the population and the sample is called the sampling variability.

When you are looking for a quick and simple definition for sampling variability, then you can state that it is the extent to which the measures of a sample differ from the measure of the population. However, there are certain details that you need to keep in mind. 

Looking At The Parameters And Statistics

When you are looking at measures that involve a population, you need to know that it is incredibly rare to measure them. For example, you just can’t assume that you can measure the mean height of all Americans. Instead, what you need to do is to take a random selection of Americans and then actually measure their mean height. 

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Knowing this mean height means that you already have a parameter. So, you can then say that a parameter is just the value that refers to the population like the mean, deviation, among others, that you just don’t know. 

Notice that it is impossible to measure a parameter; what you do have is a possible estimate using statistics. This is why a measure that refers to a sample is called a statistic. A simple example is the average height of a random sample of Americans. As you can easily understand, the parameter of the population never changes because there is only one population. But a statistic changes from sample to sample. 

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What is Sampling Variability?

If you recall, sampling variability is the main purpose of this blog post. However, we needed to take a look at the previous concepts (statistics and parameters) to ensure that you understand what sampling variability is. 

Simply put, the sampling variability is the difference between the sample statistics and the parameter. 

Whenever you are looking at a measure, you can always assume that there is variability. After all, variability comes from the fact that not every participant in the sample is the same. For example, the average height of American males is 5’10” but I am 6’2″. I vary from the sample mean, so this introduces some variability.

Generally, we refer to the variability as standard deviation or variance.

The Uses Of Sampling Variability

As you can imagine, you can use sampling variability for many different purposes and it can be incredibly helpful in most statistical tests. After all, the sampling variability gives you a sense of different the data are. While you may not be in the average height since you may be taller, the truth is that there are also people who are shorter than the average height. And with sampling variability, you can know the amount of difference between the measured values and the statistic. 

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In case the variability is low, it means that the differences between the measured values and statistics are small, such as the mean. On the other hand, if the variability is high, it means that there are large differences between the measured values and the statistics. 

As you probably already figured out, you are always looking for data that has low variability. 

Sampling variability is used often to determine the structure of data for analysis. For example, principal component analysis analyzes the differences between the sampling variability of specific measures to determine if there is a connection between variables.

Sampling is crucial in statistics. After all, samples are just parts of a population. 

Let’s say that you have information about 100 people out of 10,000 people. The 10 people represent your sample while the 10,000 represents the population. So, you can then use this sample to make some assumptions about the behavior of the entire population. 

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While this may seem a very simple process, the truth is that it isn’t. The reality is that you need to come up with a sample that has the right size. It can’t be too big or too small. However, the problems don’t end here. You then need to decide about the technique that you’re going to use to collect the sample from the population. 

In order to do this, you have different methods at your disposal:

#1: Probability Sampling: 

This sampling process simply uses randomization to select your sample members. 

#2: Non-Probability Sampling:

This sampling process isn’t random; it is based on the researcher. 

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Sampling Types

The reality is that you have many different sampling types. One of the things that you need to keep in mind is that these may include taking a sample with or without replacement. 

Here are some of the most common sampling types that you can use: 

#1: Bernoulli Samples:

These include independent Bernoulli trials on the population elements. With these trials, you will be able to determine who belongs to your sample and who doesn’t. However, all elements of the population have the same odds or chances of getting into the sample. 

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#2: Cluster Samples:

As you can easily imagine by its name, this sampling types divides the population into clusters or groups. After that, you will need to have a random sample chosen from these clusters. This sampling type is usually used when the researcher knows the population groups or subsets but he doesn’t know the individuals in the population. 

#3: Systematic Sampling:

In this case, you can choose the sample elements from an ordered frame. 

#4: SRS: 

With the SRS sampling type, you will choose each one of the elements of your sample completely randomly. 

#5: Stratified Sampling: 

In this case, you will sample each subpopulation independently. 

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How To Tell The Difference Between Different Sampling Methods

Step #1: 

The first thing you need to do is to discover if the study sampled from individuals. This may show you that this sampling was made using the random method or the systematic sampling method. 

Step #2: 

You will then need to figure out if the study picked groups of participants. When you have a large number of people, it may be easier to use the simple random sampling. 

Step #3: 

Determine if the study that you are looking at includes data from more than one defined group. Some real-life examples could be a study about renters and homeowners, democrats and republicans, country folks and city dwellers, among so many others. 

Now, just look at the data that you have. When you can see that you have data about the individuals in the groups, you have access to stratified data. So, you will need to perform random sampling. On the other hand, if you see that you only have information about the group in general, then you need to treat it as a cluster sample.  

Step #4: 

Finally, you will need to know if it was hard or easy to get the sample.