With all the letters used in statistics, it is easy to become confused with all the variables and what they actually mean. To make matters even more confusing, the same letter is used to denote several variables.

If you are looking for a clear explanation for what n is in statistics then you are in the right place. Here is what it all means:

## What Does n Represent in Statistics?

**In statistics, n refers to the size of the sample that is chosen from within a population – it is meant to serve as a representation of a population as a whole – when there are samples from more than one population, the denotation will be n _{1}, n_{2}, etc**.

## What Function Does n Serve in Statistics?

n is the sample that is taken from within a population. The population, as a whole, is denoted by N. So, what is the function of n in statistics?

Well, n represents a certain percentage of the population for a survey or an experiment.

To explain this a little better, let’s imagine that a group of people would like to discover what the most popular brand of coffee is within the state of Massachusetts. Now, the combined number of coffee drinkers within the state would be the population – or N.

However, most surveyors or researchers don’t have the time, money, or resources to question every single coffee drinker in the region. This population is likely to be in a neighborhood of several million.

Due to this, the researchers will often choose a sample of the population. They may decide to choose the three cities with the highest population and interview those individuals. This would be the sample size or n.

In some instances, there is just one sample size chosen from one population. In this case, the sample size would be denoted by n.

In case each sample size comes from a different population, then each sample would be denoted by n_{1}, n_{2}, etc.

## What is the Difference Between n and N, p and P?

When the same letter or a few different letters are used over and over again, it can be rather confusing for students. Do these mean the same thing? Or, do they denote separate elements?

Well, as already mentioned, N represents an entire population. n, on the other hand, represents the sample size – this is a specific portion of the population.

Now, to make matters a bit more confusing, sometimes, the population and the sample size are the same. Borrowing from the above example, the researchers may choose to actually take a survey from every coffee drinker in Massachusetts.

In this case, the sample size is the population. When this happens, N denotes both the population as well as the sample size.

Then, where do P and p come in? What are these values and how do they differ?

In most instances, p refers to the p-value. This denotation can be a bit more difficult to understand, but here is the gist:

Statistical experiments have a null hypothesis – this is the belief that there is no relationship between your variables of interest. Now, the p-value lets you know the probability of the null hypothesis being true or false.

For instance, let’s imagine you were given a p-value of 0.05. This means that there is a 5 percent chance of the null hypothesis being true. As you can see, the probability of this being the case is unlikely.

On the other hand, if you had a p-value of 0.95, though, this would mean that there is a 95 percent chance of the null hypothesis being true. In all likelihood, it would ensure that the null hypothesis has to be accepted.

For the most part, p and P can refer to the same thing. However, as far as the p-value goes, it is best to denote it as p.

In some instances, P may refer to probability. This is the likelihood of a particular event occurring given a certain set of circumstances.

This is typically written as P(A), P(B), though, to refer to the exact event for which the probability is being calculated.

## What are the General Techniques for Finding n?

If you are dealing with a smaller population for your research, then your top option may be as simple as taking a consensus. You simply have to ask your population or sample size a series of questions to gather data points for a certain topic.

In case someone else has already done research on the topic you are studying, a sample may already be available to you. You may be able to find these samples on your academic database, allowing you easy access to your sample size.

The only issue here is that there is a risk of inaccuracy regarding sample size. Since you can’t confirm the numbers for yourself, you will have to take them on blind faith. As a result, errors may affect every step of the process.

In the event that your area of study is generic, then you may want to look for a clinical study relating to the subject matter. You are likely to find a table of the sample size and you can use this for your calculations.

Finally, you have the option of using a sample calculator. These are available online. Some of these calculators are fairly simple and generic. Others, are more specialized and have more complex features.

## What are the Formulas for Finding n?

Your other route to finding the sample size is to use a formula. Here are the most popular options available to you:

### Cochran’s Formula

This is meant to be used for large populations. This formula allows you to calculate an ideal model size based on a chosen level of precision, confidence level, and an estimated proportion of the necessary attribute within a population.

It looks like this:

n_{0 }= Z^{2}pq/e^{2}

Here, e is the desired level of precision or the margin of error, p is the estimated proportion of the population, and q is 1 – p.

### Yamane’s Formula

This formula uses fewer variables, here it is:

n = N/ 1 + N (e)^{2}

Here, e is the precision level and N is equal to the population size.

### Finding a Sample Size Using Confidence Level and Width

In some instances, you know the confidence level you are dealing with as well as the width, but you don’t know the population standard deviation. In this case, you should follow these steps:

Step 1:

Divide the confidence level by 2. This will give you the z score.

Then, divide the given width by 2. This will give you a margin of error.

Step 2:

For p̂, use the given percentage. If this hasn’t been provided assume that it is 0.5.

For q̂, calculate with 1 – p̂

Multiply p̂ by q̂

Step 3:

Divide the z score by the margin of error.

Step 4

Square the answer that you get when you divide the z score by the margin of error.

Step 5:

Multiply Step 2 with Step 4

This gives you the number of people that you have to survey.

## What is n in Statistics?

n in statistics refers to the sample size – this is a particular portion of the population based on certain factors – the sample size is meant to represent a population in surveys, research experiments, etc., and can be an accurate representation.