In this article, you will discover the differences between **point estimates** and **confidence intervals**. If you have little statistical experience, you will tend to observations based on **point estimates** (without even knowing it). On the other hand, if you are experienced, or simply want to get better at statistics, you’ll prefer the bigger picture. That’s when you’ll realize that **confidence intervals** actually have an edge over **point estimates**.

So what’s this **point estimate** vs **confidence interval estimate** distinction about?

First, let’s introduce the concept of an **estimator. **An **estimator** of a population parameter an approximation depending solely on sample information.

A specific value is called an **estimate**.

## The Two Types of Estimates: Point Estimate and Confidence Interval Estimate

There are two types of **estimates** – **point estimates** and **confidence interval estimates**.

A **point estimate** is a single number. Whereas, a **confidence interval**, naturally, is an interval.

The two are closely related. In fact, the **point estimate** is located exactly in the middle of the **confidence interval**. However, **confidence intervals** provide much more information and are preferred when making inferences.

There are a few **estimates** which you may have seen already.

The **sample mean**, ** x bar**, is a

**point estimate**of the

**population mean**

**! Moreover, the sample**

*mu***variance**

**is an**

*S*^{2}**estimate**of the population

**variance**:

**.**

*sigma*^{2}## The Two Properties of Different Estimators: Bias and Efficiency

There may be many **estimators** for the same variable. However, they all have two properties: *bias* and *efficiency*.

We will not prove them as the mathematics associated is out of the scope of our tutorials. However, you should have an idea about the concepts.

**Estimators** are like judges – we are always looking for the most **efficient unbiased estimators**.

**Biased and Unbiased Estimators**

An **unbiased estimator** has an expected value equal to the population parameter.

**Providing an Example**

Let’s think of a **biased estimator** to explain that point. What if somebody told you that you will find the average height of Americans by:

- Taking a sample
- Finding its
**mean** - And then adding 1 foot to that result.

So, the formula is **x bar** + 1 **foot**.

Well, I hope you won’t trust them. They gave you an **estimator**, but a **biased** one. It makes much more sense that the average height of Americans is approximated just by the **sample mean**. We say that the bias of this **estimator** is 1 foot.

**Efficient Estimators**

Let’s move onto efficiency!

The most **efficient estimators** are the ones with the least variability of outcomes. It is enough to know that most **efficient** **means**: the **unbiased estimator** with the smallest **variance**.

## What’s the Difference Between Estimators and Statistics?

A final note worth making is about the difference between **estimators** and **statistics**. The word ‘*statistic’* is the broader term. A **point estimate** is a *statistic*.

*Author’s note: Fancy statistics? You can learn more in our tutorials Exploring the OLS Assumptions, Measuring Explanatory Power with the R-squared, Central Limit Theorem, and Measures of Variability.*

## What’s the Disadvantage of the Point Estimator?

**Point estimators** are not very reliable, as you can guess. Imagine visiting 5% of the restaurants in London and saying that the average meal is worth 22.50 pounds.

You may be close, but chances are that the true value isn’t really 22.50 but somewhere around it. When you think about it, it’s much safer to say that the average meal in London is somewhere between 20 and 25 pounds. In this way, you have created a **confidence interval** around your **point estimate** of 22.50!

**What’s the Advantage of the Confidence Interval?**

A **confidence interval** is a much more accurate representation of reality. However, there is still some uncertainty left which we measure in **levels of confidence**. So, getting back to our example, you may say that you are 95% confident that the population parameter lies between 20 and 25 quid.

**Side note:** Keep in mind that you can never be 100% confident unless you go through the entire population!

And there is, of course, a 5% chance that the actual population parameter is outside of the 20 to 25 pounds range.

We’ll see that if the sample we have considered deviates significantly from the entire population.

**The Level of Confidence**

There is one more ingredient needed: the **level of confidence**. It is denoted by: 1 – ** alpha**, and is called the

**confidence level of the interval**.

** Alpha** is a value between 0 and 1.

For example, if we want to be 95% confident that the parameter is inside the interval, ** alpha** is 5%.

If we want a higher confidence level of, say, 99%, ** alpha** will be 1%.

## Point Estimate and Confidence Interval Formula

The formula for all **confidence intervals** is: **FROM** the **point estimate** – the reliability factor * the **standard error** **TO** the **point estimate** + the reliability factor * the **standard error**.

We know what the **point estimate** is – values like ** x bar** and

**. We have also covered what the**

*s bar***standard error**is.

## The Relationship Between Confidence Interval and Point Estimate

Now, we will go over the **point estimates** and **confidence intervals** one last time.

Imagine that you are given a dataset with a **sample mean** of 10. In this case, is 10 a **point estimate** or an **estimator**? Of course, it is a **point estimate**. It is a single number given by an **estimator**. Here, the **estimator** is a **point estimator** and it is the formula for the **mean**.

Now, about the relation between a **confidence interval** and a **point estimate**. The **point estimate** is simply the midpoint of the **confidence** **interval**.

*For more on mean, median and mode, read our tutorial Introduction to the Measures of Central Tendency. *

## Point Estimate vs Confidence Interval

In conclusion, there is one main factor which you should keep in mind when deciding which one to use. And that is, whether or not you want to be as accurate as possible. A **confidence interval** will provide valid result most of the time. Whereas, a **point estimate** will almost always be off the mark but is simpler to understand and present.

Now, if you want to learn something new related to statistics, but you are tired of all the numbers and calculations, we have just the right thing for you. Check out Introducing the Normal Distribution and Examples of Different Distributions. Then figure out what the **Student’s t distribution** is all about by diving into our tutorial.

The article first appeared on: https://365datascience.com/point-estimates-confidence-intervals/