degrees of freedom

If there is something that I could point to that people have asked me many times, then hands down, it has to be degrees of freedom.

This is not the freedom that you are going to enjoy. Instead, it is a concept that is related to statistics. And the meaning of the phrase also changes from time to time or from context to context. It is a topic that can get difficult to understand. That is why I am trying to be as explanatory as possible with this one.

If you are trying to understand the concept of degrees of freedom, then hop onto your seats, and let’s start with the journey! Scroll down to learn more…

Degrees Of Freedom: What Is It?

What Is Degrees of freedom

To speak to the point, the phrase’ degrees of freedom’ is used in statistics to refer to the maximum number of values that are free to vary in a given calculation.

It can also be defined as the least or the minimum number of coordinates that are free to be independent and vary in a given equation without breaking the constraints of the equation. In other words, the degree of freedom (DF) indicates the minimum number of times the values involved are free to vary in a statistical equation or calculation. 

The first question that many can ask is how that can be determined, or how does that work? Want to know how to calculate degrees of freedom? Keep reading to learn more.

Calculating Degrees Of Freedom

Calculating Degrees Of Freedom

In order to understand that, you need to first take a look at this example.

Suppose you have 7 outfits that you have decided to wear for the 7 days of the week. So on the first day, you have the freedom to choose any of the outfits that you want from the set. After you have selected the outfit, you will see that you have 6 options left for the remaining days.

The options keep decreasing as you approach the end of the week.

Even on the 6th day of the week, you have the freedom to choose from 2 sets of clothes or outfits. However, you do not have any option left on the last day. You will have to wear the only outfit remaining. You do not have the freedom this time.

This means that as the number of days reached the end, the number of times you had the freedom to choose your options also kept decreasing.

Now think of this situation as something in the world of statistics.

If there is a set that has 20 values, the summation of all the 20 values must be equal to the product of the average of all the values and the number of values (that is 20, in this case). The average or mean of all the 20 values is the constraint in this case. Under no circumstance can the product of the two exceed or be lesser than the sum.

The first value in the set of 20 can be any number. So this is the freedom of that value.

So let’s say the first number is 10. The next value has the freedom to be anything as the total sum is still not 20. The next number can be 5. The third number can be -20. It still adds up to -5.

The list can go on till it reaches the 20th value. The 20th value does not have the freedom to be anything that it wants. It has to be something that makes the product of the average and the number of values equal to the sum of all the values.

If I let the whole thing fall under a formula, then it goes like this:

Degree of Freedom (DF) = number of values (N) - 1

In this case, it is:

DF = 20 - 1

DF = 19

The set has the freedom to have any value as it wants for 19 times, that is, till it reaches the last value.

Degree Of Freedom: Examples

Keeping in mind that the degree of freedom formula is

DF = N - 1

Let’s say that the number of data or values present in a given set is 5. This means that N is equal to 5.

The sample values in this set are:


Then the summation of all the numbers is:

10 + 2 + 8 + 6 + 14 = 40

The average or mean value is total divided by N:

Average = 40/5 = 8

This means that the product of this average and the number of values is:

P = 8 x 5 = 40

As you can see here, the product (P) equals the sum of the numbers (40).

DF = N - 1

DF = 5 - 1

DF = 4

This means that the first 4 numbers in this data set have the freedom to be anything. On the other hand, the last number (5th one) does not have that freedom. It has to be a number that makes the product of the average and the number of values (N) equal to the sum of the number.

While you are giving a test, you will not be given a few values. That is where you have to estimate the constraint. That is what makes the topic interesting as well as difficult at times.

Frequently Asked Questions (FAQs):

1. How Do You Determine The Degrees Of Freedom?

To calculate the degrees of freedom, you need to subtract one (1) from the size of the sample (the number of values).

To put it in formula,

DF = N – 1

Here, DF is the Degree of Freedom, and N is the number of values or the size of the sample.

2. What Is DF In A Test?

The full form of DF is Degrees of Freedom. In a mathematical calculation, the degrees of freedom indicate the maximum amount of values that have the freedom to be how much they want, or to vary.

3. What Is A High Degree Of Freedom?

It can be difficult to determine a fixed degree of freedom as the number keeps changing from one equation to another.
However, whenever there is a high degree of freedom, the value has the most power to reject a false hypothesis, and find a better significant result.

Wrapping It Up!

The degree of freedom is indicated as the maximum number of times the values have the freedom to be anything it likes. It is a concept that is used in statistics. The first few values can be anything as they have the freedom to.

However, the last value has to keep the constraint in mind. It has to be the exact value that makes the product of the average number of values and the number of values equal to the sum.

If you have been looking for ways to determine the degrees of freedom, I hope this article has been of help to you.

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