In this lesson, we are going to discuss the Kolmogorov-Smirnov Goodness of Fit test, how and when to perform it.

Remember that the Kolmogorov-Smirnov Goodness of Fit test is one of the non-parametric tests discussed previously. See What are Non-Parametric Tests

Here we are going to cover

The K-S Goodness of Fit Test is a non-parametric test that compares a given data with a known distribution and helps you determine if they have the same distribution.

The K-S test does not assume any particular distribution.

The K-S test is applied to test the normality of your data to see if it comes from a normally-distributed population.

It is also used in Analyis of Variance(ANOVA) to check the assumption of normality.

In summary, the K-S test can be used to answer the following questions:

Follow the steps the peform the K-S Test

Step 1: Set up the Null and alternate hypothesis

This could be of the form

Step 2: Create the EDF for your data

EDF stands for Empirical Distribution Function

Step 3: Specify a parent distribution

This is the distribution that you will like to compare your sample data to

Step 4:Plot the two distributions togeter

Step 5: Measure the greatest vertical distance between the two graphs

Step 6: Calculate the Test Statistic

Step 7: Find the Critical Value from the K-S table

Step 8: Compare the Crital Value to the calculated value

Step 9: State your conclution

This is a statistical table just like other tables used to look up critical values of statistics.

To get the P-Value, you need:

##

Remember that the Kolmogorov-Smirnov Goodness of Fit test is one of the non-parametric tests discussed previously. See What are Non-Parametric Tests

**Content**Here we are going to cover

- What is Kolmogorov-Smrmov Test
- When to use the K-S Test
- How to Perform the Kolmogorov-Smirmov Test
- Komogorove-Smirnov Test P-Value Table
- Pros and Cons of the Kolmogorov-Smirnov Test
- Final Notes

## 1. What is the Kolmogorov-Smirnov Test(K-S Test)?

The K-S Goodness of Fit Test is a non-parametric test that compares a given data with a known distribution and helps you determine if they have the same distribution.

The K-S test does not assume any particular distribution.

## 2. When to Apply the K-S Test

The K-S test is applied to test the normality of your data to see if it comes from a normally-distributed population.

It is also used in Analyis of Variance(ANOVA) to check the assumption of normality.

In summary, the K-S test can be used to answer the following questions:

- Is the data taken from a normal distribution?
- Is the data taken from a log-normal distribution?
- Is the data taken from an exponential distribution?
- Is the data taken from a logistic distribution?

## 3. How to Perform the Kolmogorov-Smirnov Test

Follow the steps the peform the K-S Test

Step 1: Set up the Null and alternate hypothesis

This could be of the form

**H**The groups are independent_{0}:**H**: The values are not dependent_{a}Step 2: Create the EDF for your data

EDF stands for Empirical Distribution Function

Step 3: Specify a parent distribution

This is the distribution that you will like to compare your sample data to

Step 4:Plot the two distributions togeter

Step 5: Measure the greatest vertical distance between the two graphs

Step 6: Calculate the Test Statistic

Step 7: Find the Critical Value from the K-S table

Step 8: Compare the Crital Value to the calculated value

Step 9: State your conclution

## 4. The K-S Test P-Value Table

This is a statistical table just like other tables used to look up critical values of statistics.

To get the P-Value, you need:

- degrees of freedom
- level of significance