How to use the CHISQ.DIST function in Excel

In this article, we will learn How to use the CHISQ.DIST function in Excel.

What is Chi square distribution and degree of freedom?

The Chi Square distribution is the distribution of the sum of squared standard normal deviates. For example we sample two variables from a standard normal distribution, square each variable, and sum the squares. What is the probability that the sum of these two squares will be six or higher? Since two variables are taken as sample, the answer can be found using the Chi Square distribution with two degrees of freedom. CHISQ.DIST function can be used to find that the probability of a Chi Square (with 2 degree of freedom) being six or higher is 0.050.

Degree of freedom

Now you must be wondering what is the degree of freedom (also known as df). Mathematically, the degree of freedom(df) of a distribution is equal to the number of standard normal deviations being summed. But how can we understand the concept of degree of freedom? Degree of freedom is the number of independent possibilities in an event. For example if we toss a coin 100 times and say heads occur 48 times and then we can conclude the tails occured 52 times so the degree of freedom is 1. But if we say on a route of traffic lights (generally has 3 color lights) we want to know the probability of red light in any given sample of time. For this the degree of freedom will be 2 as we will require information for at least 2 color lights. See how degrees of freedom (df) affect the chi square density distribution in the different plots shown below.

Let's learn how to use the CHI SQUARE distribution using the CHISQ.DIST function to calculate the cumulative or probability density for the variable x.

CHISQ.DIST Function in Excel

The CHISQ.DIST function in Excel returns the chi-squared percentage of something across samples, such as the fraction of the day people spend watching television. The function takes variable and degrees of freedom for the distribution along with type of distribution (cdf or pdf).

CHISQ.DIST Function syntax:

=CHISQ.DIST(x , deg_freedom , cumulative)

x : value at which distribution is evaluated

deg_freedom : degrees of freedom

cumulative : logical value that determines the form of the function. If cumulative is TRUE, CHISQ.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.


Example :

All of these might be confusing to understand. Let's understand how to use the function using an example. Here we have a sample variable x and degree of freedom. We need to calculate the chi square percentage using the CHISQ.DIST function in Excel 

Use the formula:


The chi square value is in decimal you can convert the value to percentage changing the format of the cell to percentage.

The chi square value at least 0.5 comes out to be 22% for the probability mass distribution. Now calculate chi square pdf or probability density value for the same parameters.

Use the formula:


The chi square value at exact 0.5 value comes out to be 39% for the cumulative distribution.The Chi Square distribution is very important because many test statistics are distributed as Chi Square. Chi Square distributions are tests of deviations between theoretically expected and observed frequencies.

Here are all the observational notes using the CHISQ.DIST function in Excel
Notes :

  1. The function only works with numbers. If any argument other than cumulative is non numeric, the function returns #VALUE! error.
  2. The function returns #NUM! Error.
    1. If x is negative
    2. If the degree of freedom is < 1 or >10^10.
  3. The cumulative argument can be used with boolean numbers (0 and 1) or (FALSE or TRUE).
  4. Value in decimal and value in percentage id the same value in Excel. Convert the value to percentage, if required.
  5. You can feed the arguments to the function directly or using the cell reference as explained in the example.

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