# How to use the CHISQ.DIST function

**What is the CHISQ.DIST function?**

The CHISQ.DIST function calculates the probability of the chi-squared distribution. Use this function to check if a hypothesize is valid. It allows you to calculate the cumulative distribution or the probability density function.

The CHISQ.DIST function was introduced in Excel 2010 and has replaced the CHIDIST function.

#### Table of Contents

## 1. Introduction

**What is a chi-squared distribution?**

The chi-squared distribution is a theoretical probability distribution modeling the sum of squared standard normal random variables used in inferential statistics for estimation, confidence intervals, and hypothesis testing.

**What is the probability of the chi-squared distribution?**

The probability of the chi-squared distribution determines the likelihood that the sum of squared standard normal variables will take on a value less than or equal to a given number, depending on its degrees of freedom parameter.

**What is a hypothesize?**

In statistics, a hypothesis is an assumption about some aspect of a population parameter or probability model that can be tested using observations and data to determine if there is sufficient evidence in the sample to support the assumed hypothesis.

**What is a cumulative chi-squared distribution?**

The cumulative chi-squared distribution function gives the probability that the sum of squared standard normals will result in a value less than or equal to a specified number x, giving the accumulated area under the probability density curve.

**What is a probability density function of a chi-squared distribution?**

A chi-squared probability density function is a function that defines the relative likelihood of different outcomes for the sum of squared standard normals based on its degrees of freedom parameter, integrating to a total area of 1 over the domain.

**Wh****at is ****inferential statistics for estimation?**

Inferential statistics for estimation involve using a random sample to estimate characteristics and parameters about a larger population using statistical techniques like confidence intervals and point estimation to quantify uncertainty about the estimates.

**Wh****at is confidence intervals****?**

A confidence interval provides a range of plausible values for an unknown population parameter centered around a sample estimate, describing the uncertainty around the estimate at a specified level of confidence.

*What is the sum of squared standard normal variables?*

The sum of squared standard normal variables refers to summing multiple independent normally distributed random variables each with a mean of 0 and variance of 1, which results in a chi-squared distribution that can be used for statistical modeling and analysis.

## 2. CHISQ.DIST Function Syntax

CHISQ.DIST(*x,deg_freedom,cumulative*)

## 3. CHISQ.DIST Function Arguments

x |
Required. A numerical value representing a point in the probability distribution you want to be evaluated. |

deg_freedom |
Required. A numerical value representing the degrees of freedom. |

cumulative |
Required. A boolean value. TRUE - Cumulative distribution function FALSE - Probability density function |

**What are the degrees of freedom?**

The degrees of freedom in a chi-squared distribution refers to the number of standard normal random variables being squared and summed, which affects the shape of the distribution and occurs in statistical tests as the sample size minus the number of estimated parameters.

**What is a boolean value?**

A Boolean value is a logical data type having only two possible states - true or false - which logic gates and circuits are based on.

## 4. CHISQ.DIST Function Example 1

**What is the probability density function for a chi-squared distribution with a degree of freedom of one for an x value of 1.3?**

The CHISQ.DIST function has three arguments:

*x*- which is specified in cell C16 and is 1.3 in this example.*deg_freedom*- The degree of freedom is 1 and is specified in cell C17.*cumulative*- FALSE meaning the CHISQ.DIST function calculates the density probability function.

The image above shows a chart demonstrating both the cumulative chi-squared distribution (blue line) and the density probability function (orange line) between x values of 0 to 10. These distribution lines change based on the degree of freedom value. In this example the degree of freedom is 1.

Formula in cell C20:

The formula in cell C6 returns approx. 0.183. This value can be found in the chart above. The orange line shows the density probability function, the x value is found on the x-axis. 1.3 on the x-axis corresponds to the 0.18 value on the y-axis based on the orange line.

## 5. CHISQ.DIST Function Example 2

**What is the cumulative distribution function for a chi-squared distribution with a degree of freedom of two, for an x value of 2?**

The CHISQ.DIST function has three arguments:

*x*- which is specified in cell C16 and is 2 in this example.*deg_freedom*- The degree of freedom is 2 and is specified in cell C17.*cumulative*- TRUE meaning the CHISQ.DIST function calculates the cumulative distribution function.

The image above shows a chart demonstrating both the cumulative chi-squared distribution (blue line) and the density probability function (orange line) between x values of 0 to 10. These distribution lines change based on the degree of freedom value, note that the chart lines are different than in example 1, section 4. In this example the degree of freedom is 2.

Formula in cell C20:

The formula in cell C6 returns approx. 0.632. This value can be found in the chart above. The orange line shows the density probability function, the x value is found on the x-axis. 0.632 corresponds to the area below the orange line between 0 and 2.

The blue line shows the cumulative distribution function, 2 on the x-axis corresponds to 0.632 on the y-axis based on the blue line.

## 6. CHISQ.DIST Function Example 3

**What is the complement of the cumulative distribution function for a chi-squared distribution with a degree of freedom of eight, for an x value of 8?**

The complement of the cumulative distribution function is the area below the orange line from x value 8 to infinity. We can calculate the cumulative probability for x value 8 and then calculate the complement by subtracting 1 with the cumulative probability from the CHISQ.DIST function.

Formula in cell C20:

The blue line shown in the image above demonstrates the cumulative distribution function for chi squared distribution with the following arguments:

*x*- which is specified in cell C16 and is 8 in this example.*deg_freedom*- The degree of freedom is 8 and is specified in cell C17.*cumulative*- TRUE meaning the CHISQ.DIST function calculates the cumulative distribution function.

Number 8 on the x-axis corresponds to value approx. 0.57 on the left y-axis, however, we need the complement meaning the area below the orange line. The orange line shows the density probability function of a chi squared distribution from 8 on the x-axis to infinity. 1 minus 0.57 is approx. 0.43.

## 7. CHISQ.DIST Function not working

The CHISQ.DIST function returns

- #VALUE! error value if
*x,*or*deg_freedom*argument is non-numeric.*cumulative* - #NUM! error value if:
*x*< 0 (zero)1*deg_freedom <*10^10*deg_freedom >*

* deg_freedom *argument is converted into integers.

### 'CHISQ.DIST' function examples

The following article has a formula that contains the CHISQ.DIST function.

Table of Contents How to use the BETADIST function How to use the BETAINV function How to use the BINOMDIST […]

### Functions in 'Statistical' category

The CHISQ.DIST function function is one of 73 functions in the 'Statistical' category.

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