# How to use the CHISQ.INV function

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

The CHISQ.INV function was introduced in Excel 2010 and calculates the inverse of the left-tailed probability of the chi-squared distribution. It has replaced the CHIINV 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.

**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 left-tailed probability of the chi-squared distribution?**

The left-tailed probability of the chi-squared distribution gives the chance that the sum of squared standard normals is less than or equal to a specified value x, focusing only on the lower portion of outcomes under the density curve.

**What is the inverse of a left-tailed probability of the chi-squared distribution?**

The inverse of a left-tailed chi-squared probability determines the value x that corresponds to a given cumulative probability for the lower tail, calculating the sum of squares threshold that captures the specified proportion of possible outcomes.

## 2. CHISQ.INV function Syntax

CHISQ.INV(*probability,deg_freedom*)

## 3. CHISQ.INV function Arguments

probability |
Required. A numerical value representing the probability of the chi-squared function distribution. |

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

**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.

## 4. CHISQ.INV Function Example 1

**What is x for a cumulative chi-squared distribution with 1 degree of freedom for a a probability of 0.842700792949715?**

The image above shows a chart displaying the chi square distribution for a degree of freedom of 1. The blue line is the cumulative chi square distribution and the orange line is the density probability function.

Below the chart are the arguments specified:

- probability : 0.842700792949715
- deg_freedom : 1
- cumulative : TRUE

The formula in cell C20 calculates the inverse of the left-tailed probability of the chi-squared distribution based on the specified arguments above.

Formula in cell C20:

Find the probability value (0.8427) on the y-axis, then find where the cumulative chi square distribution which is the blue line intersects 0.8427. Now find the x value on the x-axis which is 2. This value matches the calculated value in cell C20.

Cell C21 contains the CHISQ.DIST function, it calculates the probability based on the calculated value in cell C20, the number of degrees of freedom specified in cell C17, and the TRUE in cell C18 which corresponds to the cumulative chi square distribution.

The value in cell C21 matches the value in cell C16 which demonstrates the relation between the CHISQ.DIST function and the CHISQ.INV function.

## 5. CHISQ.INV Function Example 2

**What is x for a cumulative chi-squared distribution with two degrees of freedom for a a probability value of 0.77686983985157?**

The picture above demonstrates a chart displaying the chi square distribution for a degree of freedom of 2. The blue line is the cumulative chi square distribution and the orange line is the density probability function.

Below the chart are the arguments specified:

- probability : 0.77686983985157
- deg_freedom : 2
- cumulative : TRUE

The formula in cell C20 calculates the inverse of the left-tailed probability of the chi-squared distribution based on the specified arguments above.

Formula in cell C20:

Find the probability value (0.7769) on the y-axis, then find where the cumulative chi square distribution which is the blue line intersects 0.7769. Now find the x value on the x-axis which is 3. This value matches the calculated value in cell C20.

Cell C21 contains the CHISQ.DIST function, it calculates the probability based on the calculated value in cell C20, the number of degrees of freedom specified in cell C17, and the TRUE in cell C18 which corresponds to the cumulative chi square distribution.

The value in cell C21 (0.77686983985157) matches the value in cell C16 which demonstrates the relation between the CHISQ.DIST function and the CHISQ.INV function.

## 6. CHISQ.INV Function Example 3

**What is x for a cumulative chi-squared distribution with 8 degrees of freedom for a a probability value of 0.566529879633291?**

The image above shows a chart displaying the chi square distribution with 8 degrees of freedom. The blue line is the cumulative chi square distribution and the orange line is the density probability function.

Below the chart are the arguments specified:

- probability : 0.566529879633291
- deg_freedom : 8
- cumulative : TRUE

The formula in cell C20 calculates the inverse of the left-tailed probability of the chi-squared distribution based on the specified arguments above.

Formula in cell C20:

Find the probability value (0.5665) on the y-axis, then find where the cumulative chi square distribution which is the blue line intersects 0.5665. Now find the x value on the x-axis based on where the blue line intersects 0.5665 which is 8. This value matches the calculated value in cell C20.

Cell C21 contains the CHISQ.DIST function, it calculates the probability based on the calculated value in cell C20, the number of degrees of freedom specified in cell C17, and the TRUE in cell C18 which corresponds to the cumulative chi square distribution.

The value in cell C21 (0.5665) matches the value in cell C16 which demonstrates the relation between the CHISQ.DIST function and the CHISQ.INV function.

## 7. CHISQ.INV function not working

The CHISQ.INV function returns

- #VALUE! error value if
*probability*orargument is non-numeric.*deg_freedom* - #NUM! error value if:
*probability*< 0 (zero)*probability*> 1 (zero)1*deg_freedom <*

* deg_freedom *argument is converted into integers if necessary.

### Functions in 'Statistical' category

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

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