# How to use the CHISQ.INV.RT function

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

The CHISQ.INV.RT function was introduced in Excel 2010 and calculates the inverse of the right-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 right-tailed probability of the chi-squared distribution?**

The right-tailed probability of the chi-squared distribution gives the chance that the sum of squared standard normals exceeds a specified value x, equal to 1 minus the cumulative distribution function evaluated at x.

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

The inverse of a right-tailed chi-squared probability finds the sum of squares value x that matches a given cumulative probability for the upper tail. This returns the threshold corresponding to the specified proportion of the distribution's upper outcomes.

## 2. CHISQ.INV.RT function Syntax

CHISQ.INV.RT(*probability,deg_freedom*)

## 3. CHISQ.INV.RT 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.RT function Example 1

**A researcher is conducting a study to investigate the relationship between smoking habits and life span. Determine the critical value of the chi-square distribution for a right-tailed test with a significance level of 0.05 and 3 degrees of freedom?**

The image above shows a chart displaying a blue line that represents the cumulative chi squared distribution for the right tail with three degrees of freedom. Three degrees of freedom is specified in cell C17.

The significance level is specified in cell C16, The formula in cell C20 calculates the critical value of the chi squared distribution for a right-tailed test with a probability of 0.05.

Formula in cell C20:

Find value 0.05 on the y-axis, go horizontally until you find the blue line. Go to the x-axis and read the value. This x-axis value matches the value in cell C20.

Cell C21 contains the CHISQ.DIST.RT function, it calculates the probability based on a given chi-square χ^{2} value. This example uses the calculated value in cell C20. This returns the probability specified in cell C16.

## 5. CHISQ.INV.RT function Example 2

**An ecologist is studying the diversity of plant species in different habitats. Determine the critical value of the chi-square distribution for a right-tailed test with a significance level of 0.025 and 6 degrees of freedom?**

The chart illustrates the cumulative chi-squared distribution for the right tail with sixdegrees of freedom, depicted by a blue line. Cell C17 contains the degrees of freedom used in this example.

Cell C16 holds the significance level, which is a probability value that the user has specified. In this case, the formula in cell C20 is calculating the critical value of the chi-squared distribution for a right-tailed test, using the probability value stored in cell C16, which is 0.025 (or a 2.5% significance level).

The formula in cell C20 is:

This formula uses the CHISQ.INV.RT function, which takes two arguments: the probability value (C16) and the degrees of freedom (C17). The result of this formula is the critical value of the chi-squared distribution for a right-tailed test with a probability of 0.025 and six degrees of freedom.

To visualize this critical value on the chart, one can locate the probability value of 0.025 on the y-axis and trace a horizontal line until it intersects with the blue line representing the cumulative chi-squared distribution. From this point of intersection, a vertical line can be drawn down to the x-axis, and the corresponding x-axis value is the critical value calculated in cell C20.

Additionally, cell C21 contains the CHISQ.DIST.RT function, which calculates the probability based on a given chi-squared value. In this example, the function uses the critical value calculated in cell C20 as its input. The result of this function should match the probability value stored in cell C16, confirming the accuracy of the critical value calculation.

## 6. CHISQ.INV.RT function Example 3

**A geneticist is analyzing the inheritance patterns of a particular trait in a population. Find the critical value of the chi-square distribution for a right-tailed test with a significance level of 0.001 and 2 degrees of freedom?**

The image displays a chart showing the cumulative chi-squared distribution for the right tail with two degrees of freedom, represented by a blue line. The number of degrees of freedom is specified in cell C17.

The significance level, or the probability value, is entered in cell C16. The formula in cell C20 calculates the critical value of the chi-squared distribution for a right-tailed test with a probability of 0.001 (0.1% significance level).

The formula in cell C20 is:

To find the critical value corresponding to a probability of 0.001, you can locate the value 0.001 on the y-axis of the chart and trace a horizontal line until it intersects with the blue line representing the cumulative chi-squared distribution. From this intersection point, you can follow a vertical line down to the x-axis and read the corresponding value. This x-axis value matches the value calculated in cell C20, which is the critical value of the chi-squared distribution for a right-tailed test with a probability of 0.001 and two degrees of freedom.

Cell C21 contains the CHISQ.DIST.RT function, which calculates the probability based on a given chi-squared (χ^2) value. In this example, the function uses the calculated value in cell C20 as the input. The result of this function should match the probability specified in cell C16, confirming the correctness of the critical value calculation.

## 7. CHISQ.INV.RT function not working

The CHISQ.INV.RT function returns

- #VALUE! error value
- if
*probability*orargument is non-numeric.*deg_freedom* - if the iterative search can't find a solution after 64 iterations.

- if
- #NUM! error value if:
*probability*< 0 (zero)*probability*> 1 (zero)1*deg_freedom <*

* deg_freedom *argument is converted into integers if necessary. CHISQ.DIST.RT and CHISQ.INV.RT are related:

- CHISQ.DIST.RT(
*x, deg_freedom*) =*probability* - CHISQ.INV.RT(
*probability,deg_freedom*) =*x*

### Functions in 'Statistical' category

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

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