# How to use the CHISQ.DIST.RT function

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

The CHISQ.DIST.RTÂ function was introduced in Excel 2010 and calculates the right-tailed probability of the chi-squared distribution. It has replaced the CHIDIST functionÂ and RT in the function name stands for right-tailed.

#### 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.

**W****hat 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 normal variables exceeds a given value x, equal to 1 minus the cumulative distribution function evaluated at x, focusing on the upper tail rather than full distribution.

*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.

**What is independent normally distributed random variables?**

Independent normally distributed random variables are uncorrelated random variables whose distributions follow the normal distribution each with their own mean and standard deviation parameters, often hypothesized in statistics when modeling unknown true distributions.

**Wh****at isÂ ****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.

## 2. CHISQ.DIST.RT Function Syntax

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

## 3. CHISQ.DIST.RT Function Arguments

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

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.DIST.RT Function Example 1

**What is the right-tailed probability when the x value is 2 and the chi squared distribution has one degree of freedom?**

This example demonstrates how to calculate the right-tailed probability based on an x value on a given number of degrees of freedom.

The image above shows the CHISQ.DIST.RT formula in cell C20 calculating the right-tailed probability based on the following arguments:

- x = 2
- deg_freedom = 1

Formula in cell C20:

The formula returns approx. 0.157 which represents the area below the orange line from x value 2 to infinity. In other words, the right-tailed probability which is the same as the value based on the blue line where it intersectsÂ x value 2 shown in the chart above. The y-axis value is some where around 0.84, however, the right-tailed probability is the complement to 0.84 which is 1- 0.84 = 0.16. This value is close to 0.157.

Cell C21 contains the CHISQ.INV.RT function that calculates the inverse of the right-tailed probability of the chi-squared function. This value matches the x argument in cell C16.

## 5. CHISQ.DIST.RT Function Example 2

**What is the right-tailed probability when the x value is 3 and the chi squared distribution has two degrees of freedom?**

This example demonstrates how to calculate the right-tailed probability based on an x value on a given number of degrees of freedom.

The image above shows the CHISQ.DIST.RT formula in cell C20 calculating the right-tailed probability based on the following arguments:

- x = 3
- deg_freedom = 2

Formula in cell C20:

The formula returns approx. 0.223 which represents the area below the orange line from x value 3 to infinity. In other words, the right-tailed probability which is the same as the value based on the blue line where it intersectsÂ x value 2 shown in the chart above. The y-axis value is some where around 0.78, however, the right-tailed probability is the complement to 0.78 which is 1- 0.78 = 0.22. This value is close to 0.223.

Cell C21 contains the CHISQ.INV.RT function that calculates the inverse of the right-tailed probability of the chi-squared function. This value matches the x argument in cell C16.

## 6. CHISQ.DIST.RT Function Example 3

**What is the right-tailed probability when the x value is 9 and the chi squared distribution has eight degrees of freedom?**

This example demonstrates how to calculate the right-tailed probability based on an x value on a given number of degrees of freedom.

The image above shows the CHISQ.DIST.RT formula in cell C20 calculating the right-tailed probability based on the following arguments:

- x = 9
- deg_freedom = 8

Formula in cell C20:

The formula returns approx. 0.342 which represents the area below the orange line from x value 9 to infinity. In other words, the right-tailed probability which is the same as the value based on the blue line where it intersectsÂ x value 9 shown in the chart above. The y-axis value is some where around 0.66, however, the right-tailed probability is the complement to 0.66 which is 1- 0.66 = 0.34. This value is close to 0.432.

Cell C21 contains the CHISQ.INV.RT function that calculates the inverse of the right-tailed probability of the chi-squared function. This value matches the x argument in cell C16.

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

The CHISQ.DIST.RT function returns

- #VALUE! error value if
*x*orÂÂ argument is non-numeric.*deg_freedom* - #NUM! error value if:
*xÂ*< 0 (zero)Â 1*deg_freedomÂ <*Â 10^10*deg_freedomÂ >*

* deg_freedom *argumentÂ is converted into integers.

### Functions in 'Statistical' category

The CHISQ.DIST.RT function function is one of 74 functions in the 'Statistical' category.

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