# How to use the CHITEST function

The CHITEST function calculates the test for independence, the value returned from the chi-squared statistical distribution and the correct degrees of freedom. Use this function to check if hypothesized results are valid.

**What is a test for independence?**

A test for independence is a statistical hypothesis test that checks if two categorical variables are related or independent based on observed data, commonly done using Pearson's chi-squared test or G-test to compare observed and expected frequency counts.

**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 an hypothesis?**

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 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.

*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 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.

## CHITEST Function Syntax

CHITEST(*actual_range,expected_range*)

## CHITEST Function Arguments

actual_range |
Required. A range of data. |

expected_range |
Required. A range of data. |

## CHITEST Function Example

**How to check if hypothesized results are valid when using the CHISQ.TEST function?**

To check if results from the CHISQ.TEST function are valid, look at the calculated test statistic and compare it to the critical value from the chi-squared distribution with degrees of freedom equal to (number of rows - 1) * (number of columns - 1) at the desired significance level, rejecting independence if the test statistic exceeds the critical value.

Formula in cell C12:

## CHITEST Function not working

Independence is indicated by a low number of Ï‡2.

The CHITEST function returns

- #N/A error value if the number of data points in the arguments doesn't match.

## How is the CHITEST Function calculated?

CHITEST function equation:

Aij = actual frequency in the i-th row, j-th column

Eij = expected frequency in the i-th row, j-th column

r = number of rows

c = number of columns

### Functions in 'Compatibility' category

The CHITEST function function is one of 21 functions in the 'Compatibility' category.

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