# CHISQ.DIST

The CHISQ.DIST function calculates the probability of a chi-squared distribution, which is commonly used in statistical analysis to assess the likelihood of observed data differing from expected data. This function is helpful in various scientific and research scenarios for hypothesis testing and model fitting.

## Syntax

=CHISQ.DIST(`x`

, `deg_freedom`

, `cumulative`

)

`x` | The value at which to evaluate the chi-squared distribution. | ||

`deg_freedom` | The degrees of freedom for the chi-squared distribution. | ||

`cumulative` | A logical value that determines the form of the function. If TRUE or omitted | it returns the cumulative distribution function; if FALSE | it returns the probability density function. |

`x` | The value at which to evaluate the chi-squared distribution. | ||

`deg_freedom` | The degrees of freedom for the chi-squared distribution. | ||

`cumulative` | A logical value that determines the form of the function. If TRUE or omitted | it returns the cumulative distribution function; if FALSE | it returns the probability density function. |

`x` | The value at which to evaluate the chi-squared distribution. | ||

`deg_freedom` | The degrees of freedom for the chi-squared distribution. | ||

`cumulative` | A logical value that determines the form of the function. If TRUE or omitted | it returns the cumulative distribution function; if FALSE | it returns the probability density function. |

`x` | The value at which to evaluate the chi-squared distribution. | ||

`deg_freedom` |

## About CHISQ.DIST

When engaging in statistical analyses and aiming to gauge the conformity of observed data with expected distributions, the CHISQ.DIST function in Excel emerges as a pivotal tool. It plays a fundamental role in assessing the probabilities associated with chi-squared distributions, an integral concept in hypothesis testing, goodness-of-fit evaluations, and model comparisons across diverse fields encompassing science, research, and data analysis. By leveraging CHISQ.DIST, users can ascertain the likelihood of observed data deviating from the anticipated patterns, thereby facilitating informed decision-making rooted in statistical insights. This function operates on the principles of chi-squared statistical theory, providing valuable outputs to support rigorous statistical inferences in various domains.

## Examples

Suppose you have conducted an experiment with a chi-squared distribution and obtained a test statistic of 8 with 4 degrees of freedom. To calculate the probability that the test statistic is less than or equal to 8 (i.e., the cumulative distribution function), you would use the CHISQ.DIST formula as follows: CHISQ.DIST(8, 4, TRUE)

Consider a research study in which the chi-squared test statistic is found to be 15 with 8 degrees of freedom. To determine the probability density at this statistic value, you can utilize the CHISQ.DIST function in its non-cumulative form: CHISQ.DIST(15, 8, FALSE)

## Questions

**What does the degrees of freedom parameter refer to in the CHISQ.DIST function?**

The degrees of freedom parameter in the CHISQ.DIST function pertains to the number of independent observations in a statistical test or model. It signifies the flexibility in variability within the data and plays a crucial role in determining the shape and characteristics of the chi-squared distribution.

**How is the cumulative argument used in the CHISQ.DIST function?**

The cumulative argument in the CHISQ.DIST function controls the form of the output. When set to TRUE or omitted, the function calculates the cumulative distribution function, yielding the probability that the chi-squared random variable is less than or equal to the specified value. If set to FALSE, it computes the probability density function, providing the probability density at the given value.

**In what scenarios is the CHISQ.DIST function commonly employed?**

The CHISQ.DIST function is frequently used in statistical testing, hypothesis evaluations, goodness-of-fit assessments, and model comparisons. It serves as a fundamental tool in various scientific and research disciplines, such as biology, social sciences, engineering, and data analysis, among others.

## Related functions

CHISQ.DIST.RT

CHISQ.INV

CHISQ.INV.RT