# A to Z of Excel Functions: The CHIDIST Function

8 May 2017

*Welcome back to our regular A to Z of Excel Functions blog. Today we look at the CHIDIST function. *

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**The CHIDIST function**

In probability theory and statistics, the chi-squared distribution (also chi-square or **χ2**-distribution) with **k** degrees of freedom is the distribution of a sum of the squares of **k** independent standard normal random variables. It is one of the most widely used probability distributions in inferential statistics, *e.g.* in hypothesis testing or in construction of confidence intervals.

The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a proposed theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation.

If **Z _{1}**, ...,

**Z**are independent, standard normal random variables, then the sum of their squares

_{k}is distributed according to the chi-squared distribution with **k** degrees of freedom. This is usually denoted as

Thus, the chi-squared distribution has one parameter: **k** — a positive integer that specifies the number of degrees of freedom.

As aforementioned, the chi-squared distribution is used primarily in hypothesis testing. Unlike more widely known distributions such as the normal distribution and the exponential distribution, the chi-squared distribution is rarely used to model natural phenomena. It arises in the following hypothesis tests, among others.

The primary reason that the chi-squared distribution is used extensively in hypothesis testing is its relationship to the normal distribution. Many hypothesis tests use a test statistic, such as the **t** statistic in a **t-test**. For these hypothesis tests, as the sample size, **n**, increases, the sampling distribution of the test statistic approaches the normal distribution (**Central Limit Theorem**). Since the test statistic (such as **t**) is asymptotically normally distributed, provided the sample size is sufficiently large, the distribution used for hypothesis testing may be approximated by a normal distribution. Testing hypotheses using a normal distribution is well understood and relatively easy. The simplest chi-squared distribution is the square of a standard normal distribution. So wherever a normal distribution could be used for a hypothesis test, a chi-squared distribution could be used.

A chi-squared distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom, *etc.*

The **CHIDIST** function returns the right-tailed probability of the chi-squared distribution. The **χ2 **distribution is associated with a **χ2** test. It is used to test the **χ2** test to compare observed and expected values. For example, a genetic experiment might hypothesise that the next generation of plants will exhibit a certain set of colours. By comparing the observed results with the expected ones, you can decide whether your original hypothesis is valid.

The **CHIDIST **function employs the following syntax to operate:

**CHIDIST(x , deg_freedom)**

The **CHIDIST** function has the following arguments:

**x:**this is required and represents the value at which you want to evaluate the distribution**deg_freedom:**this is also required. This represents the number of degrees of freedom (**k**).

It should be further noted that:

- if either argument is nonnumeric,
**CHIDIST**returns the*#VALUE!*error value - if
**x**is negative,**CHIDIST**returns the*#NUM!*error value - if
**deg_freedom**is not an integer, it is truncated - if
**deg_freedom**< 1 or**deg_freedom**> 10^10,**CHIDIST**returns the*#NUM!*error value **CHIDIST**is calculated as**CHIDIST**=**P(X>x)**, where**X**is a**χ2**random variable.

Please see my example below:

*We’ll continue our A to Z of Excel Functions soon. Keep checking back – there’s a new blog post every other business day.*