CHISQ.DIST in Google Sheets

What Is CHISQ.DIST in Google Sheets?

The CHISQ.DIST function in Google Sheets returns the left-tailed cumulative probability of a chi-square distribution. In other words, it demonstrates the probability of getting a chi-square statistic less than or equal to a given value. It is very helpful in hypothesis testing when one compares the observed data with the expected data. This holds good, especially in goodness-of-fit tests.

For instance, if we have a chi-square value of 6.25 with 4 degrees of freedom. Let us find the cumulative probability by using the following function:
=CHISQ.DIST(6.25, 4, TRUE)

Syntax

Before we go about using the function, let us look at the syntax for CHISQ.DIST in Google Sheets.

=CHISQ.DIST(x, degrees_freedom, cumulative)

The arguments mean the following:

1. x – The chi-square value that we will evaluate. (mandatory – non-negative number)
2. degrees_freedom – The degrees of freedom for the mentioned distribution; (mandatory – positive number)
3. cumulative – A logical value that is TRUE or FALSE. If TRUE, it returns the cumulative distribution; if FALSE, it returns the probability density function at x.

The CHISQ.DIST function is useful when one must assess how well the observed data fits an expected distribution. This is often used in goodness-of-fit tests.

How To Use CHISQ.DIST Function in Google Sheets?

As mentioned in the definition, CHISQ.DIST in Google Sheets is used to calculate the left-tailed cumulative probability of a chi-square distribution. It helps understand how likely it is to get a value less than or equal to a provided test statistic, using the degrees of freedom.

In layman’s terms, we can use it for applications like determining if there is an association between a person’s age and their preference for a particular soda drink. Another such scenario is a dice manufacturer testing the fairness of each face landing with equal fairness. It is particularly useful in analyzing categorical data and performing goodness-of-fit tests.

There are two ways to use this function.

1. Enter CHISQ.DIST in Google Sheets manually
2. Through the Google menu bar

Enter CHISQ.DIST in Google Sheets Manually

Let’s walk through a simple example to understand how to use this function.

Step 1: Let us open ablank Google Sheet to enter the values for our test.

We enter the chi-square statistic in B1 and the degrees of freedom in B2.

Step 2: Click on the cell where you want to see the result. We type in the following formula based on its syntax.

=CHISQ.DIST(B1, B2, TRUE)

Open the parentheses, after the function name, enter the arguments in order, separated by commas, and close the parentheses.

Step 3: Press Enter. The result is the cumulative probability (a value between 0 and 1). A higher value indicates that the observed data is closer to the expected results under the null hypothesis.

Using the Menu Bar

1. Select the cell where you want the result to appear.
2. Go to Insert → Function → Statistical → CHISQ.DIST.
3. Fill in the inputs for the arguments chi-square value, and degrees of freedom, and select TRUE for cumulative.
4. Press Enter to see the result.

Examples

Let us look at some examples to help understand how the CHISQ.DIST function works in real-life situations. These examples show its uses in real-life scenarios.

Example #1 – Find the cumulative probability of getting a chi-square value of 4.5 with 2 degrees of freedom (df) when testing genetic inheritance patterns

To show its practical uses, let’s consider its use in genetics. A scientist is testing whether observed traits in some plants follow Mendel’s expected inheritance ratios. They collect data and calculate the chi-square statistic, which is 4.5. The scientist wants to find the cumulative probability of obtaining a result less than or equal to 4.5, assuming the null hypothesis is correct. The degree of freedom is 2.

Step 1: Open a Google Sheet and input the data, as shown below.

The chi-square statistic is calculated by adding the difference between observed values (O) and expected values (E) after squaring, divided by the expected value. The formula is as shown: χ² = Σ(O – E)² / E. 

Step 2: Click on cell B3 and enter the formula:

=CHISQ.DIST(A2, B2, TRUE)

Step 3: Press Enter. Google Sheets gives the scientist the left-tailed cumulative probability of getting a value of 4.5 or less with 2 degrees of freedom.

It shows them how well the observed traits match Mendel’s expected pattern.

A higher cumulative probability (0.89) suggests the result is likely under the null hypothesis, and the inheritance pattern most probably follows the expectations.

Example #2 – Estimate the cumulative chance of observing a low discrepancy in customer service ratings across four stores (chi-square = 3.6, df = 3)

In this example, an organization wants to check whether the customer service ratings across four of its stores are significantly different. On initial analysis after collecting the data, the calculated chi-square value is 4.2. Thedegrees of freedom are 4-1 = 3. Now, the manager wants to know the cumulative probability of getting a chi-square statistic less than or equal to 4.2, as it would suggest that the customer ratings are consistent across the four stores.

Step 1: In a Google Sheet, we enter the inputs as shown below.

Step 2: Click on an empty cell and type the formula:

=CHISQ.DIST(B1, B2, TRUE)

Step 3: Press Enter. The formula returns the cumulative probability for the provided chi-square value and degrees of freedom.

As the value is a relatively high, it indicates there’s a fair chance that the differences in ratings are due to random reasons, and the customer service is fairly consistent across stores.

Example #3 – Calculate the likelihood that observed purchase behavior deviates only slightly from expected brand preferences (chi-square = 5.2, df = 3)

Let us look at how to calculate the p-value that shows if the observed purchase behavior deviates only slightly from expected brand preferences using a practical example. Here too, the chi-square and degrees of freedom are calculated, and we use the CHISQ.DIST in Google Sheets for the result.

100 customers are surveyed to find out which of the four brands they prefer. Under an ideal scenario, we expect 25 per brand (100 ÷ 4 = 25). But our chi-square value that is calculated is 5.2. 

Step 1: Now, let us calculate the degrees of freedom and enter both values in a sheet.

df= 4−1=3

Step 2: Enter the following formula.

=CHISQ.DIST(5.2, 3, TRUE)

Instead of entering the cell references, we have entered the values directly.

The result gives the cumulative probability which is the area to the left of 5.2. It means that the likelihood of deviating less than 5.2, i.e., a small or moderate deviation.

There is an 84.2% chance that the observed behavior deviates only slightly from expectations.

Important Things to Note

1. The degrees_freedom argument is truncated to an integer if it is a non-integer.
2. The degrees_freedom must be at least 1 and should be below 10^10.
3. Both the arguments,  x and the degrees_freedom  must be numeric.
4. The function returns the left-tailed cumulative distribution function if the cumulative argument is TRUE. If it is FALSE, it returns the probability density function.

Frequently Asked Questions (FAQs)

Download Template

This article must help understand CHISQ.DIST Function in Google Sheets with its formulas and examples. You can download the template here to use it instantly.

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