CHISQ.DIST.RT in Google Sheets

What Is CHISQ.DIST.RT in Google Sheets?

The CHISQ.DIST.RT function in Google Sheets calculates the p-value of a chi-square distribution. It tells you how likely it is to observe a value greater than or equal to a given chi-square statistic. It is done assuming the null hypothesis is true. This function is very useful in hypothesis testing, especially when one wishes to test how well-observed data fits with expected values. It is commonly in goodness-of-fit tests or tests for independence in contingency tables.

To understand the above description better, let us look at an example. If one conducts a chi-square test and gets a test statistic of 11.07 with 3 degrees of freedom, one can use the following function:

=CHISQ.DIST.RT(11.07, 3).

A result of a small value (like 0.01) would suggest the observed data is unlikely under the assumption that the null hypothesis is true, leading you to possibly reject the null hypothesis.

Syntax

Before we do a deep dive into the topic, let us look at its syntax. The syntax for CHISQ.DIST.RT is as follows:

=CHISQ.DIST.RT(x, degrees_freedom)

Here,

1. “x” is the value at which to evaluate the right-tailed chi-square distribution. It should not be negative.
2. “degrees_freedom” represents the degrees of freedom in the chi-square distribution. It should also be a positive integer.

This CHISQ.DIST.RT function in Google Sheets helps perform hypothesis tests in statistical analysis involving categorical data.

How To Use CHISQ.DIST.RT Function in Google Sheets?

The CHISQ.DIST.RT function in Google Sheets is used to calculate the right-tailed probability of a chi-square statistic. This is helpful when one wished to find how likely it is to get a test statistic equal to or more than the one observed in the given data.

Let’s look through how to use this function using a simple example. Suppose we have a chi-square statistic value of 10.5 with 5 degrees of freedom.

Step 1: Let us enter these details in a Google Sheet. In cell B1, we type the chi-square value: 10.5. In cell B2, we type the degrees of freedom: 5

Step 2: Click on a blank cell where you want the result to appear. Type in the formula:
=CHISQ.DIST.RT(B1, B2). Press Enter.

Step 3: Let us see the calculated probability or p-value for the chi-square test. A lower value suggests that the result is less likely to occur by chance.

Using the Menu Bar:

1. Select the cell where you wish to see your result.
2. Click on Insert → Function → Statistical → CHISQ.DIST.RT
3. Enter the required inputs as shown in the syntax above, close the parentheses and press Enter to apply.

This approach allows you to quickly apply the function without remembering the syntax.

Examples

Let’s explore a few examples to understand how the CHISQ.DIST.RT function works in real scenarios. These examples will demonstrate how to apply the function to calculate right-tailed probabilities for different chi-square values and degrees of freedom.

Example #1 – Calculate the right-tailed chi-squared distribution for a value of 10 with 2 degrees of freedom

Let’s look at a practical example where a researcher performs a chi-square test. A researcher might check if there’s a relationship between medicine and disease cure rates and gender and political preference. He obtains a test statistic of 10. He wishes to know the probability (p-value) of observing a value this large or larger, assuming the null hypothesis is true, with 2 degrees of freedom.

Step 1: Let us enter the above details in a Google Sheet. In cell A2, we type the chi-square value: 10. In cell B2, we type the degrees of freedom: 2

Step 2: Now, click on cell C2 and enter the Google formula:
=CHISQ.DIST.RT(B1, B2)

Step 3: Press Enter. Google Sheets will return the right-tailed probability, which represents the likelihood of getting a chi-square value of 10 or more with 2 degrees of freedom.

This result can help the researcher decide whether to reject the null hypothesis based on how small the p-value is.

Example #2 – Check if a dice game is fair by comparing actual rolls for a 15 chi-square value, 5 degrees of freedom

In this example, we are analysing the results of a dice game to check if it’s fair. After comparing the expected and actual outcomes, we must calculate a chi-square statistic of 15, got from several rolls. Since there are 6 sides on a die, the degrees of freedom is 5 (6 – 1). We wish to find the probability of getting a chi-square value of 15 or higher.

Step 1: Enter the values below in a sheet.

• Chi-square value: 15
• Degrees of freedom: 5

Step 2: Click on a blank cell and enter the formula:

=CHISQ.DIST.RT(B1, B2)

Step 3: Press Enter. The function will return the right-tailed probability (p-value).

If the resulting p-value is small (typically below 0.05), it suggests the dice might not be fair, and the observed results are unlikely to have happened by chance. If the results are similar to what you’d expect, the p-value will be larger, suggesting the dice are fair. 

Example #3 – Compare expected vs. actual voter turnout across US districts in 2024 election for an 18 chi-square value, 10 degrees of freedom

In this example, we are analyzing voter turnout across different U.S. districts in the 2024 election. Let us assume we have the expected turnout data and compare it with the actual numbers. After performing a chi-square test, we calculate a chi-square statistic of 18 with 10 degrees of freedom The degrees of freedom are based on the number of districts or categories minus one.

Step 1: Let us enter the details in a Google sheet as done in the examples above.In cell A2, enter the chi-square value: 18 and in B2, we enter the degrees of freedom: 10

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

=CHISQ.DIST.RT(B1, B2)

Step 3: Press Enter to get the p-value.

The result tells you how likely it is to observe a voter turnout variation this big or bigger if the expected turnout model is correct. A low p-value indicates a significant difference between expected and actual turnout patterns.

Important Things to Note

1. The degrees_freedom argument is truncated to an integer if it is a non-integer.
2. All arguments of CHISQ.DIST.RT in Google Sheets must be numeric.
3. The function calculates the probability of obtaining a value greater than or equal to the given chi-square statistic.
4. Note that the CHISQ.DIST.RT function does not handle left-tailed or two-tailed distributions.

Frequently Asked Questions (FAQs)

Download Template

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

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