CHISQ.INV Google Sheets

What Is CHISQ.INV function in Google Sheets?

CHISQ.INV calculates the inverse of the left-tailed chi-squared distribution. Simply put, CHISQ.INV helps find the value that falls within a specific probability range in a chi-square distribution. It is used to determine the likelihood that the observed categorical data is drawn from an expected distribution. It is helpful in scenarios such as hypothetical testing, evaluation of financial models, etc.

Let us look at a simple example to understand this. Suppose you have a sample of 50 observations. You must find the chi-squared value when the probability is 5% and 5 degrees of freedom. Apply the CHISQ.INV Google Sheets function as follows:

=CHISQ.INV(0.05, 5)

You get a result of 1.145476226. Let’s go ahead and look at the CHISQ.INV function in Google Sheets in detail. It is important to understand how to use CHISQ.INV to analyze data and make informed decisions.

Syntax

The syntax for CHISQ.INV is as follows:

=CHISQ.INV(probability, degrees_freedom)

Here,

1. “probability” is the desired probability between 0 and 1. It is the area to the left of the chi-square value.
2. “degrees_freedom” represents the degrees of freedom associated with the chi-square distribution. It should be a positive integer.

This CHISQ.INV Google Sheets formula can be useful in many real-life scenarios.

How To Use CHISQ.INV function in Google Sheets?

As discussed before, CHISQ.INV in Google Sheets returns the inverse of the chi-squared cumulative distribution. It can be useful in statistical analysis when you need to find the critical value for a given probability and degrees of freedom. Let us look at how to apply this function in Google Sheets. It can be entered in two ways.

1. Manually enter the CHISQ.INV function
2. Through the Google Menubar

#1 – Manually Enter the CHISQ.INV Function

Open a Google sheet and enter the following data.

• Probability associated with a chi-square distribution – 0.06
• Degree of Freedom – 8

Step 1: Select the cell where the result of the CHISQ.INV function should appear. Type the following formula into the selected cell:

=CHISQ.INV(B1, B2)

Step 2: Please note that the probability value should be between 0 and 1. The “degrees_freedom” value should be an integer representing the degrees of freedom for the distribution. Now, press Enter.

We can now observe the result of the CHISQ.INV function in cell B3.

Thus, you can leverage the power of the CHISQ.INV Google Sheets function to accurate statistical calculations.

#2 – Through the Google Menubar

1. Choose the cell where you want to enter the CHISQ.INV function.
2. Go to the menu bar and click on “Insert” ➝ “Function” ➝ “Statistical” ➝ “CHISQ.INV.”
3. Enter the arguments and close the braces. Press Enter.

Examples

The examples below highlight the practical applications of CHISQ.INV in various scenarios ensures you have adequate knowledge to apply this function.

Example #1

Let us calculate the inverse of the chi-squared distribution for the example data in the below table. Here, the degrees of freedom are 5, and you must find the value at which the probability of observing a chi-squared value is lower than 0.05. Similarly, determine the value at which the probability of obtaining a chi-squared value is less than 0.01 and the degree of freedom is 10.

Step 1: Let us enter all the details in a Google Sheet as shown below.

Step 2: Enter the following formula in cell C2.

=CHISQ.INV(A2,B2)

Step 3: Press Enter. Now, drag the formula to cell C3 as well to get the inverse of the left-tailed chi-squared distribution.

Example #2

Suppose you have a financial model predicting monthly returns, and you want to test whether the observed returns fit the expected distribution based on historical data. You want to perform a chi-squared test for goodness-of-fit with a 90% confidence level. Let the degrees of freedom be 5.

Step 1: Enter the observed frequencies into Column A and the expected frequencies into Column B.  

Step 2: Calculate the Chi-Squared Statistic for the values using the following formula.

=(A2 – B2)^2 / B2

Step 3: Drag it all the way down to C6.

Now, use the CHISQ.INV Google Sheets formula for 90% confidence level and 5 degrees of freedom.

=CHISQ.INV(0.90, 5).

Compare the chi-squared statistic you calculated with the critical value obtained from the CHISQ.INV function. If the chi-squared statistic is greater than the calculated value, you can reject the null hypothesis.

When the test statistic is greater than the critical value obtained from CHISQ.INV indicates that the null hypothesis could be rejected with a certain level of confidence. However, if the test statistic is less than the critical value, it suggests that there is not enough evidence to reject the null hypothesis.

Example #3

You can use the CHISQ.INV Google Sheets function to estimate a 90% confidence interval for the variance of a population with a sample of 25 observations. 

Let us look at how we can implement this and get the result.

Step 1: Let us calculate the degrees of freedom.

Its formula is sample size – 1. Here it is 25-1 = 24.

Step 2: Now, you must find the critical values.

• For the upper limit, use CHISQ.INV for the upper 5% tail
• For the lower limit, use CHISQ.INV for the lower 5% tail

Let us apply both formulas in Google Sheets.

Step 3: You get the chi-squared critical values corresponding to the 95th and 5th percentiles, respectively. These can be used to calculate the upper and lower bounds of the confidence interval for the variance.

The chi-squared distribution is mainly used in goodness-of-fit tests to compare an observed distribution to a proposed theoretical one. It is also extremely useful for hypothesis testing. 

It is also commonly used to study variation in the percentage of something we wish to note, such as the time people spend on social media, across samples.

Important Things To Note

• If the deg_freedom, the second argument, is not an integer, it is truncated.
• If deg_freedom is less than one or > 10^10, it returns the #NUM! error.
• The shape of each distribution for CHISQ.INV depends on the number of degrees of freedom.
• For a goodness-of-fit test, the degrees of freedom are calculated as: = number of categories – 1.
• The CHISQ.INV Google Sheets function helps you find the critical value to compare with your test statistic and decide whether to reject the null hypothesis.

Frequently Asked Questions (FAQs)

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