T.INV in Google Sheets

What Is T.INV in Google Sheets?

The T.INV function in Google Sheets finds the t-value or the critical value for a given probability and degrees of freedom from a t-distribution. This is very helpful in hypothesis testing. The TINV function is useful for small sample sizes to make predictions about a population from the sample data. Let us say that we are testing something, like if the rise in a viral illness has happened after a change in season. The t-distribution makes it easier to infer how likely it is that our test result happened by chance.

In the example below, we have a probability of 0.05 (which corresponds to a 95% confidence level) and 15 degrees of freedom. We use T.INV to calculate the t-value for a two-tailed t-distribution as follows:

0.025 corresponds to the 95% confidence level as it’s two-tailed. Hence, we have 2.5% on each side..

0.025 corresponds to the 95% confidence level as it’s two-tailed. Hence, we have 2.5% on each side.

=T.INV(0.025, 15)

Thus, the t-value at a 95% confidence interval with 15 degrees of freedom is approximately -2.131.

T.INV in Google Sheets returns the inverse of the Student’s T-distribution, which is a hypothetical probability distribution.
It is very helpful in finding critical values in confidence intervals,hypothesis testing, and various other calculations.
The syntax for the T.INV function is as follows: =T.INV(probability, degrees_freedom
When we use the T.INV for hypothesis testing, we set a significance level and use the function to find the critical t-value for a one-tailed or two-tailed test.

Syntax

The syntax of T.INV in Google Sheets is as follows:

=T.INV(probability, degrees_freedom)

probability – The probability associated with the t-distribution.

It must be a value between zero and one.

degrees_freedom – The number of degrees of freedom.

It will be truncated to an integer if a non-integer is provided as an argument and must be greater than or equal to 1.

How To Use T.INV Function in Google Sheets?

T.INV is an important function in statistical analysis and is often used for calculations. You can use the function in Google Sheets in two ways.

Enter T.INV manually
Enter through the Google menu

Enter T.INV Manually

Let us look at how to use the function manually. This is a simple way of using it. We have a gym with 20 members enrolled. We must find the t-value at a 92% confidence level to calculate the confidence interval for their average weight.

Step 1: Open the spreadsheet where you must enter your data. As a first step, let us calculate the values including the probability and the degrees of freedom.

Since there are 20 members, the degrees of freedom will be 20 – 1 = 19

We want a 92% confidence interval, which is 4% in each tail as it is a two-tailed test. Hence, the probability is 0.04

Step 2: Now, input the T.INV Function: Click on an empty cell where you want the result, cell B3 in this case.

Type =T.INV(0.04, 19) or T.INV(B3,B2) and press Enter.

The t-value is -1.849 approximately.

A negative t-value with a small p-value (e.g., p < 0.05) suggests that the observed difference between the groups is statistically significant and that the mean of the first group is significantly lower than the mean of the second group.

Entering T.INV Through The Menu Bar.

Place the cursor where you want to enter the formula.
Go to the Insert tab in Google Sheets. Select the Function option and then click on Statistical.
From the list of functions, scroll down and select the T.INV function.

Examples

The T.INV in Google Sheets is used to calculate the inverse of the Student’s t-distribution. It helps you prove your observations with statistical evidence, giving you more confidence in them. Let us look at how to use it in some simple examples.

Example #1

In this example, we analyze a sample of test scores from a class of 12 students. Let us determine the t-value for a 95% confidence interval and compare these scores to a regional average.

Step 1: As a first step, let us calculate the probability and degree of freedom. For a 95% confidence interval, the probability is 0.05 (1 – 0.95).

Calculate the degrees of freedom for 12 scores, which is 11 (12 – 1).

Step 2: In a cell, enter the following formula =T.INV(0.05, 11).

The formula will return the t-value, which you can use to compare the class scores against the regional average.

This will return the t-value of around -1.795 which means that 5% of the area under the t-distribution curve with 11 degrees of freedom lies to the left of this t-value.

Example #2 – Find the Threshold Credit Score for Loan Approval At a 90% Confidence Level

In this example, let us find the threshold credit score for loan approval at a 90% confidence level. For this, we use the T.INV function. Let us look at the steps to do the same. In this, the sample size is 30 as there are 30 applicants for the loan.

Step 1: Let us calculate the degree of freedom.

Degrees of freedom (df) = 30 – 1 = 29.

Step 2: We must find the threshold credit score at a 90% confidence level. This means a 5% significance level in one tail.

Enter the following formula to find the t-value for a 90% confidence interval:

=T.INV(0.05, 29)

The result will give you the t-value for the 90% confidence level with 29 degrees of freedom. Here, the result is -1.699.

Step 3: To convert this t-value into a credit score threshold, we use the following formula:

Threshold = Mean Credit Score + (t-value * Standard Error)

Let’s assume the average credit score in the sample is 800 and the standard error of the credit scores is 40. The threshold will be as shown below

800 + (-1.699 * 40)= 732.04

Hence, the threshold credit score for loan approval at a 90% confidence level would be approximately 732.04. It means that applicants with a credit score above 732 would be approved, at a 90% confidence interval.

Example #3 – Find the t-Value for a Stock Market Return Analysis At a 95% Confidence Interval

As shown in the heading above, here we will find the t-value for a stock market return analysis at a 95% confidence interval. Let us follow these simple steps. The confidence level is 95%. We have 20 data points.

Step 1: We have the T.INV function which calculates the t-value for a 95% confidence interval. Thus, the probability is 2.5% in each tail of the distribution.

Enter the following formula:

=T.INV(0.025, 19)

19 is the degrees of freedom, which is n – 1.

Step 2: The result gives the t-value for the 95% confidence interval with 19 degrees of freedom.

The result should be approximately -2.093. Therefore, the t-value for a stock market return analysis at a 95% confidence interval with 19 degrees of freedom is approximately -2.093.

Here, it means that 2.5% of the area under the t-distribution curve with 19 degrees of freedom lies to the left of this t-value.

This t-value can be used in analysis, such as performing hypothesis tests.

Important Things To Note

T.INV is used to find the negative inverse of the one-tailed TDIST function.
Both arguments of the function must be numeric.
Always set the right probability level. Usually, 0.05 is a common choice; however, ensure that it aligns with your specific analysis needs.
If the deg_freedom, the second argument, is not an integer, it is truncated.
Always remember to subtract one from your sample size to get the degrees of freedom.

Frequently Asked Questions (FAQs)

What are the errors you can get when using T.INV in Google Sheets?

Some of the common errors using the T.INV function include:

1, If the deg_freedom argument is less than T.INV returns the #NUM! Error value.
2. If either of the arguments of the function is non-numeric, T.INV returns the #VALUE! Error.
3. If the probability argument is less than or equal to zero and greater than one, it returns #NUM! Error value.
4. If the degree of freedom is not an integer, it is truncated.

What do the two arguments of the T.INV function represent?

The probability argument represents the probability of observing a t-value that is less than or equal to the returned value.

The value lies between 0 and 1. The degrees_freedom argument represents the degrees of freedom of the given data sample and is usually calculated as the sample size minus one (n – 1).

What is the difference between T.INV.2T and T.INV in Google sheets?

In Google Sheets, we use the T.INV function to calculate the negative inverse of the one-tailed Student’s t-distribution. Meanwhile, T.INV.2T calculates the t-value for a two-tailed test for a given probability and degrees of freedom. As an example, in a two-tailed test for a 94% confidence level, the critical value would correspond to the 97th percentile on the right tail and the 3rd percentile on the left tail.

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

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T.INV in Google Sheets