How to Use T.DIST Function in Google Sheets

The T.DIST function in Google Sheets is useful when you need to return the Student distribution of a value x.

The Student distribution is often used when handling data sets of a small sample size. Its shape is similar to a normal distribution but with slightly heavier tails.

The rules for using the T.DIST function in Google Sheets are as follows:

  • The function requires three arguments: x, degrees_freedom, and cumulative
  • The function then outputs a numerical value that corresponds to the Student distribution of a given x.

In statistics, Student’s t-distribution is used to estimate the mean of a population where the sample size is small and the standard deviation is unknown. The t-distribution is symmetric and bell-shaped like the normal distribution. One difference, however, is that the Student distribution has heavier tails.

Let’s look at a scenario where we can use the T.DIST function.

We have a random sample of heights from less than 30 students. We want to compute for the left-tailed distribution from this sample. Since there are a small number of samples, you can use the Student t-distribution.

With the T.DIST function, it becomes quite easy to find this distribution without knowing the formula. We can also use the t-distribution to construct a confidence interval for the true mean.

The degrees of freedom are calculated by subtracting the sample size by 1. For example, if the sample size is 25, the degree of freedom is equal to 24. As the degrees of freedom increase, the t-distribution more closely resembles the normal distribution. 

Now that we know when to use the T.DIST function let’s look into how to write the function on a spreadsheet.

 

 

The Anatomy of the T.DIST Function

The syntax of the T.DIST function is as follows:

T.DIST(x, degrees_freedom, cumulative)

Let’s dissect this formula and understand what each of these terms means:

  • = the equal sign is how we start any function in Google Sheets.
  • T.DIST() is our T.DIST function. It computes the Student distribution of a given value x.
  • x refers to the value to evaluate the distribution at.
  • degrees_freedom refers to the degrees of freedom to use for computation.
  • cumulative argument controls whether the function will use the cumulative probability for x. If set to FALSE, it will return the probability density function for x.
  • If deg_freedom is less than 1, the formula returns the #NUM! error.

 

 

A Real Example of Using T.DIST Function

Let’s look at a real example of the T.DIST function being used in a Google Sheets spreadsheet.

In the example below, we can compare two different inputs for the T.DIST function. It’s essential to know the actual sample size of your data set since we’ll need it to derive our degrees of freedom.

Use T.DIST Function in Google Sheets to compare different samples

 

To get the values in Column C, we just need to use the following formula:

=T.DIST(B3, B2-1, B4)

You can make your copy of the spreadsheet above using the link attached below. 

If you’re ready to try out the T.DIST function in Google Sheets, let’s begin writing it ourselves!

 

 

How to Use T.DIST Function in Google Sheets

In this section, we will go through each step needed to start using the T.DIST function in Google Sheets. This guide will show you how to get the t-distribution from a given input list.

 

Let’s go through each step needed to begin using the T.DIST function:

  1. First, we must select the cell we’ll use for the T.DIST function. In this case, we’ll use cells B5 and C5.
  2. Next, we just simply type the equal sign ‘=‘ to begin the function, followed by ‘T.DIST(‘.
    Note that there are three versions of the T.DIST function. We’ll focus on using the default option for now. This option returns the left-tailed t-distribution.
  3. Click on the arrow found on the top-right-hand corner of the box to minimize the tooltip pop-up if needed.
    type T.DIST function into the formula bar
  4. Next, select the input value to the distribution, also known as x. In this table, we’ll put in reference to cell B3.
    Select the x input for the T.DIST Function in Google Sheets
  5. Our second argument requires you to get the sample size of the dataset and subtract 1 from it.
    Subtract 1 from the sample size to get degrees of freedom
  6. The last argument must be a boolean value that indicates whether we use the cumulative probability or not. Once you have all three arguments, hit the Enter key to evaluate your formula.
    last argument is a boolean that determine whether we use cumulative probability
  7. We’ve added additional input for sample B. We can then drag the formula in cell B5 to the right to fill out the t-distribution value.
    Use T.DIST Function in Google Sheets on other samples

 

 

Following this guide will let you quickly start using the T.DIST function in Google Sheets. This formula makes it easy for you to get the Student t-distribution of your data set.

The T.DIST function is just one example of a statistical function you may use in Google Sheets. With so many other Google Sheets functions out there, you can surely find one that suits your data.

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