Enter the sample mean, the population mean, standard deviation, and sample size into the t-statistic calculator to determine the t-value of that set of data. This calculator can also calculate the sample mean, the population mean, standard deviation, and sample size given the other values.

T Statistic Formula

The following formula can be used to calculate the t statistic of a data set. 

t = [ x - μ> ] / [ s / sqrt( n ) ]
  • Where X is the sample mean
  • μ is the population mean
  • s is the standard deviation of the sample
  • n is the sample size

To calculate the t-statistic, subtract the population mean from the sample mean, then divide by the result of the standard deviation of the sample divided by the square root of the sample size.

The most important point to note about this formula is that the standard deviation is of the sample, not the entire population.

To calculate the T statistic, take the difference between the population mean and the sample mean, then divide the result by the result of the standard deviation divided by the square root of the sample size.

T Statistic Definition

A t statistic is a statistic that defines the relationship between a sample and a population. In other words a measure of the accuracy of a sample.

How to calculate t statistic?

Example Problem:

First, determine the sample mean. For this example problem, the sample mean is found to be 45.

Next, determine the population mean. In this case, the population mean is calculated to be 50.

Next, determine the standard deviation of the sample. For this problem, the standard deviation of the sample (important to note this is not the sample deviation of the population), is found to be 2.5.

Next, determine the sample size. The sample size for this example is 400.

Finally, calculate the t-statistic using the formula above:

t = [ x – μ> ] / [ s / sqrt( n ) ]

t = [ 50 – 45 ] / [ 2.5 / sqrt( 400 ) ]

t = 40

FAQ

What is a T Statistic?

A T statistic, also known as t value, is a term used to describe the relationship between a sample set to a population set. It’s used to condense large amounts of data into a single value.

How to calculate a t statistic

  1. First, determine the sample mean

    Calculate the sample mean of the data set

  2. Next, determine the population mean

    Calculate the mean of the entire population

  3. Calculate the standard deviation of the sample

    Use the formula for standard deviation

  4. Finally, Calculate the t-statistic

    Using the values from steps 1-3 and the sample size, calculate the t-statistic through the formula above.