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# What Is The t-Distribution?

The t-distribution, also called Student’s t-distribution, is a normal distribution used when the data involved is approximately normally distributed. The sample size is small, and the variance of the data is unknown.

Mathematically, the t-distribution can be expressed as:

where is the sample mean, μ is the population mean, s is the standard deviation of the sample, and n is the sample size.

As this formula shows, as the degrees of freedom (total number of observations minus one) increase, the t-distribution converges to a normal distribution. When the amount of degrees of freedom is infinite, the t-distribution equals a normal distribution.

In practice, when the degrees of freedom are 30 or more, it can be assumed that the distribution is normal. The main advantage of this assumption is that the variance of a normal distribution is known. However, it is essential to note that the t-distribution should NOT be used with small samples that are not approximately normal.

The variance of a t-distribution is calculated based on the degrees of freedom of the data set as:

Where* v* is the degrees of freedom and *v* > 2.

As this formula suggests, as the degrees of freedom increase, the variance converges to one.

The t-distribution was developed by William Sealy Gosset, who worked at the Guinness Brewery in Dublin, Ireland, and published it under “Student.” Later, British statistician Ronald Fisher popularized it, called the distribution “Student’s distribution,” and represented the test value with the letter t.

### Why Is The t-Distribution Valuable?

The t-distribution plays a significant role in statistics and analytics. Its wide range of uses includes the Student’s t-test, the creation of confidence intervals, linear regression analysis, and Bayesian analysis.

### t-Distribution and LogicPlum

At the core of LogicPlum’s platform is statistics. Therefore, the t-distribution is a critical component of this platform.

It is considered when comparing samples when samples are small in size and have a quasi-normal distribution, and throughout many of the automated calculations.

###### Additional Resources

- jbstatistics. (2013).
*An Introduction to the t Distribution*. Available athttps://www.youtube.com/watch?v=T0xRanwAIiI