# What is a t-score?

##### 1 Answer

A t-score is closely related to its cousin the z-score

#### Explanation:

A z-score is based upon a Standard Normal distribution with a mean of 0 and standard deviation of 1.

The t-distribution was created by William Gossett to take into account **small** sample sizes. Like the Standard Normal, the t-distribution is perfectly symmetric about a mean of 0.

As the sample size (n) increases toward infinity, the t-distribution approaches the standard normal distribution.

The chart below compares the two:

Source: http://ci.columbia.edu/ci/premba_test/c0331/s7/s7_4.html

As you can see, the t-distribution (n=12) is **flatter** and more spread out.

When calculating a **confidence interval** , the t-distribution will result in a wider interval compared to the z-distribution. This is more conservative given the smaller sample size and increases the interval to better **capture** the true population parameter.

Hope that helps