StATS: What is a t statistic?

The t statistic is a measure of how extreme a statistical estimate is. You compute this statistic by subtracting the hypothesized value from the statistical estimate and then dividing by the estimated standard error. In many, but not all situation, the hypothesized value would be zero.

You have an indication that the hypothesized value is reasonable when the t-statistic is close to zero.  Alternately, you have an indication that the hypothesized value is not large enough when the t-statistic is large positive. Finally, you have an indication that the hypothesized value is too large when the t-statistic is large negative.

To formalize this approach, you need to compare the t-statistic to a percentile from the t-distribution. The t-statistic is sometimes also referred to as a t-test, t-ratio, or Wald statistic.

In a study of how low triiodothyronine in pre term infants affects IQ at 8 years follow up (BMJ 1996; 312: 1132-1133), the estimated deficit in IQ and standard error was 6.6 (3.0) for overall IQ, 8.5 (3.6) for verbal IQ and 5.0 (3.0) for performance IQ. These deficits were adjusted for sex, gestation, birth weight, Apgar score at 5 minutes, and days of ventilation. We wish to compare these estimated deficits to a hypothesized deficit of zero. The t-statistics would be:

Since the t-statistics are large positive, this gives some indication that the deficit is greater than the hypothesized value of zero.

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Definitions, Category: Definitions, Category: Hypothesis testing.