Difference Between Z Score and T Score

Z Score vs T Score

Z score and T score are used in statistics and are referred to as standard scores. They indicate how many SD an observation in a data is above or below the mean. Most commonly used in a z-test, z-score is similar to T score for a population. It is similarities between the two tests that confuse students. However, there are differences and this article will highlight these differences to remove doubts from the minds of the readers.

When you know the population standard deviation and population mean for a population, it is better to use Z test. When you do not have all this information and instead have sample data, it is prudent to go for T test. In Z test, you compare a sample to a population. On the other hand, T test can be performed for a single sample, two distinct samples that are different and not related or for two or more samples that are matching. When the sample is large (n greater than 30), Z- score is normally calculated but T-score is preferred when the sample is less than 30. This is because you do not get a good estimate of the standard deviation of the population with a small sample and this is why a T score is better.

One place where Z scores are very common is hospitals where bone mass density of a person is interpreted using these scores. Bone density machines used different kinds of units which is why it became a common practice to report the results of bone density tests in terms of Z scores. A person who has a Z score of zero and is at 50th percentile is considered to be average.

These Z scores are also used by pediatricians to make sense of height of kids. If a kid is at 5th percentile which is Z score of –i.65, he or she is considered to be short for his age.

Z score = (patient’s BMD- expected BMD)/SD

It is easy to calculate T score once you know the Z score of a person and the formula is as follows

Z score= T score – reference T score

Z Score vs T Score

• T scores and Z scores are measures that measure deviation from normal.

• In case of T scores, the average or normal is taken as 50 with a SD of 10. So a person scoring more or less than 50 is above or below average.

• The average for Z score is 0. To be considered above average, a person has to get more than 0 Z score.