What is the Difference Between Z Score and T Score?

The main difference between Z-scores and T-scores lies in the information they provide and how they are used.

• Z-scores are used to compare an individual's score to the mean of a population. They represent the number of standard deviations a data point is from the mean. A Z-score of 0 indicates that the data point is equal to the population mean, while a positive Z-score indicates the data point is above the mean, and a negative Z-score indicates the data point is below the mean.
• T-scores are used when the population standard deviation is unknown and need to be estimated using the sample standard deviation. They are used to compare an individual's score to the mean of a sample. Like Z-scores, T-scores also represent the number of standard deviations a data point is from the mean, but they are based on the sample standard deviation rather than the population standard deviation.

In summary, Z-scores are used when the population standard deviation is known and T-scores are used when the population standard deviation is unknown. Both scores are used to compare an individual's score to the mean of a population or sample, respectively, but they are based on different standard deviations.

Comparative Table: Z Score vs T Score

The main difference between z-scores and t-scores lies in the distribution they follow and the information required for their calculation. Here is a summary of their differences:

In summary, z-scores are used when you know the population standard deviation and mean, and the sample size is large (typically above 30). On the other hand, t-scores are used when the population standard deviation is unknown or has to be estimated, and the sample size is relatively small (typically below 30).