T scores are also standardized norm scores, where the mean value is 50 and standard deviation value is 10, in contrast to Z scores where mean value is "0" and standard deviation value is 1.
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Z scores are used for standardized testing done by most school districts. It is the most common way of standardizing data. IQ scores can be standardized using z scores. The mean is 100 and the standard deviation is 15. You use the t score when the sample is small, <30 often. Many behavior ratings use t scores.
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Because t-score isn't as accurate as z-score, you should use 40 as a safety sample size, rather than 30 as you would for a z-score.
T-scores and z-scores measure the deviation from normal. The normal for T-score is 50 with standard deviation of 10. if the score on t-score is more than 50, it means that the person scored above normal (average), and vise versa. The normal for Z-score is 0. If Z-score is above 0, then it means that person scored above normal (average), and vise versa.
Because as the sample size increases the Student's t-distribution approaches the standard normal.