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When working with a normal distribution, the z-score can be interpreted as the number of standard deviations from the mean a given value is. ($z=2$ means that $ x $ is 2 standard deviations from the mean of the normal distribution $ \mu $.) Is there a similar interpretation for a t-score? (i.e. Does a t-score of 2 refer to a value that is 2 "standard errors" from the center of the distribution?)

Glen_b
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ZachTheRiah
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    Does the answer to this question cover what you want to know? There may be some value in this question as well – Glen_b Apr 26 '16 at 01:36
  • NB your title refers to a t-statistic; this is not necessarily the same thing as a t-score (which the body text asks about). Indeed, "t-score" could potentially mean more than one thing. Can you please quote from what you're looking at? (preferably a part that defines the statistic that is actually being discussed in the source material) – Glen_b Apr 26 '16 at 01:43
  • @Glen_b Your answer in the first post suffices for this question. I am referring to a t-score in reference to a hypothesis test: $ t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}} $ – ZachTheRiah Apr 26 '16 at 04:01
  • Okay, that wasn't clear -- then yes, the t-statistic is a studentized sample mean (where the standard error of the mean is estimated from the data) and tells you how many standard errors (of $\bar{x}$) that $\bar{x}$ is from $\mu$. I think that with your clarification the question isn't quite answered by that first link, and some additional details are needed for an answer. I'll try to post one. – Glen_b Apr 26 '16 at 04:09

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