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Question 297:



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The t-statistic, also called the student t-statistic is similar to the z-statistic or z-score except that you need to take into account the size of the sample. The z-score assumes your sample is large or you are using the whole population. The t-statistic converges toward the z-statistic as the sample increases and the two are identical when the sample size is infinity.

There is no formula for the t-statistic, just like the z-statistic and instead iterative algorithms are used to approximate the area under the curve (often called Newton-Raphson procedures). This is why the values are tabled in backs of books because the computations are intense or one needs access to a computer.  Typical computer formula use approximations, one popular one is based on the work by Abramowitz and Stegun, which is what this site uses.

Obtaining a t-statistic is what occurs when you conduct a t-test. See question 290 for an example. Excel also calculates the t-statistic using the formula TDIST.

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