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On stattrek, there's a calculator that computes the t-score given the

  • degree of freedom
  • cumulative frequency

The formula is given on the page as:

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Without the population mean, how did the calculate on the top of the stattrek page calculate t-score? http://stattrek.com/online-calculator/t-distribution.aspx

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  • $\begingroup$ from scipy import stats; tscore = stats.t.ppf(cumprob,degfree) ? $\endgroup$
    – alvas
    Commented Mar 28, 2017 at 5:57

2 Answers 2

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The formula you quote relates t to quantities derived from a data set. The calculator uses the theory behind the t-distribution to determine P(t) given t, or t given P(t). This will only accurately relate the t calculated from your data set to the empirical distribution function of your data set if the null hypothesis that underlies the t-test is true for your experiment.

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The theoretical T distribution's shape is only determined by its degrees of freedom, and if you know the shape and tail area of the distribution you know how far you are from the mean (imputed to be zero with scale parameter 1).

It's analogous to a Z score, the mean and variance are immaterial if you know the cumulative probability density and where you lie on it (since the shape is always normal i.e. for a t distribution approaching infinity).

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