The "Empirical Rule" states that if your data is normally distributed, 95.45% of that data should fall within "2" standard deviations of your Mean. There doesn't appear to be any reference to sample size in the literature regarding the Empirical Rule and a Normal Distribution.(adsbygoogle = window.adsbygoogle || []).push({});

By contrast, however, the Student's T Distribution table, for a two-tailed test, has multipliers that differ from the Empirical Rule. Although where N=10000, at 9999 degrees of freedom, the .0455 level is "2" sd like the Empirical Rule, where N=20, at 19 degrees of freedom, the .0455 level is "2.14" sd.

In sum, then, I don't understand the difference between the "normal distribution" and the "Student's T-Distribution". Is the difference that the Empirical Rule assumes that your data is both normal and "stationary" whereas the Student's T Distribution (i.e., degrees of freedom) assumes that your data is not stationary and that your Mean and Standard Deviations for any period of N will shift with the addition of new data? It's the only thing I can think of since the formulas for confidence intervals for Means and prediction intervals for individual outcomes use the numbers from the Student's T-Distribution.

Thanks in advance.

Kimberley

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# Normal Distribution v. Student's T Distribution

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