Normal Distribution v. Student's T Distribution

In summary, the Empirical Rule and Student's T-Distribution are two different statistical methods for analyzing data. The Empirical Rule assumes that the data is both normally distributed and stationary, while the Student's T-Distribution does not make these assumptions and is used when the population standard deviation is unknown. The Student's T-Distribution also takes into account the sample mean, while the Empirical Rule only considers the standard deviation.
  • #1
kimberley
14
0
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.

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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  • #2
Wikipedia said:
Student's distribution arises when (as in nearly all practical statistical work) the population standard deviation is unknown and has to be estimated from the data. Textbook problems treating the standard deviation as if it were known are of two kinds: (1) those in which the sample size is so large that one may treat a data-based estimate of the variance as if it were certain, and (2) those that illustrate mathematical reasoning, in which the problem of estimating the standard deviation is temporarily ignored because that is not the point that the author or instructor is then explaining.
http://en.wikipedia.org/wiki/T_distribution
http://en.wikipedia.org/wiki/Normal_distribution
 
  • #3
I believe that the Student distribution does not assume that the sample mean is the true (underlying) mean. So it is not just the variance or SD that is taken from the data, and I would say that the fact that the sample mean is used is more important than that the sample standard deviation is estimated from the data.
 

FAQs about Normal Distribution v. Student's T Distribution

1. What is the difference between Normal Distribution and Student's T Distribution?

Normal Distribution is a probability distribution that is symmetrical and bell-shaped, while Student's T Distribution is also a probability distribution but it has heavier tails and is less symmetrical.

2. Which distribution should I use for my data?

Normal Distribution is used when the sample size is large and the population standard deviation is known, while Student's T Distribution is used when the sample size is small or the population standard deviation is unknown.

3. Can I use Normal Distribution for any type of data?

No, Normal Distribution is only suitable for continuous data that is normally distributed, meaning it follows a bell-shaped curve.

4. How do I determine if my data follows Normal Distribution or Student's T Distribution?

This can be determined by plotting a histogram of the data and visually inspecting if it follows a bell-shaped curve. Additionally, statistical tests such as the Shapiro-Wilk test can be performed to assess the normality of the data.

5. Is one distribution better than the other?

It depends on the data and the purpose of the analysis. Normal Distribution is more widely used and has more established properties, but Student's T Distribution can be more robust for small sample sizes or when the population standard deviation is unknown.

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