Significance Tests

These tests are much and many. Each test is designed to deal with certain types of situations. Each test varies in broadness of the applicability, in thier accuracy, in their efficiency, and in the amount of arithmetic which they entail. So to know some of these tables is only half the battle the second part of the battle is to use the correct table and the only way to learn this is to practice, practice, practice.

The book titled Statistics (Cliff Notes) described that the concept uses several terms: probability, area of the curve, Type I error rate, and so forth. Another common representation of Significance is the letter p (for pobability) and a number between 0 and 1. There are several ways to refer to the significance level of tests, and it is important to be familar with them. All of the following statements, for example, are equivalent:

  The finding is significant at the .05 level.
  The confidence level is 95%.
  The Type I error rate is .05.
  The alpha level is .05.
  There is a 95% certainty that the result is not due to chance.
  There is a 1 in 20 chance in obtaining this result.
  The area of the region of rejection is .05.
  The p-value is .05.
  p = .05.

Whenever you come across a result which is statistically significant the book titled, Practical Statistics stated that you must still access whether the difference is of any practical consequence or not. There are times when a tiny, but real, difference can save millions of dollars, and other times when such a difference is not worth knowing about.

There is alot of information on this subject and I found the perfect website that does a great job explaining how the "level of statistical significance" is calculated, why the "Normal distribution" is important, illustration of how the normal distribution is used in statistical reasoning (induction) and are all test statistics normally distributed?

There are many websites that describe the Significance Tests, for example there iis a webite that explains some of the Signifcance Tests, I found this one interesting and educating.   For the person who understands the Significance Test, this site is full of formulas.