ExplanationThe Standard Normal Distribution
Imagine that you took every point in your data and calculated its z-score. That is, you took each point, subtracted the mean and divided by the standard deviation. You would have a new data set with some interesting properties:- The mean would equal zero;
- The standard deviation would be one;
- The z score of any of these new values would equal the value itself (as any number minus zero, divided by 1 remains the same).
If your original data had a normal distribution, then this new data has what is known as the Standard Normal Distribution. It is also sometimes called the z-distribution for obvious reasons. Why Do We Need a Standard Normal Distribution?
This new distribution is simply the z-scores for all of your data. It is useful for all the same reasons that z-scores are useful. It is just that you convert all of your data at once. The section in this tutorial on probability distributions explains how you can convert from z-scores to probabilities. The useful thing about the z-distribution is that its values (being z-scores) can be looked up directly in z-tables and hence converted to probabilities. Of course, you could convert your original values to z-scores as and when you needed to. |
The Normal Distribution
