Intervals & Tests
The following is an excerpt from The Quality Engineering Handbook by Thomas Pyzdek, © QA Publishing, LLC.
Statistical inference generally involves four steps:
1. Formulating a hypothesis about the population or "state of nature,"
2. Collecting a sample of observations from the population,
3. Calculating statistics based on the sample,
4. Either accepting or rejecting the hypothesis based on a pre-determined acceptance criterion.
There are two types of error associated with statistical inference
· Type I error (α error)–The probability that a hypothesis that is actually true will be rejected. The value of α (alpha) is known as the significance level of the test.
· Type II error (ß error)–The probability that a hypothesis that is actually false will be accepted.
Type II errors are often plotted in what is known as an operating characteristics curve. Operating characteristics curves will be used extensively in subsequent chapters of this book in evaluating the properties of various statistical quality control techniques.
Confidence intervals are usually constructed as part of a statistical test of hypotheses. The hypothesis test is designed to help us make an inference about the true population value at a desired level of confidence. We will look at a few examples of how hypothesis testing can be used in quality control applications.
Learn more about the Statistical Inference tools for understanding statistics in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Intro. to Statistics short course (only $89) or his online Black Belt certification training course ($875).