Have Confidence in Your Statistical Analysis!: Learning How to Use Confidence Intervals
08/17/2009 5:10:00 PM EDT
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Confidence intervals are the most valuable statistical tools available to decision makers. However, for a variety of reasons, confidence intervals are not used as frequently as they should. This article answers two questions that are often misunderstood:
- Why are point estimates useless for making decisions?
- What is the best confidence level?
Why are Point Estimates Useless for Making Decisions?
Example 1: Suppose I measure the hardness of five steel parts, and the measurements are 57, 55, 57, 56 and 55. The mean of these measurements is 56. Usually, we expect this value to represent something about a larger population of parts. The population mean µ cannot be known with certainty, but the sample mean, 56, is our best estimate of the population mean, based only on these five parts. The number 56 is a point estimate of the population mean.
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Contributor:
Andy Sleeper |
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Its nice article. I think the example 3 is reversed in mentioning Type I & Type II risk.
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Agreed this is a good article. A point estimate may though not be another useless number. If the standard deviation is already well known, such as a test for which a comprehensive GRR has been performed (where repeats >>10) or a control is being run on a frequent basis, then the std dev from these can be used. The std dev from these can be much better since it's based on far more repeats. A finite interval is given even when the number of repeats is 1. Use the Z in that case. A greater amount of repeat measurements is needed when one wants a tighter range of 95% conf limits.
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Hi rschweiger, Initially I also thought the same way as you did. Your statement (rejecting good part is type I risk) also correct. If we see the type1 risk in confidence interval perspective, wrongly estimating the population mean is type 1 risk - ie., our calculated confidence interval do not have population mean. Example if we calculate CI 100 times by taking samples from population, we may be wrong 5 times for 95% Confidence interval, but we do not know when this 5 times going wrong is not known. In this example type 1 error is 5%. Type 1 error for CI is risk based on result of estimation. Type 1 error in sampling inspection is risk based on result of action taken.
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thanks for sharing the article.
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Excellent article. Do you have your Type I and Type II risks reversed in examples 3 and 4? Usually, rejecting something when it is actually good is the Type I risk. Or am I being overly simplistic and/or missisng something?
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