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Quick reference
Alpha and Beta Risk
When using inferential statistics, there is the possibility of making a wrong decision. This is known as alpha risk and beta risk. The magnitude of these risks are related to the confidence level and the sampling approach.
When to use
Whenever inferential statistics are used, there is the possibility of alpha risk and beta risk. The alpha risk is determined as soon as the confidence level is set and the beta risk is based upon the sampling approach and the characteristics of the data.
Instructions
Hypothesis testing provides a statistic that is used to either reject the Null hypothesis or fail to reject the Null hypothesis. However, that decision is based upon comparing the statistic to some threshold value. Depending upon where that value is set, there is the possibility of making a wrong decision.
- False Positive – Rejecting the Null hypothesis when it is true. This is known as the alpha risk or Type I error
- False Negative – Failing to reject the Null hypothesis, even though it is not true. This is known as the beta risk or Type II error.
A truth table reflecting these conditions is shown below:
Needless to say the desire is to always make the right decision. But at times there is an overlap in the sample data sets and that leaves a zone where a statistical value could be reached with either truth condition. In that case, the alpha and beta risks are inversely related. When one gets larger the other gets smaller. Consider the drawing below. If the threshold line is moved to the right, the alpha risk will decrease but the beta risk will increase. And the opposite will happen if the threshold line is moved to the left.
Increasing the sample size will reduce these risks because the confidence interval will be reduced.
The alpha risk is determined by subtracting the confidence level from 1. So a confidence level of .95 will create an alpha risk of .05. This is also referred to as the significance level. The alpha risk creates a bias towards the Null hypothesis. If a wrong decision is made, we prefer that we fail to recognize a difference rather than thinking we have seen a difference when one is not there; and then spending money and effort fixing a problem that does not exist.
The beta level will be determined by the differences in the data and the sampling approach used. The Beta risk is referred to as the Power of a test. The Power provides a sense of the effectiveness of the hypothesis test.
When conducting hypothesis testing, you must choose an alpha risk level and it is related to your confidence level. Generally, the higher the impact, the higher the confidence level and therefore the smaller the alpha risk. The table below shows some typical confidence levels and associated alpha risks for different business conditions. Most Lean Six Sigma projects operate at the 95% confidence level which is a .05 alpha risk.
Effect of Error |
Confidence Level |
α Risk |
Low Cost Rework |
.9 |
.1 |
High Cost Rework |
.95 |
.05 |
Personal Injury |
.99 |
.01 |
Single Death |
.999 |
.001 |
Multiple Deaths |
.9999 |
.0001 |
Hints & tips
- Lean Six Sigma projects normally use a .95 confidence level. Coordinate closely with stakeholders and Black Belts before changing that value.
- The principle of “innocent until proven guilty” is being applied to the Null hypothesis. That is the alpha risk is so low, It is essentially saying that there is only a 5% chance of a False Positive.
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