Alpha and Beta Risks

Alpha Risk

Alpha risk is the risk of incorrectly deciding to reject the null hypothesis. If the confidence interval is 95%, then the alpha risk is 5% or 0.05.

For example, there is a 5% chance that a part has been determined defective when it actually is not. One has observed or made a decision that a difference exists but there really is none. Or when the data on a control chart indicates the process is out of control but in reality the process is in control. 

Alpha risk is also called False Positive and Type I Error.

Confidence Level = 1 - Alpha Risk

Alpha is called the significance level of a test. The level of significance is commonly between 1% or 10% but can be any value depending on your desired level of confidence or need to reduce Type I error. Selecting 5% signifies that there is a 5% chance that the observed variation is not actually the truth.

The most common level for Alpha risk is 5% but it varies by application and this value should be agreed upon with your BB/MBB. 

In summary, it's the amount of risk you are willing to accept of making a Type I error.

If a carbon monoxide alarm goes off indicating a high level alert but there is actually not a high level then this is Type I error.

If conducting a 2-sample T test and your conclusion is that the two means are different when they are actually not would represent Type I error:

Beta Risk

Beta risk is the risk that the decision will be made that the part is not defective when it really is. In other words, when the decision is made that a difference does not exist when there actually is. Or when the data on a control chart indicates the process is in control but in reality the process is out of control. 

If the power desired is 90%, then the Beta risk is 10%.

There is a 10% chance that the decision will be made that the part is not defective when in reality it is defective. 

Power  = 1 - Beta risk

Beta risk is also called False Negative and Type II Error.

The Power is the probability of correctly rejecting the Null Hypothesis.

The Null Hypothesis is technically never proven true. It is "failed to reject" or "rejected".

"Failed to reject" does not mean accept the null hypothesis since it is established only to be proven false by testing the sample of data.

Guidelines: If the decision from the hypothesis test is looking for:

  • Large effects or LOW risk set Beta = 15% (which is Power of 0.85)
  • Medium effects, MEDIUM risk but not catastrophic, legal or safety related the set Beta = 10%
  • Small effects, HIGH risk, legal, safety, or critical set Beta from 5% to near 0%.

If conducting an F-test and your conclusion is that the variances are the same when they are actually not would represent a Type II error.

Same note of caution as for Alpha,  the assumption for Beta should be agreed upon with your BB/MBB. 

Decision Matrix

Alpha and Beta Risk

Hypothesis Testing Steps
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  1. Define the Problem
  2. State the Objectives
  3. Establish the Hypothesis (left tailed, right tailed, or two-tailed)
  4. State the Null Hypothesis (Ho)
  5. State the Alternative Hypothesis (Ha)
  6. Select the appropriate statistical test
  7. State the Alpha Risk level
  8. State the Beta Risk level
  9. Establish the Effect Size
  10. Create Sampling Plan, determine sample size
  11. Gather samples
  12. Collect and record data
  13. Calculate the test statistic and/or determine the p-value

If p-value is < than alpha-risk, reject Ho and accept the Alternative, Ha

If p-value is > than alpha-risk, fail to reject the Null, Ho

Try to re-run the test (if practical) to further confirm results. The next step is to take the statistical results and translate it to a practical solution.

It is also possible to determine the critical value of the test and use to calculated test statistic to determine the results. Either way, using the p-value approach or critical value provides the same result.

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Visual Relationship of Alpha & Beta Risk

Alpha and Beta Risks

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