Alpha & Beta Risk
Explain the conceptual and quantitative relationships between Alpha risk and Beta risk when testing hypotheses, and include the impact sample size plays in managing these risk levels.
This is a double-discussion assignment (80 points) that should be submitted as a Microsoft Word or Adobe Acrobat document submission. There are no responses to other students required (therefore, the assignment will close and lock shortly after the due date and time).
Some students have been asking how many words this essay should be. Generally I worry more about quality than quantity, but it’s a fair question. It’s a double discussion with no responses required, so… since each discussion would typically be up to 200 words on your initial post, plus another hundred on each response, you would typically be in the 400-500 word range for a solid discussion. Since this is a double, you might best aim for the 800-1000 word range. It’s possible to adequately cover the topic with a bit less, but it would require good solid writing to do so.
If you are struggling with what to talk about in this essay, I recommend you re-watch the alpha-and-beta videos in Unit 10. Don’t just write a brief blurb about the definitions of alpha and beta error. In particular, you should be writing about the ways that accepting an Alpha risk increase can impact total risk — this is what we concentrate on as engineers. Hypothesis testing is a statistical technique, but risk management is an engineering requirement. Also consider what happens to these distributions as we increase the sample sizes being analyzed (Hint: What happens to the standard error as n increases?).
The distinction between Type I and Type II error — also know as Alpha and Beta error — is introduced, with an emphasis on recognizing that different engineering applications will want to optimize a balance between these two types of error differently. It is a common misconception that Type I error should always be minimized. In fact, this approach maximizes Type II error which might be the worst possible thing to do in an engineering design.
DISTINGUISHING ALPHA VS. BETA ERROR
Alpha error derives directly from the selection of the confidence boundary or interval selected during analysis – it is in the control of the statistician selecting it. Beta error is a result of that Alpha choice PLUS the reality of the true population represented by the sample — it is unknown, and often unknowable. The Power of our statistical test is a result of the interaction of these two factors.
CHANGES TO BETA RISK WITH INCREASING DEVIATION
While Alpha risk is known by selection, the actual Beta risk is unknown because we don’t know the true population. As the true value deviates from our estimate, the Power of the hypothesis test increases, meaning that the more wrong our estimate is, the more likely our hypothesis test will detect it and reject the Null hypothesis.
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