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Alpha Levels Impact on LSD Decisions: Finding Balance in Error Costs

Explore survey results on alpha levels, perceptions, and their impacts on least significant difference (LSD) decisions. Understand the costs of decision errors and the balance between Type I and Type II errors. Learn how to minimize losses and make informed choices. Discover valuable insights in data analysis and decision-making processes. Engage in discussions to enhance your decision-making skills.

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Alpha Levels Impact on LSD Decisions: Finding Balance in Error Costs

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  1. Jim RouseSCC-33 / UCTA1/27/2010 Alpha dogs: The significance of the LSD Rouse@iastate.edu515-294-5604

  2. Today’s topics • Alpha levels—survey results • Perceptions of alpha • Impact on LSD • Costs of decision errors

  3. Survey: What level do you use? n=27 (21 Public, 6 industry)

  4. Survey comments • Software provides LSD at 0.05 and 0.2. … often calculate my own at 0.1, because …0.05 is too inclusive …0.2 is too exclusive. • We use 0.1, but will use 0.05 if we really want to select hard. • Which one is accurate?

  5. Impact on LSD • Increase in alpha will decrease LSD • 0.05 is indeed more inclusive

  6. Least significant difference

  7. Making Decisions • H0 No differences • HA  Differences

  8. Making Decisions • Type I error rate = α, typically 0.05 • Type II error rate = β, typically unspecified and unknown

  9. Making Decisions • α is inversely related to β • Lower prob of Type I error = higher prob of Type II error • Key: What is appropriate balance? • Based on cost of errors

  10. Decision Errors • What is the cost of Type I error? • 2 hybrids are “same”, but we think not • Result: Choose one over another • No difference, no cost • Grower’s perspective only!

  11. Decision Errors • What is the cost of Type II error? • 2 hybrids are “different”, but we think not • Result: Choose either • Choose the better one, no cost • Choose the worse one, cost • Half the time, T-II errors cost growers • Loss depends on true difference • Yield difference between choices

  12. Finding Value in the Data • Determine relative cost of errors • Adjust α to minimize losses • (a la Carmer in Crop Science, 1976) • Difference between reality and theory? • Many growers use α = 1 • Eliminates Type II errors

  13. That’s all! Questions—Comments—Discussion

  14. New truths… “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.” —Max Planck (founder of quantum theory)

  15. Background “I have great faith in fools; self-confidence my friends call it.” —Edgar Allan Poe “Don’t math it all up.” —Glenda Rouse, my wife

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