[email protected] science to fuel and feed our global society Jim Rouse SCC-33 / UCTA...

[email protected] Applying science to fuel and feed our global society

Jim RouseSCC-33 / UCTA

1/27/2010

Alpha dogs:The significance of the LSD

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Today’s topics

• Alpha levels—survey results• Perceptions of alpha• Impact on LSD• Costs of decision errors


Survey: What level do you use?

n=27 (21 Public, 6 industry)

0.05 0.1 0.2 0.2502468101214161820


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?


Impact on LSD

• Increase in alpha will decrease LSD• 0.05 is indeed more inclusive


Least significant difference

locsreps

ErrorMeanSquaretLSD

*

2


Making Decisions

• H0 No differences

• HA Differences

H0 is true H0 is false

Accept H0 Correct Type II error

Reject H0 Type I error Correct / T-III


Making Decisions

• Type I error rate = α, typically 0.05• Type II error rate = β, typically

unspecified and unknown


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


• 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!

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

Decision Errors


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


That’s all!

Questions—Comments—Discussion


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)


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

[email protected] science to fuel and feed our global society Jim Rouse SCC-33 / UCTA...

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