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Section 10.4.2 Power

Section 10.4.2 Power. AP Statistics March 11, 2008 CASA. What is Power?. Power is a test of sensitivity. Your statistical test may be able to detect differences, but how well does it detect difference of a pre-determined nature?

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Section 10.4.2 Power

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  1. Section 10.4.2Power AP Statistics March 11, 2008 CASA

  2. What is Power? • Power is a test of sensitivity. • Your statistical test may be able to detect differences, but how well does it detect difference of a pre-determined nature? • The Power procedure allows to state the probability of our procedure to catch the differences. AP Statistics, Section 8.2.1

  3. Power Procedure • Begin by stating your H0 and Ha as usual. • Find the z* or t* that would allow you to reject H0. • Find the x-bar that matches up with the z* or t*. • Assuming that you have a particular true mean, what is the probability that you would be to still reject the H0? AP Statistics, Section 8.2.1

  4. Power Example: Example 10.23 • Can a 6-hour study program increase your score on SAT? A team of researchers is planning as study to examine this question. Based on the result of a previous study, they are willing to assume that the change has σ=50. Research would like significance at the .05 level. AP Statistics, Section 8.2.1

  5. Power Example: Example 10.23 • A change of 50 points would be considered important, and the researchers would like to have a reasonable chance of detecting a change is this large or larger. Is 25 subjects a large enough sample for this project? AP Statistics, Section 8.2.1

  6. Step 1: State your hypothesis • H0: µ=0 • Ha: µ>0 • Where µ represents the change is in the SAT score. AP Statistics, Section 8.2.1

  7. Step 2: Find the z* value and find the data value • We'll set α=.05, invNorm(.95) gives us a z*=1.645. • What is the lowest x-bar would show significance? • Summary: If we had a study with n=25 and x-bar>16.45, we would have significance. AP Statistics, Section 8.2.1

  8. Step 3: Chance at importance • We stated that gains of 50 points would be considered "important". We state this as the alternative µ=50. • The power against the alternative µ=50 increase is the probability that H0 is rejected whenµ=50. • Restated: What the area from 16.45 to ∞ under a normal curve centered at µ=50. AP Statistics, Section 8.2.1

  9. Step 3 • normalcdf(16.45,1E99,50,50/√(25))=.9996 • Summary: because the power is so high, there is a great chance of finding a significance when the real increase is 50. AP Statistics, Section 8.2.1

  10. Increase Power by… • increase alpha • increase sample size AP Statistics, Section 8.2.1

  11. Exercises • 10.71-10.77 odd, 10.79-10.89 AP Statistics, Section 8.2.1

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