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Visualizing Statistical Power of Hypothesis Tests

Visualizing Statistical Power of Hypothesis Tests
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2014-07-22 09:35
Coordinate GeometryCalculusProbability & StatisticsSlider AnimationGraphing
In collections AP Statistics
This example demonstrates the concept of statistical power visually, illustrating the relationship between power, sample size, and standard deviation in hypothesis testing. Key math concepts include hypothesis testing, statistical power, sample size, standard deviation, and normal distributions. It is constructed using GeoGebra commands like Point, InverseNormal, Normal, Segment, IntegralBetween, Textfield, and Vector, making it suitable for high school students and beginners in statistics learning hypothesis testing and power analysis.

GeoGebra Commands & Parameters

  1. Point(baseline) → mu1Point
  2. InverseNormal(mu0, sigma0, 1 - alpha / 2) → nullRightThreshold
  3. InverseNormal(mu0, sigma0, alpha / 2) → nullLeftThreshold
  4. Normal(mu0, sigma0, x) → nullDist
  5. Segment((nullLeftThreshold, nullDist(nullLeftThreshold)), (nullLeftThreshold, 0)) → leftThresholdLine
  6. Segment((nullRightThreshold, nullDist(nullRightThreshold)), (nullRightThreshold, 0)) → rightThresholdLine
  7. IntegralBetween(f, baseline, nullLeftThreshold, nullRightThreshold) → T2Region
  8. IntegralBetween(f, baseline, Min[leftBound, mu1 - (4 * sigma1)], nullLeftThreshold) → leftPowerRegion
  9. IntegralBetween(f, baseline, nullRightThreshold, Max[rightBound, mu1 + (4 * sigma1)]) → rightPowerRegion
  10. Textfield(alpha) → alphaInputBox
  11. IntegralBetween(nullDist, 0, leftBound, nullLeftThreshold) → t1lefttail
  12. IntegralBetween(nullDist, 0, nullRightThreshold, rightBound) → t1righttail
  13. Segment((nullLeftThreshold, nullDist(nullLeftThreshold)), (nullLeftThreshold, 0.6)) → leftRejectLine
  14. Segment((nullRightThreshold, nullDist(nullRightThreshold)), (nullRightThreshold, 0.6)) → rightRejectLine
  15. Vector((nullLeftThreshold, 0.55), (nullLeftThreshold - 0.8, 0.55)) → leftRejectArrow
  16. Vector((nullRightThreshold, 0.55), (nullRightThreshold + 0.8, 0.55)) → rightRejectArrow
  17. Textfield(difference) → differenceInputBox
  18. Segment((nullLeftThreshold, 0), (nullLeftThreshold, offset)) → leftThresholdLine2
  19. Segment((nullRightThreshold, 0), (nullRightThreshold, offset)) → rightThresholdLine2
  20. Segment(Point[{mu0, offset - 0.09}], Point[{mu0, offset - 0.11}]) → differenceLineLeftEnd
  21. Segment(Point[{mu1, offset - 0.09}], Point[{mu1, offset - 0.11}]) → differenceLineRightEnd
  22. Segment(Point[{mu0, offset}], Point[{mu0, offset - 0.017}]) → altOriginMark
  23. Segment((mu0, 0), (mu0, offset)) → mu0Guideline
  24. Vector((mu0, offset - 0.1), (mu1, offset - 0.1)) → differenceLine

AI Drawing Prompt Reference

Create a visualization of statistical power in hypothesis tests, featuring horizontal lines for critical values, a normal distribution curve, and integral regions for type I and type II errors. Use sliders to adjust standard deviation and sample size, showing how power changes with different parameters. Include arrows and text annotations to label key areas and parameters.
The prompt above was compiled from the original drawing commands and is for reference only.