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Step Through Chi-Square Goodness of Fit Test

Step Through Chi-Square Goodness of Fit Test
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2013-11-21 07:16
Probability & StatisticsGeometric ConstructionSlider AnimationGraphing
In collections Statistics Step Through Applets
This example demonstrates the chi-square goodness of fit test process through various instances, showing how data matches theoretical distributions. Key math concepts include statistical hypothesis testing, frequency distribution, chi-square distribution, and statistical characteristics. GeoGebra commands like Element, CountIf, Sum, Sequence, If, Segment are used, along with objects such as Val1-Val6, Frq1-Frq6, DataSet. Suitable for high school students and beginners in statistics for learning hypothesis testing methods, teaching demonstrations, and data analysis practice.

GeoGebra Commands & Parameters

  1. Element(FrqSeq, DataSet) → Frq
  2. Element(ValSeq, DataSet) → Val
  3. CountIf(x ≠ (0, 0), Frq) → K
  4. Sum(Frq) → Size
  5. Element(ConfSeq, Confidence) → Conf
  6. Sequence(round(ExpVal * 100) / 100, k, 1, K) → ExpSeq
  7. Sequence(Element[Frq, k] - ExpVal, k, 1, K) → OmEC
  8. Sequence(Element[OmEC, k]^(2), k, 1, K) → OmEsqC
  9. Sequence(Element[OmEsqC, k] / ExpVal, k, 1, K) → OmEsqdEC
  10. Element(OutSeq, DataSet) → Out
  11. Sequence(round((Element[Frq, k] - ExpVal) * 100) / 100, k, 1, K) → OmES
  12. Sequence(round(Element[OmEC, k]^(2) * 100) / 100, k, 1, K) → OmEsqS
  13. Sequence(round(Element[OmEsqC, k] / ExpVal * 100) / 100, k, 1, K) → OmEsqdES
  14. If(PVal1 ≥ 1.0E-4, PVal1, 1.0E-4) → PVal2
  15. If(PVal1 < 1.0E-4, " < ", " = ") → IE1
  16. If(PVal1 < Sig, "less than", "not less than") → Relate
  17. If(PVal1 < Sig, "Reject", "Keep") → Decis
  18. If(PVal1 < Sig, "IS", "IS NOT") → IOA
  19. Sequence(Text[Element[Frq, j], (0.2, 4.6 - 0.6 * j)], j, 1, K) → OSqTx
  20. Sequence(Text[ExpVal, (1.5, 4.6 - 0.6 * j)], j, 1, K) → ESqTx
  21. Sequence(Text[Element[OmES, j], (3, 4.6 - 0.6 * j)], j, 1, K) → OMESqTx
  22. Sequence(Text[Element[OmEsqS, j], (4.3, 4.6 - 0.6 * j)], j, 1, K) → OMEsqSqTx
  23. Sequence(Text[Element[OmEsqdES, j], (5.8, 4.6 - 0.6 * j)], j, 1, K) → OMEsqdESqTx
  24. Element(DWSq, DataSet) → DW
  25. Sequence(Text[Element[Val, j], (0.3 + DW * (j - 1), 8.5)], j, 1, K) → ValSqTx
  26. Sequence(Text[Element[Frq, j], (0.3 + DW * (j - 1), 8)], j, 1, K) → FrqSqTx
  27. Sequence(Segment[(0.25 + k * DW, 8.85), (0.25 + k * DW, 7.9)], k, 0, K) → VrtLnSq
  28. Segment((0.25, 7.9), (0.25 + K * DW, 7.9)) → TbBt
  29. Segment((0.25, 8.35), (0.25 + K * DW, 8.35)) → TbMd
  30. Segment((0.25, 8.85), (0.25 + K * DW, 8.85)) → TbTp

AI Drawing Prompt Reference

Create a statistical chart demonstrating the chi-square goodness of fit test. Include bar charts for theoretical and actual frequency distributions, along with calculated statistics like expected values, observed values, and squared residuals. Adjust parameters using a slider to display test results under different confidence levels, with text annotations for key values. The layout should feature multiple sections showing data, calculations, and conclusions.
The prompt above was compiled from the original drawing commands and is for reference only.