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Goodness of Fit Tests: Writing Conclusions

Goodness of Fit Tests: Writing Conclusions
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2016-11-02 03:19
FunctionSequenceProbability & StatisticsSlider AnimationGraphing
This GeoGebra example provides an interactive demonstration of chi-square goodness-of-fit tests, focusing on how to write statistical conclusions based on the test statistic, degrees of freedom, and significance level. It simulates the entire process from generating random samples, calculating observed and expected frequencies, to constructing the chi-square statistic and deciding whether to reject the null hypothesis. Core mathematical concepts include the chi-square distribution, hypothesis testing, p-values, degrees of freedom, comparison of observed versus expected frequencies, and the influence of significance level on conclusions. In terms of construction, the example employs GeoGebra commands such as Element, CountIf, Sum, Sequence, If, Segment, Mean, SigmaXX, and ChiSquared, along with objects like PrmFct, seed, Frq1 through Frq6, DataSet, ExpVal, and TS. Sliders and buttons control the random seed, sample size, and confidence level, updating frequency tables, the chi-square statistic, and conclusion text in real time. This resource is suitable for high school to university-level statistics courses, particularly for teaching the steps and interpretation of chi-square tests, helping students understand how to make rigorous statistical inferences from data.

GeoGebra Commands & Parameters

  1. Element(FrqSqSq, DataSet) → Frq0
  2. CountIf(x ≠ (0, 0), Frq0) → K
  3. Sum(Frq0) → Size
  4. Element(CnfSq, Confidence) → Conf
  5. Sequence(round((ExpVal * 100)) / 100, k, 1, K) → ExpSq
  6. Sequence(Element[Frq0, k] - ExpVal, k, 1, K) → OmEC
  7. Sequence(Element[OmEC, k]^(2), k, 1, K) → OmEsqC
  8. Sequence(Element[OmEsqC, k] / ExpVal, k, 1, K) → OmEsqdEC
  9. Element(OutSeq, DataSet) → Out
  10. Sequence(round(((Element[Frq0, k] - ExpVal) * 1000)) / 1000, k, 1, K) → OmES
  11. Sequence(round((Element[OmEC, k]^(2) * 1000)) / 1000, k, 1, K) → OmEsqS
  12. If(PV1 ≥ 1.0E-4, PV1, 1.0E-4) → PV2
  13. If(PV1 < 1.0E-4, " < ", " = ") → IE1
  14. If(PV1 < Sig, "less than", "not less than") → Relate
  15. If(PV1 < Sig, "rejected", "kept") → TstDcs
  16. If(PV1 < Sig, "is", "is not") → IOA
  17. Element(DWSq, DataSet) → DW
  18. Sequence(Text[Element[Frq0, j], (0.3 + (DW * (j - 1)), 8)], j, 1, K) → FrqSqTx
  19. Sequence(Segment[(0.25 + (k * DW), 8.85), (0.25 + (k * DW), 7.9)], k, 0, K) → VrtLnSq
  20. Segment((0.25, 7.9), (0.25 + (K * DW), 7.9)) → tbbt
  21. Segment((0.25, 8.35), (0.25 + (K * DW), 8.35)) → tbmd
  22. Segment((0.25, 8.85), (0.25 + (K * DW), 8.85)) → tbtp
  23. Mean(OmEsqdEC) → L2Mn
  24. SigmaXX(OmEsqdEC) → L2SXsq
  25. Sequence(round((Element[OmEsqC, k] / ExpVal * 1000)) / 1000, k, 1, K) → OmEsqdES
  26. ChiSquared(df, x, true) → chsqpdf2
  27. Element(CtSqSq, DataSet) → CtSq0
  28. Sequence(Text[Element[CtSq0, j], (0.3 + (DW * (j - 1)), 8.5)], j, 1, K) → CtSqTx