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Variable inferential statistics
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Variable inferential statistics

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  • 1. Inferential Statistics HypothesisTestingEstimation (Confidence Interval)
  • 2. Understanding the Logic of Hypothesis Testing :Claim: Our medicine reduces weight tremendously :Test: Initial average weight of 50 people is 85 kg After using medicine the average weight is 84 kg :Conclusion: I don’t think so
  • 3. Understanding the Logic of Hypothesis Testing :Claim: Our medicine reduces weight tremendously :Test: Initial average weight of 50 people is 85 kg After using medicine the average weight is 70 kg Fantastic
  • 4. Understanding the Logic of Hypothesis Testing Is there any Change? Sample Statistic is very much different from Population Parameter Sample Statistic is not very much different from Population Parameter No Change: Change is because of Sampling Error/Randomness Yes there is Change: Change is because of Systematic Change
  • 5. Hypothesis Testing Process in General State the Null & Alternate Hypothesis Select the Level of Significance Determine the Test Distribution to Use Define the Critical Region Calculate the TestValue Decision: Reject H0 or Not Conclusion:Test is Significant or Not
  • 6. Reality Innocent Guilty Decision Acquit Punish Correct Decision Wrong Decision Wrong Decision Correct Decision H1: The Accused is Guilty Type I Error Type II Error H0: The Accused is not Guilty H0:The Accused is innocent
  • 7. Reality OK Not OK Decision Accept Reject Correct Decision Wrong Decision Wrong Decision Correct Decision H0:The lot is ok H1:The lot is not ok Type I Error Type II Error
  • 8. Differentiate Between CVM and PVM CVM PVM Reject H0 Don not Reject H0 TV ≥ CV TV < CV P ≤ Significance Level P > Significance Level
  • 9. CV Alpha NRR RR Reject Ho Don’t Reject Ho TV TV CriticalValue Method of HypothesisTesting
  • 10. Alpha NRR RR Reject Ho as P ≤Alpha Don’t Reject Ho as P > Alpha TV ProbabilityValue Method of HypothesisTesting P P TV
  • 11. Inferential Statistics for One Population Quantitative Qualitative (Nominal, Ordinal) Sigma Known Sigma Unknown Normal Non Parametric Z test t test Z test t test Wilcoxon test Binomial Test Chi SquareTest Kolmogorov-Smirnov Test Runs Test
  • 12. t test for Quantitative Data Assumptions Normal Population or Large Sample Formula T = Difference / SE SPSS Procedure Analyze > Compare Means > One Population t test Example The average marks of the students was 75 last year. The data was collected from 25 students and the mean was calculated. Can we conclude that mean is more than 75?
  • 13. t test for Qualitative Data Assumptions Normal Population or Large Sample Formula T = Difference / SE SPSS Procedure Analyze > Compare Means > One Population t test Example Test whether the majority of students are satisfied or not. Data Coding zero & one
  • 14. WilcoxonTest Assumptions Symmetric Formula W = Sum of Positive Ranks SPSS Procedure Analyze > NonParametric Test> 2 Related Samples> WilcoxonTest Example Test whether marks1 is more than 70 or not
  • 15. BinomialTest Assumptions Symmetric Description Used for small sample qualitative test SPSS Procedure Analyze > NonParametric Test> legacy dialogue > Binomial Example Test whether the majority is satisfied
  • 16. Inferential Statistics for two Population Qualitative (Nominal, Ordinal) Quantitative Independent Samples Paired Samples NormalParametric Pooled or Nonpooled t tests Paired t-test Mann WhitneyTestIndependent Samples Paired Samples Paired WilcoxonTest Fisher Exact, Chi Sq Median T, MWT, KS, WW McNemar, SignTest, WilcoxonPaired Test
  • 17. Pooled t-test Assumptions Independent Samples SPSS Procedure Analyze > Compare means> Independent Samples Test Example Marks1 for boys and girls differ Nonpooled t-test Normal Populations or Large Sample Equal Sigmas
  • 18. Paired t-test Assumptions Dependent Samples SPSS Procedure Analyze > Compare means> Paired t-test Example Marks1 is different from marks2 Normal Differences or Large Sample Sigma not known
  • 19. Same Results obtained taking differences of Marks1 and Marks2 and then applying t-test for 1 sample
  • 20. MannWhitneyTest Assumptions Independent Samples SPSS Procedure Analyze > NonParametric Test> 2 independent Samples Example Marks1 is different from marks2 Same Shape Distribution