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Hypothesis Testing

Hypothesis Testing. Ginger Holmes Rowell, Ph. D. April 24, 2002. Hypothesis Testing (HT). Uses Types General Procedures Example Review of Error Types Type I & Type II. Hypothesis Testing - Uses. Medical – Clinical Trials

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Hypothesis Testing

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  1. Hypothesis Testing Ginger Holmes Rowell, Ph. D. April 24, 2002

  2. Hypothesis Testing (HT) • Uses • Types • General Procedures • Example • Review of Error Types • Type I & Type II

  3. Hypothesis Testing - Uses • Medical – Clinical Trials • Show that Drug A lowers cholesterol more than the placebo (2-Sample for difference in means) • Show that the percent of people who have side effects from from Drug A is NOT different from the group taking the placebo (2-Sample for difference in proportions)

  4. Hypothesis Testing - Uses • Agriculture • Show that fertilizer A works better than fertilizer B • Psychology Experiments • Show that Intervention A keeps kids off of drugs better than what has been done traditionally • Education • Show that teaching method A is more effective than teaching method B

  5. Two Broad Categories of HT Parametric Methods: frequently used, more common Nonparametric Methods: used if sample size is small and populations are not normal(We will not talk about this type of HT.)

  6. HT General Procedure - Steps • Conduct a literature review or pilot study • Form your hypothesis • Set your threshold of error (determine desired significance level) • Design your experiment • Determine which HT to use • Determine Needed Sample Size

  7. HT Procedure: Steps Contin. • Collect your data • Enter data into appropriate tool (calculator, statistical software) • Examine data graphically • Find descriptive statistics • Use these methods to check for typos, errors, …

  8. HT Procedure: Steps Contin. • Find your “test statistic” and use it determine whether your data supports the null or alternative hypothesis.

  9. HT Example • Research Hypothesis • Using CI Applets will help students learn more about CI’s • Set Error Limit: 5% for Type I Error • Design Experiment • Give a pre-test, students use CI applet, give a post-test

  10. Statistical Analysis • Hypothesis • Using the java applets will improve content knowledge for math teachers • Ho: mimprovement = 0 • Ha: mimprovement > 0 • Improvement = Posttest score – Pretest Score • Statistical Test • Paired difference t-test (small sample) • Average improvement was approximately normal

  11. HT Example • Decide which HT to use ??? • Decide the needed sample size • Collect Data • You helped with that part • Examine Data • Graphically, descriptive statistics • Check for typos, errors, ...

  12. HT Example - DATA Points Improved = post test score – pre test score (Each test is scored out of 5 possible points)

  13. HT Example - DATA Variable N Mean StDev SE Mean Points Improved 12 1.3 1.6 0.463

  14. HT Example • What does our data say? • Is that enough evidence to reject the null in favor of the alternative? • What do you think? • How much evidence do you need? • Especially with this small sample size.

  15. HT Example - The WORK • Test statistic • Interpretation:The test statistic tells you the number of standard deviations that the sample mean (or proportion or variance) falls from the hypothesized value.

  16. Using Your TI-83 for HT • Press STAT>TESTS>t-test • Input: DATA • m0: 0 • LIST: LI • Freq: 1 • m: > • select Calculate

  17. HT Example • Test Statistic = t= 2.70 • What does this tell us? (Remember the Empirical Rule) • If the null is true, the chance of getting a data set like ours or one that supports the alternative even more is small (1% chance). • We got our data set & did not make any errors. • Do you believe the null hypothesis is true?

  18. HT Example • Conclusion • Reject the null in favor of the alternative hypothesis • What does that mean in the context of our problem? • We can expect an average improvement in content knowledge for math teacher who use the Regression applet

  19. HT Example • Next Question: How much improvement • Answer: Find a 95% confidence interval • Review – use your calculator to do this and interpret the result.

  20. Conclusion: Regression Applet • A statistically significant improvement in their average content knowledge can be expected for math teachers using the Regression applet(Rice Probability Webs). (t=2.7, n=12, p=0.01) • We expect (with 95% confidence) that the average improvement in content knowledge of regression will be between 0.2 and 2.3 points on a 5 point scale.

  21. Review • Null Hypothesis • Alternative

  22. Type I and II Errors • Type I Error • Type II Error • Power of Test

  23. Sample Size • What is the effect of sample size on statistical power?

  24. Comments • I hope you • Understand how to think about forming a hypothesis • Understand that actually testing the hypothesis is more than looking at the two sample averages and saying whether you think they are different.

  25. Questions ????????

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