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Hypothesis Testing

Hypothesis Testing. EDU647 Laurene Johnson Jim bellini. Null Hypothesis. Evaluated using inferential statistics No differences between groups –or– no linear relationship between variables We’ll look at the equations for these later. In terms of Sneetches. Null hypothesis.

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Hypothesis Testing

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  1. Hypothesis Testing EDU647 Laurene Johnson Jim bellini

  2. Null Hypothesis • Evaluated using inferential statistics • No differences between groups –or– no linear relationship between variables • We’ll look at the equations for these later.

  3. In terms of Sneetches Null hypothesis http://www.characterent.com/blog/?m=200906

  4. In terms of Sneetches • Null hypothesis—no differences between star-bellied and plain-bellied Sneetches on mean CSB scores. • Accepting null means no significant difference in CSB scores between two types of Sneetches • Rejecting null means there is a difference in CSB scores that is unlikely to be the result of chance alone http://www.characterent.com/blog/?m=200906

  5. Goal of hypothesis testing • Demonstrate that null hypothesis is unlikely to be true • Lend support to alternative hypothesis • Alternative hypothesis states that there are differences/a linear relationship

  6. In terms of Sneetches Alternative hypothesis http://www.characterent.com/blog/?m=200906

  7. In terms of Sneetches • Alternative hypothesis—differences between star-bellied and plain-bellied Sneetches on mean CSB scores • Rejecting the null supports, but doesn’t prove, this hypothesis • When you disconfirm the null hypothesis, it only means the null isn’t true, not that the alternative is true • Unprove the negative because you can’t provethe positive http://www.characterent.com/blog/?m=200906

  8. Representations of null hypothesis • One-sample z- or t-test • H0: µ1 = µ ; where µ1 = hypothesized population mean where µ=known population mean • Independent (two) samples t-test • H0: µ1 = µ2 ; where µ1 = hypothesized population mean (based on sample M, group 1) where µ2 =hypothesized population mean (based on sample M, group 2) • Correlation • H0: rxy = 0 where rxy is the hypothesized correlation between two variables in the population

  9. In terms of Sneetches • Independent (two) samples t-test • H0: µ1 = µ2 ; where µ1 = CSB mean star-bellied where µ2 = CSB mean plain-bellied http://www.characterent.com/blog/?m=200906

  10. Representations of alternative hypothesis • One-sample z- or t-test • Ha: µ1 ≠ µ ; where µ1 = hypothesized population mean where µ=known population mean • Independent (two) samples t-test • Ha: µ1 ≠ µ2 ; where µ1 = hypothesized population mean (based on sample M, group 1) where µ2 =hypothesized population mean (based on sample M, group 2) • Correlation • Ha: rxy ≠ 0 where rxy is the hypothesized correlation between two variables in the population

  11. In terms of Sneetches • Independent (two) samples t-test • Ha: µ1 ≠ µ2 ; where µ1 = CSB mean star-bellied where µ2 = CSB mean plain-bellied • This is the hypothesis Sylvester is attempting to support http://www.characterent.com/blog/?m=200906

  12. When different means different • Statistical significance—indicates that the obtained results are not due to chance • Typically obtained when the difference between groups is so large or the relationship so strong that it occurs by chance less than 5% of the time

  13. In terms of Sneetches • Sylvester’s differences are not large enough to rule out chance (p > .05) • Null hypothesis is accepted • Two types of Sneetches are from the same population But, are we sure? http://www.characterent.com/blog/?m=200906

  14. Type 1 Error Researcher rejects the null hypothesis

  15. Type 1 Error • Researcher rejects the null hypothesis when it should have been accepted • Researcher concludes that there is a statistical difference when there isn’t • Alpha level determines the likelihood of a Type 1 Error • Alpha=.05 means 5% chance of Type I error • Alpha level is set by researcher

  16. In terms of Sneetches • Null hypothesis is accepted. • Type 1 error… http://www.characterent.com/blog/?m=200906

  17. In terms of Sneetches • Null hypothesis is accepted • Type 1 error does not apply http://www.characterent.com/blog/?m=200906

  18. Type 2Error Researcher accepts the null hypothesis

  19. Type 2 Error • Researcher accepts the null hypothesis when it should have been rejected • Researcher concludes that there isn’t a statistical difference when there actually is • Beta level determines the likelihood of a Type II error • Related to power (the likelihood of finding significancewhen it exists in the population) • Power = 1 – β • More power, less chance of Type 2 error

  20. In terms of Sneetches • Type 2 error… http://www.characterent.com/blog/?m=200906

  21. In terms of Sneetches • Type 2 error is a possibility • Possible there are differences in star- and plain-bellied Sneetches • We will never know • Diagram of Type 1 and 2 error http://www.characterent.com/blog/?m=200906

  22. Testing the null with CI Scenario: Many years ago, a group of Sneetches wandered away from the other Sneetches and became isolated on a desert island. The two groups have had no contact since they were separated. Are the island-Sneetches part of the greater Sneetch population, or are they now different enough to be something else entirely? What is the null hypothesis? What is the alternative hypothesis?

  23. Data needed • One sample t-test (comparing sample (island Sneetches) to population • Population mean on CSB µ = 100 • Estimated standard deviation of population SD = 10.83 • Sample (island Sneetches) mean on CSB M = 106 • Sample size n = 30

  24. Do the math t = M - µ SEM Calculate SEM

  25. Do the math t = M - µ SEM Calculate SEM Enter values in equation

  26. Do the math t = M - µ SEM Calculate SEM Enter values in equation106 – 100 = 2.011

  27. Do the math t = M - µ SEM Calculate SEM Enter values in equation106 – 100 = 2.983 2.011 Check t-table for 29 df and .05 level of significance Our value needs to meet or exceed 2.045

  28. Accept or reject the null? Reject! Which means… A difference of this size is unlikely due to chance Supports alternative hypothesis that Island Sneetches are different than other Sneetches

  29. Using Confidence Intervals Use t-value to calculate confidence intervals for 95% level of confidence for one sample t-test Gives us the range of mean scores for the population with 95% probability Does known population mean fall within this range of scores?

  30. Using Confidence Intervals

  31. Using Confidence Intervals

  32. Using Confidence Intervals Does the known population mean fall in that range? Do we accept or reject the null hypothesis?

  33. How strong is this effect? Calculate the effect size

  34. How strong is this effect? Calculate the effect size

  35. How strong is this effect? Calculate the effect size How strong is this effect? Medium (d=.5) according to Sprinthall

  36. Review of Hypothesis Testing Video

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