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Social Statistics: t test

Social Statistics: t test. T test for dependent. A repeated-measures study (a.k.a dependent study) is one in which a single sample of individuals is measured more than once on the same dependent variable. Main benefit: two sets of data are from the same subjects. Example.

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Social Statistics: t test

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  1. Social Statistics: t test

  2. T test for dependent • A repeated-measures study (a.k.a dependent study) is one in which a single sample of individuals is measured more than once on the same dependent variable. • Main benefit: two sets of data are from the same subjects. S519

  3. Example • Three professors at University of Alabama studied the effects of resource and regular classrooms on the reading achievement of learning-disabled children. A group of children was test before they take the 1-year daily instruction and after they took the 1-year daily instruction. • Which statistical test we should use? S519

  4. T test for dependent : the sum of all the difference between groups : the sum of the differences squared between groups n : the number of pairs of observations S519

  5. T test for dependent S519

  6. T test for dependent • Step1: A statement of the null and research hypotheses S519

  7. T test for dependent • Step2: setting the level of risk (or the level of significance or Type I error) associated with null hypothesis • 0.05 S519

  8. T test for dependent • Step3: selection of the appropriate test statistics • Following Figure 10.1 • T test for dependent = t test for paired samples = t test for correlated samples S519

  9. T test for dependent • Step4: computation of the test statistic value • t=2.45 S519

  10. T test for dependent • Step5: determination of the value needed for rejection of the null hypothesis • Table B2 • df=n-1=25-1=24 • One tailed: because research hypothesis is directed S519

  11. T test for dependent • Step6: a comparison of the t value and the critical value • 2.45>1.711 • Reject the null hypothesis S519

  12. T test for dependent • Step7 and 8: time for a decision • There is the difference between pre-test and post-test: the post-test scores are higher than the pre-test scores. S519

  13. Excel: TTEST function • TTEST (array1, array2, tails, type) • array1 = the cell address for the first set of data • array2 = the cell address for the second set of data • tails: 1 = one-tailed, 2 = two-tailed • type: 1 = a paired t test; 2 = a two-sample test (independent with equal variances); 3 = a two-sample test with unequal variances S519

  14. Excel TTEST() • It does not computer the t value • It returns the likelihood that the resulting t value is due to chance • Less than 1% of the possibility that two tests are different due to chance  the two tests are difference due to other reasons than chance. S519

  15. Excel ToolPak • T test: paired two sample for means option S519

  16. Advantages of theRepeated-Samples Design • Repeated-measures design reduces or limits the variance, by eliminating the individual differences between samples. S519

  17. Problems With theRepeated-Samples Design • Carryover effect (specifically associated with repeated-measures design): subject’s score in second measurement is altered by a lingering aftereffect from the first measurement. S519

  18. Types of t test S519

  19. Example I • A researcher is interested in a new technique to improve SAT verbal scores. It is known that SAT verbal scores have μ=500 σ=100. • She randomly selects n=30 students from this population, and has them undergo her training technique. Students are given analogy questions, and are shocked each time they get an answer wrong. • The sample then writes the SAT, and gets M = 560. S519

  20. Example II • A social psychologist is interested in whether people feel more or less hopeful following a devastating flood in a small rural community. He randomly selects n=10 people and asks them to report how hopeful the feel using a 7-point scale from extremely hopeful (1) to neutral (4) to extremely unhopeful (7) • The researcher is interested in whether the responses are consistently above or below the midpoint (4) on the scale, but has no hypothesis about what direction they are likely to go. • His sample reports M=4.7, s = 1.89. S519

  21. Example III • To test the hypothesis that people give out more candy to kids in cute costumes than scary ones, I hire 20 kids to work for me. Ten are randomly assigned to wear cute bunny costumes, and the other ten wear Darth Vader costumes. • I drop the kids off in random parts of the city, and count the total pieces of candy each has after 1 hour of trick-or-treat. • Cute bunnies: M = 120, s = 10 • Darth Vaders: M = 112, s = 12 S519

  22. Example IV • We are testing the effects of moderate amounts of alcohol on driving performance. We make the hypothesis that even a small amount of beer will degrade driving performance (an increase in obstacles hit). • To test our hypothesis, we have n=5 subjects drive around a course on Big Wheels™ covered with cardboard cutouts of children and furry animals, and we record the number of cutouts they hit. Then, they drink one beer, and do the course again; again we record the number of cutouts hit. • What is a potential confound with this experiment? S519

  23. Example V • We want to determine if IU SLIS faculty publish more than the national average of 4 papers per year (per person). We take a random sample of n=12 IU SLIS profs and survey the number of papers each has published, obtaining M=6.3, s=1.13. S519

  24. Example VI • I want to know which dog is responsible for the holes in my yard. I buy 10 German Shepherds, 10 Beagles, and randomly assign each dog to its own yard. At the end of the day, the Beagles have dug M=11.3 holes, s=2.1, and the Shepherds have dug M=5.4 holes, s=1.9. Test my hypothesis that Beagles dig more holes than German Shepherds. S519

  25. Example VII • We want to know if noise affects surgery performance. We randomly select a sample of 9 surgeons, and have them perform a hand-eye coordination task (not while performing surgery, of course). The surgeons first perform the task in a quiet condition, and then we have them perform the same task under a noisy condition. Test the hypothesis that noise will cause poorer performance on the task. S519

  26. Example VIII • ETS reports that GRE quantitative scores for people who have not taken a training course are μ=555, σ=139. We take a sample of 10 people from this population and give them a new preparation course. Test the hypothesis that their test scores differ from the population. S519

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