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Statistics Review II

Statistics Review II. Types of statistical analyses (and when you use them) one sample z test one sample t test independent samples t test paired samples t test Pearson correlation one-way chi square one-way b/w subjects ANOVA one-way w/in subjects ANOVA multi-factor ANOVA w/in subs

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Statistics Review II

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  1. Statistics Review II

  2. Types of statistical analyses (and when you use them) one sample z test one sample t test independent samples t test paired samples t test Pearson correlation one-way chi square one-way b/w subjects ANOVA one-way w/in subjects ANOVA multi-factor ANOVA w/in subs b/w subs mixed

  3. Types of statistical analyses (and when you use them) one sample z test - you know population mean and s.d. - test if sample mean differs from population mean example: you want to determine if the mean IQ of adopted children differs from the general population of children

  4. Two-Tail Test • we want to know if the IQ of the adopted kids is different from the pop. • We don’t care if the adopted kids are smarter or dumber than the pop. • We use a two-tailed test

  5. Choosing Your Criterion (alpha) • Alpha (a) is the p that you select as the cut-off point for rejecting the null hypothesis.

  6. 2.5% 2.5% m = 100 Choosing Your Criterion rejection region

  7. Determine Your Critical z score • We want to look up the z-scores in which .025 of the curve is beyond the z score • zcrit = +/- 1.96 2.5% 2.5% -1.96 m = 100 +1.96

  8. Sample z-score • You need to calculate z and compare it to zcrit • We call this zobtained (zobt) zobt = X – m sC

  9. Types of statistical analyses (and when you use them) one sample t test – the same as the z test except that SEM is estimated by s

  10. Experimental Designs Within Subjects Between Subjects

  11. Types of statistical analyses (and when you use them) independent samples t test example: you want to see if milk chocolate improves quiz scores. Ten students are given 13.7 grams of milk chocolate at study and test, and 9 students are given 16 grams of caramel at study and test. Xchoc = 85.0 Xcarm = 77.8 H0: mchoc - mcarm< 0 t (17) = .976, p > .34 1.74 t values under null hypothesis

  12. Types of statistical analyses (and when you use them) independent samples t test example: you want to see if milk chocolate improves quiz scores. Ten students are given 13.7 grams of milk chocolate at study and test, and 9 students are given 16 grams of caramel at study and test. Xchoc = 85.0 Xcarm = 77.8 H0: mchoc - mcarm< 0 t (17) = .976, p > .34 .976 1.74 t values under null hypothesis We conclude that difference b/w means is not sig., i.e. the difference is due to sampling error

  13. Types of statistical analyses (and when you use them) independent samples t test example: you want to see if milk chocolate improves quiz scores. Ten students are given 13.7 grams of milk chocolate at study and test, and 9 students are given 16 grams of caramel at study and test. Xchoc = 85.0 Xcarm = 77.8 H0: mchoc - mcarm< 0 t (17) = .976, p > .34 ways to increase power - increase N - make IV more extreme - make DV more sensitive .976 1.74 t values under null hypothesis We conclude that difference b/w means is not sig., i.e. the difference is due to sampling error

  14. Types of statistical analyses (and when you use them) paired samples t test example: Wechsler examined the practice effect in a preschool IQ test. Fifty 5-year old children were tested, then retested 2-4 months later. Xt1 = 105.6 Xt2 = 109.2 r = .91

  15. Types of statistical analyses (and when you use them) paired samples t test example: Wechsler examined the practice effect in a preschool IQ test. Fifty 5-year old children were tested, then retested 2-4 months later. Xt1 = 105.6 Xt2 = 109.2 r = .91 t (49) = 4.16, p < .05 4.16

  16. Types of statistical analyses (and when you use them) Pearson correlation example: test to see if there is a relationship b/w GRE verbal scores and final exam scores in stats (N = 20). H0: r = 0 r (18) = .543, p < .05 r = 0 r =.44

  17. Types of statistical analyses (and when you use them) Pearson correlation example: test to see if there is a relationship b/w GRE verbal scores and final exam scores in stats (N = 20). H0: r = 0 r (18) = .543, p < .05 r = .543 r = 0 r =.44

  18. Types of statistical analyses (and when you use them) one-way chi square example: in a wine tasting test, 50 participants taste an ounce of German wine and an ounce of French wine. They choose the one that they prefer.

  19. Measurement Scales nominal DV is categorical Type of wine preferred German 20 French 30

  20. Measurement Scales nominal DV is categorical Type of wine preferred Expected value - null German 20 25 French 30 25

  21. Measurement Scales nominal DV is categorical Type of wine preferred Expected value - null German 20 25 French 30 25 c2 (1) = 2.0, p > .15

  22. Measurement Scales nominal DV is categorical Type of wine preferred Expected value - null German 18 25 French 32 25 c2 (1) = 3.92, p < .05

  23. Types of statistical analyses (and when you use them) one-way b/w subjects ANOVA example: 150 students are randomly assigned to three classes, 50 students per class. The same instructor is used for all 3 classes, but a different text is used in each one. All students take the same test at the end of the course. Do the scores differ significantly across classes? (The treatment is textbook.)

  24. 1 = error variance 2 = treatment variance 3 = total variance

  25. F Distribution H0: m1 = m2 = m3 Expected value under the null hypothesis is 1

  26. Types of statistical analyses (and when you use them) one-way w/in subjects ANOVA example: 36 participants receive 3 types of lists in the DRM paradigm (semantic, phonological, hybrid), and the prop. of false recall is measured. F (2, 70) = 6.25, p < .05

  27. Experimental Designs Factorial Design – 2 Independent Variables Within Subjects Between Subjects Mixed

  28. Testing for Main Effects and Interactions (multi-factor ANOVA) Main Effect – Determining if one IV has an effect on the DV Interaction – Determining if the effect of one IV remains constant at each level of the other IV

  29. Types of statistical analyses (and when you use them) multi-factor ANOVA w/in subs b/w subs mixed

  30. Types of statistical analyses (and when you use them) multi-factor ANOVA w/in subs b/w subs mixed example: two groups of participants participate in a DRM experiment w/ 3 types of lists (semantic, phonological, hybrid). One group is warned about the CL and the other is not.

  31. Figure 1: The proportion of false recall as a function of list type and warning status

  32. Figure 1: The proportion of false recall as a function of list type and warning status List Type, F (2, 100) = 22.33, p < .05 Warning, F (1, 50)= 13.24, p < .05 List Type by Warning, F (2, 100) = 5.06, p < .05

  33. Complex Correlational Procedures Multiple Regression – predicting the values of one dependent variable from multiple predictor variables

  34. Simple Regression • predicting DV from • 1 variable • Example: • predict Stats Exam Score • from GRE-Q

  35. Multiple Regression Example: Predicting Reading Success from RR and IQ Y = bX1 + bX2 + C

  36. Research Designs – Multiple Regression Dependent Variable Reaction Time Predictor Variables Frequency Length Spelling-to-Sound Consistency Neighborhood Size etc.

  37. Research Designs – Multiple Regression Word RT Frequency Length N ace 456.3 1.46 3 11 book 463.9 3.72 4 13 caught 482.4 3.34 6 2 stealth 524.2 .60 7 0 etc.

  38. Mega Studies – e.g.,Balota, Cortese, Sergent Marshall, Spieler, & Yap (2004); Cortese & Khanna (2007) Reading Aloud Lexical Decision .01 speech (sub)lexical semantic unexplained .35 .51 .40 .49 .15 .08 .005

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