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SPSS Homework

SPSS Homework. Practice. The Neuroticism Measure = 23.32 S = 6.24 n = 54 How many people likely have a neuroticism score between 29 and 34?. Practice. (29-23.32) /6.24 = .91 area = .3186 ( 34-23.32)/6.26 = 1.71 area =.4564 .4564-.3186 = .1378 .1378*54 = 7.44 or 7 people.

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SPSS Homework

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  1. SPSS Homework

  2. Practice • The Neuroticism Measure = 23.32 S = 6.24 n = 54 How many people likely have a neuroticism score between 29 and 34?

  3. Practice • (29-23.32) /6.24 = .91 • area = .3186 • ( 34-23.32)/6.26 = 1.71 • area =.4564 • .4564-.3186 = .1378 • .1378*54 = 7.44 or 7 people

  4. Practice • On the next test I will give an A to the top 5 percent of this class. • The average test grade is 56.82 with a SD of 6.98. • How many points on the test did you need to get to get an A?

  5. Step 1: Sketch out question .05

  6. Step 2: Look in Table Z Z score = 1.64 .05

  7. Step 3: Find the X score that goes with the Z score • Must solve for X • X =  + (z)() • 68.26 = 56.82 + (1.64)(6.98)

  8. Step 3: Find the X score that goes with the Z score • Must solve for X • X =  + (z)() • 68.26 = 56.82 + (1.64)(6.98) • Thus, a you need a score of 68.26 to get an A

  9. Practice • The prestigious Whatsamatta U will only take people scoring in the top 97% on the verbal section SAT (i.e., they reject the bottom 3%). • What is the lowest score you can get on the SAT and still get accepted? • Mean = 500; SD = 100

  10. Step 1: Sketch out question .03

  11. Step 2: Look in Table C Z score = -1.88 .03

  12. Step 3: Find the X score that goes with the Z score • Must solve for X • X =  + (z)() • 312 = 500 + (-1.88)(100)

  13. Step 3: Find the X score that goes with the Z score • Must solve for X • X =  + (z)() • 312 = 500 + (-1.88)(100) • Thus, you need a score of 312 on the verbal SAT to get into this school

  14. Is this quarter fair? • How could you determine this? • You assume that flipping the coin a large number of times would result in heads half the time (i.e., it has a .50 probability)

  15. Is this quarter fair? • Say you flip it 100 times • 52 times it is a head • Not exactly 50, but its close • probably due to random error

  16. Is this quarter fair? • What if you got 65 heads? • 70? • 95? • At what point is the discrepancy from the expected becoming too great to attribute to chance?

  17. Basic logic of research

  18. Start with two equivalent groups of subjects

  19. Treat them alike except for one thing

  20. See if both groups are different at the end

  21. Or – Single Group

  22. Do something

  23. Measure DV

  24. Compare Group to Population Population Happiness Score

  25. The Theory of Hypothesis Testing • Data are ambiguous • Is a difference due to chance? • Sampling error

  26. Population • You are interested in the average self-esteem in a population of 40 people • Self-esteem test scores range from 1 to 10.

  27. 1,1,1,1 2,2,2,2 3,3,3,3 4,4,4,4 5,5,5,5 6,6,6,6 7,7,7,7 8,8,8,8 9,9,9,9 10,10,10,10 Population Scores

  28. Histogram

  29. What is the average self-esteem score of this population? • Population mean = 5.5 • Population SD = 2.87 • What if you wanted to estimate this population mean from a sample?

  30. What if. . . . • Randomly select 5 people and find the average score

  31. Group Activity • Why isn’t the average score the same as the population score? • When you use a sample there is always some degree of uncertainty! • We can measure this uncertainty with a sampling distribution of the mean

  32. EXCEL

  33. INTERNET EXAMPLE • http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/index.html • http://onlinestatbook.com/stat_sim/sampling_dist/index.html

  34. Sampling Distribution of the Mean • Notice: The sampling distribution is centered around the population mean! • Notice: The sampling distribution of the mean looks like a normal curve! • This is true even though the distribution of scores was NOT a normal distribution

  35. Central Limit Theorem For any population of scores, regardless of form, the sampling distribution of the mean will approach a normal distribution a N (sample size) get larger. Furthermore, the sampling distribution of the mean will have a mean equal to  and a standard deviation equal to / N

  36. Sampling Distribution • Tells you the probability of a particular sample mean occurring for a specific population

  37. Sampling Distribution • You are interested in if your new Self-esteem training course worked. • The 5 people in your course had a mean self-esteem score of 5.5

  38. Sampling Distribution • Did it work? • How many times would we expect a sample mean to be 5.5 or greater? • Theoretical vs. empirical • 5,000 random samples yielded 2,501 with means of 5.5 or greater • Thus p = .5002 of this happening

  39. Sampling Distribution 5.5 P = .4998 P =.5002 2,499 2,501

  40. Sampling Distribution • You are interested in if your new Self-esteem training course worked. • The 5 people in your course had a mean self-esteem score of 5.8

  41. Sampling Distribution • Did it work? • How many times would we expect a sample mean to be 5.8 or greater? • 5,000 random samples yielded 2,050 with means of 5.8 or greater • Thus p = .41 of this happening

  42. Sampling Distribution 5.8 P = .59 P =.41 2,700 2,300

  43. Sampling Distribution • The 5 people in your course had a mean self-esteem score of 9.8. • Did it work? • 5,000 random samples yielded 4 with means of 9.8 or greater • Thus p = .0008 of this happening

  44. Sampling Distribution 9.8 P = .9992 P =.0008 4,996 4

  45. Logic • 1) Research hypothesis • H1 • Training increased self-esteem • The sample mean is greater than general population mean • 2) Collect data • 3) Set up the null hypothesis • H0 • Training did not increase self-esteem • The sample is no different than general population mean

  46. Logic • 4) Obtain a sampling distribution of the mean under the assumption that H0 is true • 5) Given the distribution obtain a probability of a mean at least as large as our actual sample mean • 6) Make a decision • Either reject H0 or fail to reject H0

  47. Hypothesis Test – Single Subject • You think your IQ is “freakishly” high that you do not come from the population of normal IQ adults. • Population IQ = 100 ; SD = 15 • Your IQ = 125

  48. Step 1 and 3 • H1: 125 > μ • Ho: 125 < or = μ

  49. Step 4: Appendix Z shows distribution of Z scores under null -3 -2 -1 1 2  3 

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