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Practice

Practice. I think it is colder in Philadelphia than in Anaheim (  = .10) . To test this, I got temperatures from these two places on the Internet. Philadelphia 52 53 54 61 55. Anaheim 77 75 67. Results. Hypotheses. Alternative hypothesis H 1 :  Philadelphia <  Anaheim

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Practice

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  1. Practice • I think it is colder in Philadelphia than in Anaheim ( = .10). • To test this, I got temperatures from these two places on the Internet.

  2. Philadelphia 52 53 54 61 55 Anaheim 77 75 67 Results

  3. Hypotheses • Alternative hypothesis • H1: Philadelphia < Anaheim • Null hypothesis • H0:  Philadelphia = or >  Anaheim

  4. Step 2: Calculate the Critical t • df = N1 + N2 - 2 • df = 5 + 3 - 2 = 6 •  = .10 • One-tailed • t critical = - 1.44

  5. Step 3: Draw Critical Region tcrit = -1.44

  6. NowStep 4: Calculate t observed tobs = (X1 - X2) / Sx1 - x2

  7. X1= 275 X12= 15175 N1 = 5 X1 = 55 X2= 219 X22= 16043 N2 = 3 X2 = 73 219 275 16043 15175 3 5 5 3 5 + 3 - 2

  8. X1= 275 X12= 15175 N1 = 5 X1 = 55 X2= 219 X22= 16043 N2 = 3 X2 = 73 219 275 16043 15987 15175 15125 3 5 .2 + .33 5 3 6 = 3.05

  9. Step 4: Calculate t observed -5.90 = (55 - 73) / 3.05 Sx1 - x2 = 3.05 X1 = 55 X2 = 73

  10. Step 5: See if tobs falls in the critical region tcrit = -1.44 tobs = -5.90

  11. Step 6: Decision • If tobs falls in the critical region: • Reject H0, and accept H1 • If tobs does not fall in the critical region: • Fail to reject H0

  12. Step 7: Put answer into words • We Reject H0, and accept H1 • Philadelphia is significantly ( = .10) colder than Anaheim.

  13. So far. . . . • We have been doing independent samples designs • The observations in one group were not linked to the observations in the other group

  14. Philadelphia 52 53 54 61 55 Anaheim 77 75 67 Example

  15. Matched Samples Design • This can happen with: • Natural pairs • Matched pairs • Repeated measures

  16. Natural Pairs The pairing of two subjects occurs naturally (e.g., twins)

  17. Matched Pairs When people are matched on some variable (e.g., age)

  18. Repeated Measures The same participant is in both conditions

  19. Matched Samples Design • In this type of design you label one level of the variable X and the other Y • There is a logical reason for paring the X value and the Y value

  20. Matched Samples Design • The logic and testing of this type of design is VERY similar to what you have already done!

  21. Example • You just invented a “magic math pill” that will increase test scores. • On the day of the first test you give the pill to 4 subjects. When these same subjects take the second test they do not get a pill • Did the pill increase their test scores?

  22. HypothesisOne-tailed • Alternative hypothesis • H1: pill > nopill • In other words, when the subjects got the pill they had higher math scores than when they did not get the pill • Null hypothesis • H0: pill < or = nopill • In other words, when the subjects got the pill their math scores were lower or equal to the scores they got when they did not take the pill

  23. Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y) 1 3 2 2 Results

  24. Step 2: Calculate the Critical t • N = Number of pairs • df = N - 1 • 4 - 1 = 3 •  = .05 • t critical = 2.353

  25. Step 3: Draw Critical Region tcrit = 2.353

  26. Step 4: Calculate t observed tobs = (X - Y) / SD

  27. Step 4: Calculate t observed tobs = (X - Y) / SD

  28. Step 4: Calculate t observed tobs = (X - Y) / SD X = 3.75 Y = 2.00

  29. Step 4: Calculate t observed tobs = (X - Y) / SD Standard error of a difference

  30. Step 4: Calculate t observed tobs = (X - Y) / SD SD = SD / N N = number of pairs

  31. S =

  32. Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y) 1 3 2 2 S =

  33. Difference (D) 2 2 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y) 1 3 2 2 S =

  34. Difference (D) 2 2 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y) 1 3 2 2 D = 7 D2 =13 N = 4 S =

  35. Difference (D) 2 2 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y) 1 3 2 2 D = 7 D2 =13 N = 4 7 S =

  36. Difference (D) 2 2 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y) 1 3 2 2 D = 7 D2 =13 N = 4 7 S = 13

  37. Difference (D) 2 2 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y) 1 3 2 2 D = 7 D2 =13 N = 4 7 S = 13 4 4 - 1

  38. Difference (D) 2 2 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y) 1 3 2 2 D = 7 D2 =13 N = 4 7 S = 13 12.25 4 3

  39. Difference (D) 2 2 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y) 1 3 2 2 D = 7 D2 =13 N = 4 7 .5 = .75 4 3

  40. Step 4: Calculate t observed tobs = (X - Y) / SD SD = SD / N N = number of pairs

  41. Step 4: Calculate t observed tobs = (X - Y) / SD .25=.5 / 4 N = number of pairs

  42. Step 4: Calculate t observed 7.0 = (3.75 - 2.00) / .25

  43. Step 5: See if tobs falls in the critical region tcrit = 2.353

  44. Step 5: See if tobs falls in the critical region tcrit = 2.353 tobs = 7.0

  45. Step 6: Decision • If tobs falls in the critical region: • Reject H0, and accept H1 • If tobs does not fall in the critical region: • Fail to reject H0

  46. Step 7: Put answer into words • Reject H0, and accept H1 • When the subjects took the “magic pill” they received statistically ( = .05) higher math scores than when they did not get the pill

  47. SPSS

  48. New Step • Should add a new page • Determine if • One-sample t-test • Two-sample t-test • If it is a matched samples design • If it is a independent samples with equal N • If it is a independent samples with unequal N

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