1. Copyright © Allyn & Bacon (2007) Manual Statistical Computation Procedures Graziano and Raulin Research Methods This multimedia product and its contents are protected under copyright law. The following are prohibited by law: (1) Any public performance or display, including transmission of any image over a network; (2) Preparation of any derivative work, including the extraction, in whole or in part, of any images; (3) Any rental, lease, or lending of the program.

2. Copyright © Allyn & Bacon (2007) Measures of Central Tendency Mean Mean Median Median –The middle score when scores are arranged in order from highest to lowest Mode Mode –The most frequently occurring score –Easily identified from a frequency distribution

3. Copyright © Allyn & Bacon (2007) Measures of Variability Variance Computational Formula Variance Computational Formula Standard Deviation Standard Deviation

4. Copyright © Allyn & Bacon (2007) Computational Example Compute mean, variance, and standard deviation of the following: 2, 5, 7, 4, 6, 5 Compute mean, variance, and standard deviation of the following: 2, 5, 7, 4, 6, 5 Compute sum of X and sum of X 2 Compute sum of X and sum of X 2

5. Copyright © Allyn & Bacon (2007) Correlations Pearson product-moment correlation Pearson product-moment correlation Spearman rank-order correlation Spearman rank-order correlation

6. Copyright © Allyn & Bacon (2007) Computational Example Compute the product- moment correlation for the data at the right Compute the product- moment correlation for the data at the right Compute the sums, sums of squares, and cross products as shown Compute the sums, sums of squares, and cross products as shown Computations on next slide Computations on next slide X Y X 2 Y 2 XY X Y X 2 Y 2 XY 4 5 16 25 20 4 5 16 25 20 3 5 9 25 15 3 5 9 25 15 5 6 25 36 30 5 6 25 36 30 2 4 4 16 8 2 4 4 16 8 6 7 36 49 42 6 7 36 49 42 5 7 25 49 35 5 7 25 49 35 25 34 115 200 150 25 34 115 200 150

7. Copyright © Allyn & Bacon (2007) Product-Moment Correlation

8. Copyright © Allyn & Bacon (2007) Computational Example Compute a rank-order correlation for the ordinal data at the right Compute a rank-order correlation for the ordinal data at the right Compute the difference in ranks (d) and d 2 as shown Compute the difference in ranks (d) and d 2 as shown Computations on next slide Computations on next slide X Y d d 2 X Y d d 2 1 3 -2 4 1 3 -2 4 2 2 0 0 2 2 0 0 3 1 2 4 3 1 2 4 4 5 -1 1 4 5 -1 1 5 4 1 1 5 4 1 1 10 10

9. Copyright © Allyn & Bacon (2007) Rank-Order Correlation

10. Copyright © Allyn & Bacon (2007) The t-test For independent samples For independent samples For correlated samples For correlated samples

11. Copyright © Allyn & Bacon (2007) Computational Example Group 1 Group 2 5 3 8 5 7 2 8 3 7 Mean 7.00 3.25 SS 6.00 4.75 N 5 4 Group 1 Group 2 5 3 8 5 7 2 8 3 7 Mean 7.00 3.25 SS 6.00 4.75 N 5 4

12. Copyright © Allyn & Bacon (2007) Independent Samples t- test

13. Copyright © Allyn & Bacon (2007) Computational Example

14. Copyright © Allyn & Bacon (2007) Correlated t-test

15. Copyright © Allyn & Bacon (2007) One-Way ANOVA Formulas

16. Copyright © Allyn & Bacon (2007) One-Way ANOVA Formulas

17. Copyright © Allyn & Bacon (2007) Raw data (one-way ANOVA)

18. Copyright © Allyn & Bacon (2007) Summarized Data

19. Copyright © Allyn & Bacon (2007) Computations

20. Summary Table

21. Copyright © Allyn & Bacon (2007) Planned Comparisons Formulas Where

22. Copyright © Allyn & Bacon (2007) Computations Compare Group 3 against the average of Groups 1 and 2 from the previous ANOVA Compare Group 3 against the average of Groups 1 and 2 from the previous ANOVA

23. Copyright © Allyn & Bacon (2007) Repeated-Measures Formulas

24. Copyright © Allyn & Bacon (2007) Repeated-Measures Formulas

25. Copyright © Allyn & Bacon (2007) Raw Data (Repeated Measures)

26. Copyright © Allyn & Bacon (2007) Summarized Data

27. Copyright © Allyn & Bacon (2007) Computations

28. Summary Table

29. Copyright © Allyn & Bacon (2007) Two-Way ANOVA Formulas

30. Copyright © Allyn & Bacon (2007) Two-Way ANOVA Formulas

31. Copyright © Allyn & Bacon (2007) Raw Data

32. Copyright © Allyn & Bacon (2007) Summarized Data (1/4)

33. Copyright © Allyn & Bacon (2007) Summarized Data (2/4)

34. Copyright © Allyn & Bacon (2007) Summarized Data (3/4)

35. Copyright © Allyn & Bacon (2007) Summarized Data (4/4)

36. Copyright © Allyn & Bacon (2007) Computations (two-way) 1/3

37. Copyright © Allyn & Bacon (2007) Computations (two-way) 2/3

38. Copyright © Allyn & Bacon (2007) Computations (two-way) 3/3

39. Copyright © Allyn & Bacon (2007) Summary Table

40. Copyright © Allyn & Bacon (2007) Chi-Square Formulas Use same formula for both Use same formula for both –Chi-square goodness-of-fit test –Chi-square test-for-independence Only difference is how expected cell frequencies are computed Only difference is how expected cell frequencies are computed

41. Copyright © Allyn & Bacon (2007) Goodness-of-fit Data Set

42. Copyright © Allyn & Bacon (2007) Goodness-of-fit Computations

43. Copyright © Allyn & Bacon (2007) Data for Test-for- Indendence

44. Copyright © Allyn & Bacon (2007) Test-for-Independence Computations

45. Copyright © Allyn & Bacon (2007) Summary The Student Resource Website illustrates how to compute each of these statistical procedures and also includes the statistical tables needed to interpret the results The Student Resource Website illustrates how to compute each of these statistical procedures and also includes the statistical tables needed to interpret the results The website also shows how to do the same computations using SPSS for Windows The website also shows how to do the same computations using SPSS for Windows