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1. Week 5 ETEC 668 Quantitative Research in Educational Technology Dr. Seungoh Paek February 12, 2014

2. Tonight’s Agenda • Continuing SPSS • Introduction to PSPP • Introduction to RStudio • Introduction to Probability • Group Discussion for Research Paper

3. Continuing Week 4

4. Using SPSS

5. Using SPSS

6. Sigma Freud & Descriptive Statistics A Picture is Really Worth a Thousand Words

7. Histograms with Polygon Hand Drawn Histogram

8. Cool Ways to Chart Data • Line Chart

9. Cool Ways to Chart Data • Pie Chart

10. Using the Computer to Illustrate Data • Creating Histogram Graphs

11. Using the Computer to Illustrate Data • Creating Bar Graphs

12. Using the Computer to Illustrate Data • Creating Line Graphs

13. Using the Computer to Illustrate Data • Creating Pie Graphs

14. A Taste of PSPP

16. A TASTE of RSTudio

17. R • R is a free software environment for statistical computing and graphics.

18. RStudio • RStudio is a free and open source integrated development environment (IDE) for R, a programming language for statistical computing and graphics.

19. Probability, Samples, Bell Curve, zScores, Hypotheses, Hypothesis Testing, & significance Chapter 7 & Chapter 8

20. Probability

21. Why Probability? • Describe and predict what we don’t know from current data • Basis for the Degree of confidence a Hypothesis is “true” • statistical significance

22. Examples • Flip a coin • 2 possible outcomes • Heads or Tails • 50% chance each • Role a Die • 6 possible outcomes • 1 – 2 – 3 – 4 – 5 – 6 • 16.6% chance each • Flip 2 coins • How many possible outcomes? • What % chance for each?

23. Examples • Flip 2 coins • 4 possible outcomes • 25% chance each

24. Sample v Population

25. Definitions • Population • The large group to which you would like to generalize your findings • Sample • The smaller, representative group of the population used for research.

26. Characteristics of a sample • Needs to be representative • Truly random = representative = unbiased • Sampling error – • how well the sample represents the population • Size matters – • larger sample = more representative

27. Mathematical Symbols • Mean • Population = μ • Sample = X • Standard Deviation • Population = σ • Sample = SD • Variance • Population = σ2 • Sample = SD2 • Number of Cases • Population = N • Sample = n

28. The Normal Curve

29. The Normal curve

30. More Normal Curve

31. About Normal Curve • Almost all scores fall between -3 and +3 SD from mean • 99.74% • Specific percentages between points on x-axis • 2 or more normal curves can be compared

32. Normal Curve and Percents

33. zScores

34. The z Score • The number of standard deviations from the mean • Negative scores are below (left of) the mean • Positive scores are above (right of) the mean

35. The z Score • Standard Score • Allows you to compare apples and oranges • The probability of a score occurring =

36. Hypotheses

37. What is a Hypothesis? • An “educated guess” • Direct extension of the question • Translates problem or research question into a testable form • Two types • Null Hypothesis • Research Hypothesis

38. A Good Hypothesis • Declarative statement • Expected relationship between variables • Reflection of theory/literature • Brief, to the point • Testable

39. Why a Null Hypothesis? No amount of experimentation can ever prove me right; a single experiment can prove me wrong. ~Albert Einstein

40. The Null Hypothesis • Statement of no relationship • Two things are equal H0 : μA = μB • Refers to Population • Indirectly tested

41. The Research Hypothesis • Definite Statement • Relationship exists between variables • Two types • Nondirectional - H1 : XA ≠ XB • Directional - H1 : X1 > X2 • Refers to sample • Directly tested

42. Hypothesis Testing

43. Hypothesis Testing • All events have a probability associated with them • p = your guess of chance p < .05 • .05 or 5% in Education and Psychology • 5% likelihood of results occurring by chance alone

44. Error types • Type I • Reject H0 when you should not • Type II • Fail to reject H0 when you should

45. Error Table

46. Significance

47. Statistical • Based on probability • Research was technically successful • H0 was rejected • P value • Education p < .05 = 5% chance • Medical p < .01 or .001 = 1% or .1% chance

48. Practical • Does it mean anything to the population? • Is that new treatment worth the cost? • Are my students really doing that much better?

49. Questions?

50. Stating the Research Question February 12, 2014