Inferential Statistics

1. Inferential Statistics (a brief over view)

7. Descriptive Statistics (just the #’s) • Mean = average • Median = middle most data score • Mode = most frequently occurring data score • Range = max score – min score • Inter Quartile Range = Q3 – Q1 • Standard deviation = deviation (difference) from the mean

11. Standard deviation example

13. Example for grouped data

14. INFERential Statistics • Putting it all together….what do the statistics infer?!

15. What do the numbers tell us?!

16. The “Normal” distribution

17. Matchboxes in stavanger

19. Normal Distribution • Excel example

20. Significance tests: Is there a real difference??? • Two tailed tests • One tailed tests

21. 31 34 37 40 43 46 49 Matchboxes S = 3

22. Frank Wilcoxon • 1892-1965 • Chemist • Statistician • Inventor of….. • The Wilcoxon (T) signed ranks test!!! • (yay!)

23. Related Data: The Wilcoxon (T) Signed Ranks Test • Is for related ordinal data only • Ordinal data must be RANKED (1st, 2nd, 3rd, etc) • Lowest number always gets 1 • Used to see if there is a real (statistical) difference in the data • examples of related ordinal data:

24. The Wilcoxon (T) Signed Ranks Test For ALL statistical significance tests: 1. State the null (Ho) and alternative (Ha or H1) hypothesis. • Ho ALWAYS says no statistical difference • H1 ALWAYS says there IS a statistical difference. 2. Pick a statistical test (Wilcoxon) 3. Calculate Statistic (T) 4. Decide whether to accept or reject Ho based on alpha level

25. Example

26. The eye ball test • Does it look like there is a difference?!

27. The Wilcoxon Test • ……a slightly more accurate test that we all can agree on • Null Hypothesis: There is no signifacant difference between the two lessons. • Alternative Hypothesis: There IS a significant difference between the two lessons. • (Reject H0 if T ≤ Critical Value) • Step 1: Calculate the difference (B-A)

29. 2: Rank the data • Lowest difference is assigned a value of 1 • Ignore sign differences (take absolute value of differences) • Ignore zero values • For tied scores, use the median rank

31. 3 is the 2nd, 3rd, and 4th, rank therefore use the MEDIAN (middle) rank

32. 8 is tied for the 9th and 10th rank so use the MEDIAN (middle) rank of 9.5

34. 3. Sum up (+) vs (-) ranks • Sum (+) = 12+9.5+3+5+ 3+9.5+3+14+7+11+13= 90 • Sum (-) = 1+6+8=15 • Use the SMALLER of these two values……this is your statistic T!!! • So T = 15.

35. Find critical value: (Remember N = 14 Since we dropped 0)

36. Significance tests: Is there a real difference??? • Two tailed tests • One tailed tests

37. Average difference T =15 ≤ 21 (alpha = 0.05) T = 15 ≤ 15 (alpha =0.02) 98% of the time, you will not have this big of a difference by chance……the difference SHOULD be significant!

38. Reject H0. • Therefore we have sufficient evidence to accept H1 and we conclude: • the difference between the lecture based class and investigation based class is significant according to our data!

39. Recap: • State Null and Alternative hypothesis • Choose confidence level (usually 0.05) • Take the differences and rank data • Sum up (+) and (-) differences and use smaller of two….this is your T-value. • Find the Critical Value from the table. • Reject H0 if T ≤ C.V. • (note if T > all C.V. then there is no significant difference)

40. Some extra review… • http://www.social-science.co.uk/stats/ • http://www.youtube.com/watch?v=mbpGCxYya3M • http://www.khanacademy.org/video/statistics--standard-deviation?playlist=Statistics