1. Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain Descriptive statistics

2. Research Methods Assessment mark with n=15 32 47 76 24 66 43 56 30 43 52 46 28 74 28 65 Research Methods Assessment mark without n=15 56 29 21 49 56 39 47 34 42 44 42 53 25 41 8 Magic Brain Pills

3. Descriptive/Summary Statistics Measures of centrality Measures of dispersion

4. Summary Statistics Measures of centrality Mode, Median and Mean

5. The Mode Tally observations in set Frequency table Nominal, Ordinal, Interval or Ratio Uses?

6. Exercise: The Mode Sample one 5 5 6 9 8 9 7 4 5 8 Sample two 16 14 12 18 19 14 12 18 Sample three 81 79 78 75 81 69 75 Sample one Mode = 5 Unimodal Sample two Mode = 14 or 12 or 18 Tri or Multi-Modal Sample three Mode = 75 or 81 Bi-Modal

7. The Median Put set in rank order Median lies in middle, half values greater half lower If n is even, median = mean of the middle two positions Ordinal, Interval or Ratio Uses ?

8. Exercise: Median Sample one 5 5 6 9 8 9 7 4 5 8 Sample two 16 14 12 18 19 20 14 12 18 Sample three 81 79 78 75 81 69 75 72 Sample one Median = 6.5 (4 5 5 5 6 7 8 8 9 9) Sample two Median = 16 (12 12 14 14 16 18 18 19 20) Sample three Median = 76.5 (69 72 75 75 78 79 81 81)

9. The Arithmetic Mean Add all the values Divide by the number of values Mean =  X i /n Interval or Ratio Uses ?

10. Exercise: Mean Sample one 5 5 6 9 8 9 7 4 5 8 Sample two 16 14 12 18 19 20 14 12 18 Sample three 81 79 78 75 81 69 75 Sample one Mean = 6.6 Sample two Mean = 15.9 Sample three Mean = 76.8

11. Summary Statistics Measures of dispersion Range, Inter and Semi Interquartile Range and Standard Deviation

12. The Range Find Minimum value Find Maximum value Subtract Max-Min Uses?

13. Interquartile Range Put set in rank order Find the median = Q2 Q1 = (n+1)/4th position Q3 = 3(n+1)/4th position Q3-Q1 Interquartile range (Q3-Q1)/2 Semi-Interquartile range

14. Exercise: Interquartile Range Sample 1: Days to recovery with Rx 12 8 18 22 24 17 15 Calculate Median and Interquartile range Sample 2: Days to recovery without Rx 15 12 19 18 25 16 19 14 Calculate Median and Interquartile range

15. Answer Sample 1 12 8 18 22 24 17 15 8 12 15 17 18 22 24 Q2 = 17 (4th), n = 7 Q1= (7+1)/4th position = 2nd = 12 Q3 = 3(7+1)/4th position = 6th = 22 IQR = 10

16. Answer Sample 2 15 12 19 18 25 16 19 14 12 14 15 16 18 19 19 25 Q2 = 17 (4th + 5th / 2), n = 8

17. Answer Sample 2 12 14 15 16 18 19 19 25 Q1 = (8+1)/4th position = 2¼th; position 2 = 14 position 3 = 15  Q1 = 14 ¼ Q3 = 3(8+1)/4th position = 6¾th; position 6 = 19 position 7 = 19  Q3 =19 IQR = 4¾

18. Standard Deviation SD=  [  (Xi – ) 2  (n – 1)] (for samples <30) Calculate the mean Subtract each value from the mean Square each answer and sum Divide by n-1 Take square root of that answer

19. Standard Deviation Half x-mean = +veHalf x-mean = -ve So  (x - mean) always = 0 So Square then sum and take square root of Sum of Squares/ n-1

20. Exercise: SD Sample 1 28.0, 19.2, 25.0, 20.0, 26.6 Calculate Mean, SD, and Range Sample 2 21.7, 19.3, 21.6, 28.7, 10.3 Calculate Mean, SD, and Range

21. Answer Sample 1 Mean 23.76, SD 3.95, Range 8.8 Sample 2 Mean 20.30, SD 6.62, Range 18.4 Are they different ? Are they different enough ?

22. Magic Brain Pills With Mean 47.7 SD 17.4 Without Mean 39.1 SD 13.6 4/15 failed6/15 failed