1. Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain Frequency/Probability Polygons, and the Normal Distribution

2. Part one: Frequency Tables Un-grouped Tally observations Frequency table Histogram Polygon Grouped Set class limits Tally number in class Frequency table Histogram Polygon

3. Ungrouped Frequency Tables; Data from n = 25, rating 1-5 of RM2 teaching

4. Ungrouped Frequency Tables; Frequency Table

5. Ungrouped Frequency Tables; Data from n = 25, rating 1-5 of RM2 teaching

7. Grouped Frequency Tables; Data of weights (kg) n = 12

8. Grouped Frequency Tables; Setting class limits Find range Choose number of classes (5 20) Classes equal size (Outliers?) Choose limits at level of measurement precision Tally

9. Grouped Frequency Tables Class boundaries Half way between classes One more decimal place than limits Class intervals Distance between boundaries Midpoints Half way between boundaries Mid point of interval

10. Grouped Frequency Tables

12. Histograms Present information from Frequency tables Show distribution of the data set Columns start and end at class boundaries Midpoints are marked Join midpoints = Frequency/Probability Polygon Area represent frequency/ probability; total area under curve; p = 1.00

13. Histograms; Frequency

14. Histograms; Probability

15. Frequency/Probability Polygons

16. Part two: The Normal Distribution A type of (family) of distributions Most important of all known distributions Natural parameters in populations Symmetrical bell shaped curve

17. Normal Distribution Or  Frequency Probability SD or 

18. 68.2% ± 1SD 95.4% ± 2SD 99.7% ± 3SD

19. p = 0.682 ± 1SD p = 0.954 ± 2SD p = 0.997 ± 3SD

20. p if not exact multiple of SD away from mean ?

21. Z scores Data point of interest = x Mean =  Standard deviation =  Z score is number of multiples of SD the data point is away from mean ; z = x -  

22. Z scores Look up the Z score in Tables to find; Probability associated with values below x and vice versa. Why ???

23. Graph of number of visits to Physiotherapist for Sports rehabilitation; 16 z = (16 - 10) /4 z = 1.5  p = 0.9332  p = 1 - 0.9332  p = 0.067

24. 95% of data p = 0.95 p < 0.05