Research Methods: 2 M.Sc. PhysiotherapyPodiatryPain

1
Research Methods 2M.Sc. Physiotherapy/Podiatry/P
ain

• Descriptive statistics

2
Magic Brain Pills

• Research Methods Assessment
• mark with
• n15
• 32 47 76 24 66 43 56 30 43 52 46 28 74 28 65

• Research Methods Assessment
• mark without
• n15
• 56 29 21 49 56 39 47 34 42 44 42 53 25 41 8

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 ? Xi/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 (n1)/4th position
• Q3 3(n1)/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 (71)/4th position 2nd 12
• Q3 3(71)/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 (81)/4th position 2¼th
• position 2 14 position 3 15 ? Q1 14 ¼
• Q3 3(81)/4th position 6¾th
• position 6 19 position 7 19 ? Q3 19
• IQR 4¾

18
Standard Deviation

• SD ??(Xi )2 ? (n 1) (for samples lt30)
• 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 ve
Half 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