1. Data: Presentation and Description
Statistics for Health Research
Data: Presentation and Description
Peter T. Donnan
Professor of Epidemiology and Biostatistics

2. Overview
What is Data?
Summarising data
Displaying data
SPSS

3. Why have you collected data?
Most important question!
Related to testing hypotheses
If you have not got any hypotheses – Get some!
Return to later

4. DATA – Where from? All data is a Sample – a subset of population
How was it collected?
Potential for bias?
What does it represent?

5. Extrapolating from the sample to population
Illustrations Ian Christie, Orthopaedic & Trauma Surgery, Copyright
2002 University of Dundee

6. Quantitative Data? Observation or measurement of one or more variables
Variable is any quantity measured on a scale
Unit of analysis can be person, group (e.g. practice, specimen, cell, time……..)
Multilevel – patient and practice

7. Cross-classified 3 level multilevel model
Hospitalk
Practice levelj
Patient leveli

8. Statistics Statistics encompasses - Design of study;
Methods of collecting, and summarising data;
Analysing and drawing appropriate conclusions from data

9. Variable types Categorical (qualitative?) Numerical (quantitative)
E.g. type of drug – 1)selective 2) non-selective beta-blocker
smoking status -1) smoker 2) ex 3) non-smoker
Deciles of SIMD – 1,2,3,4,5,6,7,8,9,10
Numerical (quantitative)
E.g. age, birth weight, BP, cholesterol

10. Categorical Binary - two categories (yes, no)
Ordinal
Categories are mutually exclusive and ordered
Eg Disease stage (mild/moderate/
severe)
Nominal
Categories are mutually exclusive and unordered
Eg Blood group type (A/B/AB/O)
Binary - two categories (yes, no)

11. Takes any value in a range of values to any degree of precision
Numerical
Continuous
Takes any value in a range of values to any degree of precision
Eg Height in m, cholesterol, creatinine
Discrete
Integer values, often counts
Eg number of cigarettes smoked,
No. days in hospital

12. Organisation of data
Generally each variable in separate columns and one row per subject
Subject Age Gender Score

13. 1st step in analysis?
Look at the data!

15. Display and summarise data
To get a feel for the data
To spot errors and missing data
Assess the range of values
Also ..

17. Summarising Categorical data
1. Campylobactor
21. Giardia
2. Campylobactor
22. Crytosporidium
3. Escherichia coli 0157
23. Crytosporidium
4. Shigella sonnei
24. Campylobactor
5. Crytosporidium
25. Shigella sonnei
6. Giardia
26. SRSV
7. Crytosporidium
27. Crytosporidium
8. Campylobactor
28. Campylobactor
9. Campylobactor
29. Giardia
10. Crytosporidium
30. Giardia
11. Giardia
31. Escherichia coli 0157
12. Shigella sonnei
32. Shigella sonnei
13. SRSV
33. Crytosporidium
14. Giardia
34. SRSV
15. Escherichia coli 0157
35. Campylobactor
16. Campylobactor
36. Campylobactor
17. Giardia
37. Campylobactor
18. SRSV
38. Giardia
19. Campylobactor
39. Escherichia coli 0157
20. Crytosporidium
40. Campylobactor

18. Summarised by frequencies or percentage
Infection
N (%)
Campylobactor
12 (30.0)
Cryptosporidium
9 (22.5)
Giardia
8 (20.0)
SRSV
5 (12.5)
Escherichia coli 0157
3 (7.5)
Shigella
Total
40 (100)

19. Numerical data
Frequency distributions for continuous variable can be unfeasibly large
Grouping may be necessary for presentation

20. Cumulative relative frequency (%)
Frequency distribution for continuous variable
Age group
(years)
Frequency
Relative
(%)
Cumulative relative frequency (%)
0-4 59
12.2
5-9 83
17.1
29.3
10-14 94
19.4
48.7
15-19 72
14.8
63.5
20-24 61
12.6
76.1
25-29 48
9.9
86.0
30-34 36
7.4
93.4
35-49 32
6.6
100
485

21. Baseline measure
cholesterol
N (%)
4.0
52 (3.1)
4.1
51 (3.0)
4.2
49 (2.9)
4.3
65 (3.9)
4.4
60 (3.6)
4.5
80 (4.8)
4.6
88 (5.2)
4.7
99 (5.9)
4.8
94 (5.6)
4.9
84 (5.0)
5.0
68 (4.1)
5.1
66 (3.9)
5.2
79 (4.7)
5.3
74 (4.4)
5.4
75 (4.5)
5.5
5.6
70 (4.2)
5.7

22. Baseline group
N (%)
4.0 to 4.4
277 (16.5)
4.5 to 4.9
445 (26.5)
5.0 to 5.4
362 (21.6)
5.5 to 5.9
340 (20.3)
6.0 to 6.9
253 (15.1)
Total
1677

23. Guide for grouping data
Obtain min and max values
Choose between 5 and 15 intervals
Summarise but not obscure data especially continuous data
Intervals of equal width
Good but not essential
Remember to label tables!

24. Take care with missing values
SPSS gives % missing in output if missing left blank in data
Careful in reporting % as percentage of observed values or percentage of all subjects
These will differ!
Can use missing code (often 9) to make missing explicit in output

25. Graphs Simplicity Consistency Not duplicating tables or text
Remember Title
Remember Label axes

26. Graphs – Categorical data
Bar charts
Pie charts

27. Bar charts Used to display categorical (or discrete numerical data)
One bar per category
Height of bar equals its frequency
Each bar same width and equally spaced
Space between each bar
Vertical axis must start at zero

30. Most common cancer deaths in UK, 2009
Plots and Statistics from CRUK website

31. Pie charts
Displays one variable only
Compare 2 groups using 2 charts

33. But avoid 3-dimensional plots!

34. Graphs – Numerical data
Histograms
Frequency polygon
Scatter plots
Box plots

35. Histograms Like bar charts but no spaces y axis always begins at zero
Area of bar represents the frequency in each group

38. Check data carefully

40. Florence Nightingale’s ‘Coxcomb’ diagram of Mortality in the Crimea War

41. Summary measures – Numerical data
Central Location (average)
Spread or variability (distance of each data point from the average)

42. Central Location
Mean
Median
Mode - most frequent value

43. Mean _ x = x1 + x2 +x3+ ….. + xn N Often written as ∑xi / N
Where Sigma or ∑ is ‘Sum of’

44. _
x = 8
= 3.00

45. Mean Advantages Uses all data values
Very amenable to statistical analysis; most models use the mean
Disadvantages (advantages to politicians and estate agents!)
Distorted by outliers
Distorted by skewed data

46. Median Arrange values in increasing order Median is the middle value
Easy if odd number of values, for even number:
[ ]
Median = = 2.96 litres 2

47. Median Advantages Not distorted by outliers
Not distorted by skewed data
Disadvantages
Ignores most of the information
Less amenable to statistical modelling

48. Measures of spread
[47 52]
Mean = Median = 49.5
[51 51]
Mean = Median = 51

49. Range
[47 52]
Range or 77
[51 51]
Range or 5

50. Range from percentiles
Data ordered from smallest to largest value; then divide into equal chunks:
Percentiles
Deciles –data in equal 10ths
Quartiles = data in equal 4ths

51. Interquartile range (IQR)
Data is ordered into quartiles:
| | |
8 (lower quartile) (upper quartile)
Interquartile range (IQR) = =

52. IQR in Multiple Box-plots
Outlier
Upper Quartile
Range
Median
IQR
Lower Quartile

53. Distribution of data values around the mean

54. Variance 17 24 29 36 47 52 mean=34.16 years _ (x-x) 17 - 34.16 -17.16
24 –
29 –
36 –
47 –
52 –

55. Variance 17 24 29 36 47 52 mean=34.16 _ _ (x-x) (x-x)2
_ _
(x-x) (x-x)2

56. Variance (s2) _
S2 =  (x-x)2
n-1
S2= 5
S2=182.16

57.
Mean = years
Variance = 182.2

58. Standard deviation (s)_
Std deviation (s) = √  (x-x)2
n-1
Std deviation = √
= 13.49

59.
Mean = years
SD = 13.49
Coefficient of Variation (CV)
= SD / Mean
= 0.39
Measure of variability for comparison of different scales

60. Which central measure goes with which measure of spread?
Mean (SD)
Median (IQR or Range)

61. Summary Do not underestimate value of looking at the data
Gives a feel for the data before testing or modelling
Check for missing data
Check for outliers

62. From Jan 2010 IBM acquired copyright for SPSS

72. Statistics
Baseline LDL
N Valid 1383
Missing 0
Mean
Median
Std. Deviation
Variance .978
Skewness .039
Std. Error of Skewness .066
Range
Minimum .3345
Maximum
Percentiles

73. Implementing Kaplan-Meier in SPSS
From Colorectal.sav you need to specify:
Survival time – time from surgery (tfsurg)
Status – Dead = 1, censored = 0 (dead)
Factor – e.g. hypertension comorbidity (hyperco)
Select plot of survival

74. Implementing Kaplan-Meier plot in SPSS

75. Select options to obtain plot and median survival

76. Means and Medians for Survival Time Hypertension Meana Median
Estimate Std. Error 95% Confidence Interval Estimate Std. Error 95% Confidence Interval
Lower Bound Upper Bound Lower Bound Upper Bound
Overall
a. Estimation is limited to the largest survival time if it is censored.

77. Survival curves for women with glioma by diagnosis.
Bland J M , Altman D G BMJ 2004;328:1073

78. Practical
Read LDL.sav or colorectal.sav into SPSS (22) and explore the different types of data using appropriate tables and graphs
DEBU website (