The following lecture has been approved for

1
The following lecture has been approved for
University Undergraduate Students This lecture
may contain information, ideas, concepts and
discursive anecdotes that may be thought
provoking and challenging It is not intended
for the content or delivery to cause
offence Any issues raised in the lecture may
require the viewer to engage in further thought,
insight, reflection or critical evaluation
2
Background to Statistics for non-statisticians
Dr. Craig Jackson Senior Lecturer in Health
Psychology Faculty of Health BCU
craig.jackson_at_bcu.ac.uk
3
Types of Data / Variables Continuous Discrete
BP Children Height Age last birthday
Weight colds in last year Age
Ordinal Nominal Grade of
condition Sex Positions 1st 2nd 3rd Hair
colour Better- Same-Worse Blood group Height
groups Eye colour Age groups
4
Conversion Re-classification Easier to
summarise Ordinal / Nominal data Cut-off
Points (who decides this?) Allows Continuous
variables to be changed into Nominal variables
BP 90mmHg Hypertensive BP 90mmHg Normotensive Easier clinical
decisions Categorisation reduces quality of
data Statistical tests may be more
sensational Good for summaries Bad for
accuracy
5
Types of statistics / analyses DESCRIPTIVE
STATISTICS Describing a phenomena Frequencies H
ow many Basic measurements Meters, seconds,
cm3, IQ INFERENTIAL STATISTICS Inferences
about phenomena Hypothesis Testing Proving or
disproving theories Confidence Intervals If
sample relates to the larger population Correlatio
n Associations between phenomena Significance
testing e.g diet and health
6
Multiple Measurementor. why statisticians and
love dont mix
25 cells 22 cells 24 cells 21
cells Total 92 cells Mean 23
cells SD 1.8 cells
7
Small samples spoil research
N Age IQ 1 20 100 2 20 100 3 20 100 4 20 100 5 20
100 6 20 100 7 20 100 8 20 100 9 20 100 10 20 100
Total 200 1000 Mean 20 100 SD 0 0
N Age IQ 1 18 100 2 20 110 3 22 119 4 24 101 5 26
105 6 21 113 7 19 120 8 25 119 9 20 114 10 21 101
Total 216 1102 Mean 21.6 110.2 SD 4.2 19.2
N Age IQ 1 18 100 2 20 110 3 22 119 4 24 101 5 26
105 6 21 113 7 19 120 8 25 119 9 20 114 10 45 156
Total 240 1157 Mean 24 115.7 SD 8.5 30.2
8
Central Tendency Mode
Median Mean Patient comfort rating 10 9 8 7 6 5 4
3 2 1 31 27 70 121 140 129 128 90 80 62 Frequenc
y
9
Dispersion Range Spread of data Mean Arithmetic
average Median Location Mode Frequency SD Sprea
d of data about the mean Range 50-112
mmHg Mean 82mmHg Median 82mmHg Mode 82mmHg SD
10mmHg
10
Dispersion An individual score therefore possess
a standard deviation (away from the mean), which
can be positive or negative Depending on which
side of the mean the score is If add the
positive and negative deviations together, it
equals zero (the positives and negatives cancel
out)
11
Dispersion Range The interval between the
highest and lowest measures Limited value as it
involves the two most extreme (likely faulty)
measures Percentile The value below / above
which a particular percentage of values fall
(median is the 50th percentile) e.g 5th
percentile - 5 of values fall below it, 95 of
values fall above it. A series of percentiles
(1st, 5th, 25th, 50th, 75th, 95, 99th) gives a
good general idea of the scatter and shape of the
data
12
Standard Deviation To get around this, we square
each of the observations Makes all the values
positive (a minus times a minus.) Then sum all
those squared observations to calculate the
mean This gives the variance - where every
observation is squared Need to take the square
root of the variance, to get the standard
deviation SD ? S x2 (S x)2 / N
(N 1)
13
Grouped Data Normal Distribution SD is useful
because of the shape of many distributions of
data. Symmetrical, bell-shaped / normal /
Gaussian distribution
Non Normal Distribution Some distributions fail
to be symmetrical If the tail on the left is
longer than the right, the distribution is
negatively skewed (to the left)
If the tail on the right is longer than the left,
the distribution is positively skewed (to
the right)
14
Normal Distributions Standard Normal
Distribution has a mean of 0 and a standard
deviation of 1 The total area under the curve
amounts to 100 / unity of the observations
Proportions of observations within any given
range can be obtained from the distribution by
using statistical tables of the standard normal
distribution 95 of measurements / observations
lie within 1.96 SDs either side of the mean
15
Quincunx machine 1877
balls dropped through a succession of metal
pins..
..a normal distribution of balls
do not have a normal distribution here. Why?
16
Normal Non-normal distributions
The distribution derived from the quincunx is not
perfect
It was only made from 18 balls
17
of population
56 57 58 59
510 511 6 61 62
63 64 Height

18
Normal Non-normal distributions Galtons
quincunx machine ran with hundreds of balls a
more perfect shaped normal distribution.
Obvious implications for the size of samples of
populations used The more lead shot runs
through the quincunx machine, the smoother the
distribution in the long run . . . . .
19
Presentation of data Table of means
Exposed Controls T P n197 n178 Age 45.5
48.9 2.19 0.07 (yrs) (? 9.4) (?
7.3) I.Q 105 99 1.78 0.12 (?
10.8) (? 8.7) Speed 115.1 94.7
3.76 0.04 (ms) (? 13.4) (? 12.4)
20
Presentation of data Category tables
Exposed Controls Healthy 50
150 200 Unwell 147
28 175 197 178 375
Chi square (test of association) shows Chi
square 7.2 P 0.02
21
Bar Charts A set of measurements can be
presented either as a table or as a figure Graphs
are not always as accurate as tables, but portray
trends more easily
Title of graph
y-axis
Legend key
Data display area
y-axis label (ordinate)
scale
x-axis (abscissa)
groups
22
Bar Charts Some Real Data A combination of
distributions is acceptable to facilitate
comparisons
23
Correlation and Association
With a scatter diagram, each individual
observation becomes a point on the scatter plot,
based on two co-ordinates, measured on the
abscissa and the ordinate
ordinate
abscisaa
Two perpendicular lines are drawn through the
medians - dividing the plot into quadrants Each
quadrant should outlie 25 of all observations
24
Correlation and Association
Correlation is a numerical expression between 1
and -1 (extending through all points in between).
Properly called the Correlation Coefficient. A
decimal measure of association (not necessarily
causation) between variables
Correlations between 0 and 0.3 are
weak Correlations between 0.4 and 0.7 are
moderate Correlations between 0.8 and 1 are
strong
25
Correlation and Association
Correlation is a numerical expression between 1
and -1 (extending through all points in between).
Properly called the Correlation Coefficient. A
decimal measure of association (not necessarily
causation) between variables
26
POPULATIONS Can be mundane or
extraordinary SAMPLE Must be representative IN
TERNALY VALIDITY OF SAMPLE Sometimes validity is
more important than generalizability SELECTION
PROCEDURES Random Opportunistic Conscriptive Quota
Sampling Keywords
27
Sampling Keywords
THEORETICAL Developing, exploring, and testing
ideas
EMPIRICAL Based on observations and measurements
of reality
NOMOTHETIC Rules pertaining to the general case
(nomos - Greek)
PROBABILISTIC Based on probabilities
CAUSAL How causes (treatments) effect the outcomes
28
Clinical Research Types of clinical
research Experimental vs. Observational Longitud
inal vs. Cross-sectional Prospective vs.
Retrospective
29
Experimental Designs Between subjects
studies Within Subjects studies
Treatment group
Outcome measured
patients
Control group
Outcome measured
patients
Outcome measured 1
Treatment
Outcome measured 2
30
Observational studies Cohort (prospective)
Case-Control (retrospective)
31
Case-Control Study Smoking Cancer Cases
have Lung Cancer Controls could be other
hospital patients (other disease) or
normals Matched Cases Controls for age
gender Option of 2 Controls per Case
Smoking years of Lung Cancer cases and controls
(matched for age and sex) Cases Controls n4
56 n456 F P Smoking years 13.75 6.12 7.5
0.04 ( 1.5) ( 2.1)
32
Cohort Study Methods Volunteers in 2 groups
e.g. exposed vs non-exposed All complete health
survey every 12 months End point at 5 years
groups compared for Health Status
33
Randomized Controlled Trials in GP Primary
Care 90 consultations take place in GP
surgery 50 years old Potential problems 2 Key
areas Recruitment Bias Randomisation
Bias Over-focus on failings of RCTs
34
RCT Deficiencies Trials too small Trials too
short Poor quality Poorly presented Address wrong
question Methodological inadequacies Inadequate
measures of quality of life (changing) Cost-data
poorly presented Ethical neglect Patients given
limited understanding Poor trial
management Politics Marketeering Why still the
dominant model?
35

• Quantitative Data Summary
• What data is needed to answer the larger-scale
  research question
• Combination of quantitative and qualitative ?
• Cleaning, re-scoring, re-scaling, or
  re-formatting
• Measurement of both IVs and DVs is complex
  but can be simplified
• Binary measurement makes analysis easier but
  less meaningful
• Binary data needs clear parameters e.g exposed
  vs controls

36

• Quantitative Data Summary
• Continuous Discrete data can also be converted
  into Binary data
• Normal distribution of participants / data points
  desirable
• Means - age, height, weight, BMI, IQ, attitudes
• Frequencies / Classifications - job type, sick
  vs. healthy, dead vs alive
• Means must be followed by Standard Deviation (SD
  or )
• Presentation of data must enhance understanding
  or be redundant

37
Further Reading Abbott, P. and Sapsford.
Research methods for nurses and the caring
professions. Open University Press, Buckingham
1988. Altman DG. Designing Research. In Altman
DG (ed.) Practical Statistics For Medical
Research. Chapman and Hall, London 1991
74-106. Bland M. The design of experiments. In
Bland M. (ed.) An introduction to medical
statistics. Oxford Medical Publications, Oxford
1995 5-25. Bowling, A. Measuring Health. Open
University Press, Milton Keynes 1994 Daly LE,
Bourke GJ. Epidemiological and clinical research
methods. In Daly LE, Bourke GJ. (eds.)
Interpretation and uses of medical statistics.
Blackwell Science Ltd, Oxford 2000 143-201.
38
Further Reading Gao Smith F, Smith J. (eds.) Key
Topics in Clinical Research. BIOS scientific
Publications, Oxford 2002. Jackson CA. Planning
Health and Safety Research Projects. Croner
Health and Safety at Work Special Report 2002
62 1-16. Jackson CA. Analyzing Statistical
Data in Occupational Health Research. Management
of Health Risks Special Report, 81 Croner
Publications, Surrey, June 2003 Kumar, R.
Research Methodology a step by step guide for
beginners. Sage, London 1999. Polit, D.
Hungler, B. Nursing research Principles and
methods (7th ed.). Philadelphia Lippincott,
Williams Wilkins 2003.