Introduction to statistics in
medicine
– Part 1
Arier Lee
Introduction
• Who am I
• Who do I work with
• What do I do
Why do we need statistics
Population
Sample
The important role of statistics in
medicine
• Statisticians pervades every aspect of medical
research
• Medical practice and research generates lots of
data
• Research involves asking lots of questions with
strong statistical aspects
• The evaluation of new treatments, procedures
and preventative measures relies on statistical
concepts in both design and analysis
• Statisticians are consulted at early stage of a
medical study
Research process
Research question
Primary and secondary
endpoints
Analyse data
Study design
Interpret results
Sampling and/or
randomisation scheme
Disseminate
Power and sample size
calculation
Pre-define analyses
methods
Bias
• A form of systematic error that can affect scientific
research
• Selection bias – well defined inclusion / exclusion
criteria, randomisation
• Assessment bias – blinding
• Response bias, lost-to-follow-up bias – maximise
response
• Questionnaire bias – careful wording and good
interviewer training
Some common data types
• Continuous
age, weight, height, blood pressure
• Percentages
% of households owning a dog
• Counts
Number of pre-term babies
• Binary
yes/no, male/female, sick/healthy
• Ordinal
taste of biscuits: strongly dislike, dislike, neutral, like, strongly
like
• Nominal categorical
Ethnicity: European, Maori, Pacific Islander, Chinese etc.
Descriptive statistics for continuous
data – the average
• Mean
(sum of values)/(number in group)
• Median
The middle value, 50th percentile
• Mode
The value that occurs the most often
3 4 7 8 8 8 9 11 11 13 21 23 24
mean=11.54
median
mode=8
Descriptive statistics for continuous
data – the spread
0, 1, 2, 5, 8, 8, 9, 10, 12, 14, 18, 20 21, 23, 25, 27, 34, 43
Q1
Q2
Q3
18 numbers
• Range
Minimum and maximum numbers
• Interquartile range
Quartiles divide data into quarters
• Standard deviation
A statistic that tells us how far away from the mean
the data is spread (95% of the data lies between 2
SD) √ (xi - x) 2 /(n-1)
Estimation
– Estimation: determine value of a variable and its likely
range (ie. 95% confidence intervals)
• Statistical inference is a process of generalising results
calculated from a sample to a population
• We are interested in some numerical characteristic of a
population (called a parameter). e.g. the mean height or
the proportion of pregnant women with hypertension
• We take a sample from the population and calculate an
estimate of this parameter
Estimation – a simple example
• We want to estimate the mean height of 10
years old boys
• Take a random sample of 100 ten years old boys
and calculate the sample mean
• The mean height of my random sample is 141cm
• Based on our random sample, we estimate the
mean height of 10 years old boys is 141cm
Distribution of Data
• It is essential to know the distribution of your data so
you can choose the appropriate statistical method to
analyse the data
• Data can be distributed (spread out) in different ways
• Continuous data:
There are many
cases when the data tends to be around a central
value with no bias to the left or right – normal
distribution
Distribution of data – Normal distribution
• Many parametric methods assumes data is normally
distributed
•
•
•
•
•
Bell curve
Peak at a central value
Symmetric about the centre
Mean=median=mode
The distribution can be described by two parameters –
mean and standard deviation
Standard deviation
• Standard deviation – shows how much variation or
‘dispersion’ exists in the data.
• 95% of the data are contained within 2 standard
deviations
A simulated example – Birth weight
Histogram of birth weight
Mean=3250g
SD=550g
Some other common distributions
• Some common distributions
– Binomial distribution – gestational diabetes (Yes/No)
– Uniform distribution - throwing a die, equal (uniform)
probability for each of the six sides
– And many many more…
Sampling variability
• Because of random sampling, the estimated
value will be just an estimate – not exactly the
same as the true value
• If repeated samples are taken from a population
then each sample and hence sample mean and
standard deviation is different. This is known as
Sampling Variability
Sampling variability
• In practice we do not repeat the sampling to
measure sampling variability we endeavour to obtain
a random sample and use statistical theory to
quantify the error
• Fundamental principle to justify our estimate is
reasonable: If it were possible to repeat a study over
and over again, in the long run the estimates of each
study would be distributed around the true value
• If we have a random sample then the sampling
variability depends on the size of the sample and the
underlying variability of the variable being measured