Basic Statistics in Public Health

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Basic Statistics in Public Health
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• Types of data
• Descriptive statistics
• Confidence Intervals

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TYPES OF DATA
Age?
Sex?
Social class?
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TYPES OF DATA
BMI?
Obese or not?
Underweight / normal / overweight / obese?
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Type of data?
Source Compendium of Clinical and Health
Indicators / Health Surveys for England
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Type of data?
Source Compendium of Clinical and Health
Indicators / Health Surveys for England
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SUMMARISINGDATA
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Summarising Numerical Data

• Measures of central tendency / location-
• Mean
• Median
• Mode

• Measures of spread / variability-
• Range
• Interquartile range
• Variance
• Standard deviation

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• Mean? Median?
• 3, 4, 5, 6, 7
• 9, 10, 20, 21
• 1, 2, 3, 4, 990

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• Mean? Median?
• 3, 4, 5, 6, 7
• 9, 10, 20, 21
• 1, 2, 3, 4, 990

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5
15
15
3
200
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Mean or Median?

• For symmetric data, meanmedian
• Choose the mean (easily understood, better
  statistical properties)

• For skewed data, mean is drawn towards the tail
  of distribution
• Median can be better reflection of centre of data

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Positively skewed data ...
Median2
Mean3.8
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Negatively skewed data ...
Median40
Mean38.9
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And the Mode?

• Mode most frequently occurring value
• Hardly ever used
• Depends on how the data are grouped, and not
  always unique

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The Range

• Range maximum - minimum
• In practice, usually present as (min, max)

• Poor measure of spread-
• very dependent on sample size
• affected by outliers
• but people often want to know it! present as an
  extra

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Interquartile Range (IQR)

• Rank data from smallest to largest
• Lower Quartile has 1/4 of values smaller than it
• Upper Quartile has 1/4 of values larger than it
• Interquartile Range Upper Quartile - Lower
  Quartile
• But usually written (Lower Quartile, Upper
  Quartile)

• Better than range - not influenced by outliers or
  sample size

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Interquartile Range (IQR) - Note

• Note - quartiles are, strictly, observations
• There are 3 quartiles -
• lower quartile
• ?
• upper quartile

median

• But the word Quartiles is now often used to
  mean Quarters - i.e. the 4 groups of ranked
  observations
• Similarly Quintiles is often used to mean
  Fifths i.e. the 5 groups of ranked
  observations

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Variance

• Step 1 Calculate Deviations the difference
  between each observation and the mean of the data
• Step 2 Square these Deviations
• Step 3 Average the Squared Deviations
• this is the Variance
• (Strictly, divide by n-1, not n)

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Standard Deviation (SD)

• Step 4 Take the square root of the Variance
• this is the Standard Deviation

This returns the statistic to the same units as
the data

• Both Variance and Standard deviation use all of
  the data
• But as a result, can be over-influenced by
  outliers

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Symmetric data ...

• Summarise using Mean and Standard Deviation

Skewed data ...
Summarise using Median and Interquartile Range
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Useful Fact
If a dataset is Normally distributed, or at least
fairly symmetrical, then the central 95 of the
data will be included in the range Mean /- 2
Standard Deviations Sometimes called a
reference range or normal range Strictly
Mean /- 1.96 Standard deviations
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Central 95 of data
2.5
2.5
mean 2SD mean
mean 2SD
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CONFIDENCEINTERVALS
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Obesity data, England, 2006

• Age-standardised percentage obese 24.1
• 95 Confidence Interval 23.2 to 25.0

?
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Sample estimates of Population values

• The obesity data was based on a sample
• But has this sample given the right answer?
• First need to eliminate bias, e.g. take a random
  sample
• But even when samples are unbiased, different
  samples will still give different answers - this
  is known as sampling error or random variation

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Would like to know, How imprecise might the
sample estimate be, just as a result of sampling
variation? i.e. How far away might the sample
estimate be from the true population value?

• Depends on
• Sample size
• Variability of data (SD)

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A 95 confidence interval provides a measure of
the precision of a sample estimate-
There is a 95 probability that the true
population value lies within the 95 confidence
interval.
Narrow 95 CI precise estimate Wide 95
CI imprecise estimate
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• Age-standardised percentage obese 24.1
• 95 Confidence Interval 23.2 to 25.0

We are 95 confident that the true
age-standardised percentage obese for England,
2006, is somewhere between 23.2 and 25.0.
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FOR DISCUSSION

• Why do we calculate Confidence Intervals when our
  estimates are based on total population data,
  e.g. SMRs for cancer?

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Presenting 95 Confidence Intervals on graphs
Self-reported smoking status in women (), by
ethnic group with 95 confidence intervals
(England, 2004)
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Interpreting 95 Confidence Intervals from graphs

• What can you say about the true smoking
  prevalence for the general population?
• For which ethnic groups is the prevalence of
  smoking significantly different from 25?
• Is the prevalence of smoking significantly
  different between the Black Caribbean and Black
  African populations?
• Is the prevalence of smoking significantly
  different between the Pakistani and Bangladeshi
  populations?

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• What can you say about the true smoking
  prevalence for the general population?
• We are 95 confident that it lies approximately
  between about 22 and 24

• For which ethnic groups is the prevalence of
  smoking significantly different from 25?
• All except Black Caribbean and Irish

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• Is the prevalence of smoking significantly
  different between the Black Caribbean and Black
  African populations?
• Almost certainly, since the Confidence Intervals
  dont overlap

• Is the prevalence of smoking significantly
  different between the Pakistani and Bangladeshi
  populations?
• We cant tell when Confidence Intervals
  overlap slightly, there might still be a
  significant difference!

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Note In general, it is better to perform a
statistical significance test, than look for
overlapping or non-overlapping confidence
intervals!
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Food for thought

• What is the difference between a 95 confidence
  interval and a 95 reference range?