School of Veterinary Medicine and Science
Statistics
• Statistics are like bikinis. What they
reveal is suggestive, but what they
conceal is vital. ~Aaron Levenstein
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Nice statistics
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CONFIDENCE INTERVALS
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What is a confidence
interval?
Confidence is generally described as a
state of being certain either that a
hypothesis or prediction is correct or that
a chosen course of action is the best or
most effective
And a confidence interval?
How confident can you be that your answer
from your study is true of the whole
population?
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You only have a sample
• You can never measure the whole
population
• Even if you sample the whole population
you wont get information about all of it
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From your sample…
• Something is being quantified:
– A mean
– An odds ratio
– A disease frequency
And we get a single value = point estimate
• How close is the point estimate of your
sample to the true value in the
population?
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Point estimate
• E.g. A mean
• You can then work out a standard error,
which tells you about the precision of the
estimate of the mean of the real
population
• But an interval is easier than a standard
error….
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What is a confidence
interval?
Confidence interval: Confident that the
true population value of whatever we are
measuring is within this range of values
……………………………….not entirely true!
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The truth
If we are talking 95% confidence intervals
• If we performed the study 100 times and
calculate a 95% confidence interval each
time
• Then about 95 of the 100 confidence
intervals calculated will include the true
value of whatever we are interested in
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How do you calculate a
CI?
• Use nasty sums
……..Or a table
……..Or a computer
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Calculate a confidence
interval (mean)
1. Work out the mean
2. Work out the standard error of the mean
(how precise a measurement is the
sample mean of the population mean?)
3. The CI is some kind of multiple of the
standard errors
E.g. 95% CI = ± 1.96 (SE)
99% CI = ± 2.58 (SE)
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Why 95%?
• Convention
• You can calculate anything you like but it
is normally 90%, 95% or 99%
• NEVER 100% confident
100% confidence = arrogance
Arrogance: an attitude of superiority
manifested in an overbearing manner or in
presumptuous claims or assumptions
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So……
• To see how believable something is – you
want a confidence interval
• Don’t just believe the point estimate of a
sample is the true value in your population
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Look for…
• The point estimate, the P value and the
confidence interval – you want the actual
numbers not ‘95% confidence’
E.g.
Cases were 3 times more likely to be over the age
of 15 rather than 5-10 years old, when compared
to controls (OR = 2.87, 95% CI 1.38 – 5.99, p =
0.005).
Cases were significantly more likely to have ever
have received a vaccine of any type in their
lifetime compared to controls cats (OR = 6.8,
95% CI = 1.9 - 50.4, p = 0.03).
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Now what?
1. How wide is it?
2. What does the interpretation of the CI
mean? Clinically? Biologically?
3. Does it include the null value?
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1. Width?
• CI are calculated from standard errors
• Standard errors depend on sample size
and variation within the sample
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Sooooo…..
• Small sample = bigger standard error =
bigger CI
• More variation in sample bigger CI
• Wide CI = imprecise estimate
• Narrow CI = more precise estimate
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Examples
Cases were 3 times more likely to be over
the age of 15 rather than 5-10 years old,
when compared to controls (OR = 2.87,
95% CI 1.38 – 5.99, p = 0.005).
Cases were significantly more likely to have
ever have received a vaccine of any type
in their lifetime compared to controls cats
(OR = 6.8, 95% CI = 1.9 - 50.4, p =
0.03).
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Now what?
1. How wide is it?
2. What does the interpretation of the CI
mean? Clinically? Biologically?
3. Does it include the null value?
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2. Interpretation
• The upper and lower limits can be used to
see whether the results are useful
• A value can be significant with a low p
value but the CI interval can help tell you
whether you should get excited about it or
not!
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Examples
Cases were 3 times more likely to be over
the age of 15 rather than 5-10 years old,
when compared to controls (OR = 2.87,
95% CI 1.38 – 5.99, p = 0.005).
Cases were significantly more likely to have
ever have received a vaccine of any type
in their lifetime compared to controls cats
(OR = 6.8, 95% CI = 1.9 - 50.4, p =
0.03).
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Now what?
1. How wide is it?
2. What does the interpretation of the CI
mean? Clinically? Biologically?
3. Does it include the null value?
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The null value?
• In Odds Ratios and Risk Ratios where you
compare two groups and a value of 1
means there is no difference then 1 is the
null value
• If 1 is included in the CI e.g. 0.56-1.2,
then there is no statistically significant
effect
………………………………..dont worry I will
remind of this later in the year
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Examples
Cases were 3 times more likely to be over
the age of 15 rather than 5-10 years old,
when compared to controls (OR = 2.87,
95% CI 1.38 – 5.99, p = 0.005).
Cases were significantly more likely to have
ever have received a vaccine of any type
in their lifetime compared to controls cats
(OR = 6.8, 95% CI = 1.9 - 50.4, p =
0.03).
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Another example
The odds ratio for practice type B reporting
multiple cases compared to practice type
A was not significant
(OR = 1.02, 95% CI 0.25 – 4.10, p = 0.98)
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AT A GLANCE!
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Look at the CI
• Is it massive? If so, bin it! The power is
rubbish and no matter how small p is, you
have no confidence in it!
• Does it include values that are relevant?
Do we care about the numbers? If not bin
it!
• Does it include the null value? If it does,
bin it!
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Forest plots
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Cool words…
• Bootstrapping: refers to a group of
metaphors that share a common meaning:
a self-sustaining process that proceeds
without external help.
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Cool words…
• Jack(k)nifing: means the folding of an
articulated vehicle articulated vehicle
(such as one towing a trailer) such that it
resembles the acute angle of a folding
pocket knife.
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Similar techniques
• Repeated sampling (iterative processes)
• Use distribution of many estimates & CIs
to get an overall estimate and CI
• Help!
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BEING CONFIDENT…..
Is not that difficult….
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In the packages….
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