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Accuracy and precision
Accuracy and precision
Two terms which are often confused
Accuracy
Accuracy
How close you are to the “real” result
Accuracy
How close you are to the “real” result
but what is the “real” result
Accuracy
How close you are to the “real” result
but what is the “real” result
Can you measure “Accuracy” ?
Precision
Precision
A measure of reproducibility
Precision
A measure of reproducibility
nothing to do with the “Real result”
Precision
A measure of reproducibility
nothing to do with the “Real result”
So how is precision measured ?
Some “silly piccies” might help
Some “silly piccies” might help
A target with some “hits”
Some “silly piccies” might help
A target with some “hits”
Individually off target, but the average is spot on
Some “silly piccies” might help
A target with some “hits”
Individually off target, but the average is spot on
It’s accurate, but not precise.
Some “silly piccies” might help
A target with some “hits”
Individually off target, but the average is spot on
It’s accurate, but not precise.No good for a “one-off” test
Some “silly piccies” might help
A target with some “hits”
Some “silly piccies” might help
A target with some “hits”
Nicely reproducible, but off target
Some “silly piccies” might help
A target with some “hits”
Nicely reproducible, but off target
Precise, not accurate
Some “silly piccies” might help
A target with some “hits”
Nicely reproducable, but off target
Precise, not accurate
Not comparable with other “testers”
Some “silly piccies” might help
A target with some “hits”
Nicely reproducable, but off target
Precise, not accurate
Not comparable with other “testers”“bias” is how far we are out
Some “silly piccies” might help
A target with some “hits”
Bang on target
Some “silly piccies” might help
A target with some “hits”
Bang on target
Precise AND accurate
Some “silly piccies” might help
A target with some “hits”
Bang on target
Precise AND accurate
The ideal !
Some “silly piccies” might help
A target with some “hits”
Some “silly piccies” might help
A target with some “hits”
All over the shop
Some “silly piccies” might help
A target with some “hits”
All over the shop
Neither accurate nor precise
So now you know the difference between accuracy & precision.
So now you know the difference between accuracy & precision.
Let’s look at some simple statistical terms next
So now you know the difference between accuracy & precision.
Let’s look at some simple statistical terms next
There are lies, damned lies, and statisticsBenjamin Disreli-19th century Prime minister
So now you know the difference between accuracy & precision.
There are lies, damned lies, and statisticsBenjamin Disreli-19th century Prime minister
I’ve got a degree in maths and I don’t understand statistics !!!
Dave Styles- Author of this web site
Mean
Mean
It’s the “average”
Mean
It’s the “average”
add ’em up, divide by how many you’ve got"
Mean
It’s the “average”
add ’em up, divide by how many you’ve got"
(X)/n
Mean
It’s the “average”
add ’em up, divide by how many you’ve got" With enough attempts can be used to give an indication
of accuracy.
(X)/n
Variance
"A measure of spread from the mean”
Variance
"A measure of spread from the mean”
the sum of the squares of the differences".
Variance
"A measure of spread from the mean”
the sum of the squares of the differences".
You can look up the formula !
Variance
Oh, all right then
Variance
Oh, all right then
variance = (xi - mean)2 /n)
Variance
Oh, all right then
variance = (xi - mean)2 /n)
Variance
where xi are the individual data itemsn is how many you’ve got.
variance = (xi - mean)2 /n)
Why the squared bit ?
Variance
VarianceConsider this data set
Data: 14.0, 13.6Mean 13.8
VarianceConsider this data set
Data: 14.0, 13.6Mean 13.8
Mean deviation from the mean is((14.0-13.8) +(13.6-13.8))/2= 0
VarianceConsider this data set
Data: 14.0, 13.6Mean 13.8
Mean deviation from the mean is((14.0-13.8) +(13.6-13.8))/2= 0
this suggests there is no deviation from the mean
VarianceConsider this data set
Data: 14.0, 13.6Mean 13.8
Mean deviation from the mean is((14.0-13.8) +(13.6-13.8))/2= 0
this suggests there is no deviation from the mean
RUBBISH
VarianceThe units of variance make it impractical to use
VarianceThe units of variance make it impractical to use
Take for example the variance of a run of white cell counts
Variance
Take for example the variance of a run of white cell counts
the units would be 1018/l2 ie a squared liter. - nine dimensional ?!?!?!
The units of variance make it impractical to use
Standard deviation
Standard deviationThe positive square root of the variance
n = (xi - mean)2 /n)1/2
Standard deviationThe positive square root of the variance
Standard deviation
Standard deviation
has a better S.D. than
Standard deviation
has a better S.D. than
Standard deviationAn example
Standard deviationAn example
what’s best of these data sets ?
Actual value Estimate Actual value Estimate10 11 10 1010 8 10 610 12 10 1210 10 10 1410 9 10 8
Standard deviationAn example
what’s best of these data sets ?
Actual value Estimate Actual value Estimate10 11 10 1010 8 10 610 12 10 1210 10 10 1410 9 10 8
Both have the same mean, but one is clearly less variable than the other.
OK - so what ?
OK - so what ?What do we do to ensure precision and/or accuracy in the lab ?
OK - so what ?What do we do to ensure precision and/or accuracy in the lab ?
blood counts ?
OK - so what ?What do we do to ensure precision and/or accuracy in the lab ?
blood counts ?coagulation ?
OK - so what ?What do we do to ensure precision and/or accuracy in the lab ?
blood counts ?coagulation ?flow cytometry ?
OK - so what ?What do we do to ensure precision and/or accuracy in the lab ?
blood counts ?coagulation ?flow cytometry ?haemoglobinopathy investigations ?
OK - so what ?What do we do to ensure precision and/or accuracy in the lab ?
blood counts ?coagulation ?flow cytometry ?haemoglobinopathy investigations ?Microbiological cultures ?
OK - so what ?What do we do to ensure precision and/or accuracy in the lab ?
blood counts ?coagulation ?flow cytometry ?haemoglobinopathy investigations ?Microbiological cultures ?Histological staining
