Accuracy and precision. Two terms which are often confused

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