Accuracy, Precision, and Error Types

hi this is an introduction to accuracy

and precision and also the types of

error that affect them my goal is for

you to understand the difference between

accuracy and precision because they're

often used interchangeably but they are

not the same thing and to understand

what kind of errors contribute to go

so have you ever serviced I know I've

been in conversation and somebody says

something it's just so right like yes

precisely what do you mean when you say

that usually people are like yeah I

totally agree with you you're right okay

being right is actually being accurate

yes precisely technically means you got


reproducibly not usually what we mean

when we're talking about this in public

so most of us use the word precisely

incorrectly or wrong given the wrong

names and accurate okay so what am I

trying to get here that correct is

accurate Versailles is reproducible all

right hopefully that as you go forward

with your life you will now think every

time somebody says yes precisely you're

using that wrong okay moral of the story

here is the accuracy and precision are

often confused with each other and so if

you're struggling with keeping the two

straight then it's understandable but

you do want to know the difference

so accuracy and precision are usually

covered with the dartboard

we've got four darts boards here so one

thing you want is a happy one is this

one right here you want to hit the

bull's eye every single time the

bullseye is your target it is the truth

the correct value here and so to be

accurate means you've got nearness to

the truth you're right so on average

you've got an accurate situation so here

which is also precise because

reproducibly you're able to hit the

bull's eye with very low spread but

you're also right around here okay so

that one's accurate as well but its

imprecise um I like to say that this is

the way I play dart because I rarely hit

the bull's eye but I'll say well on

average I hit the bull's eye it doesn't

really fly right if you want both

accurate and precise you want to be in

the top-left corner here but there's

also the other condition the other two

plots here are when you do not have

accuracy okay here and not averaging to

hit the bull's eye and so yes precisely

could mean this graph as well okay where

you keep the hit the same place over and

over again but you're not hitting the

bull's eye I like to call that when I'm

playing darts be admire the grouping

effect okay that's cute that's funny not

what you want from an analytical

chemistry analysis now what you really

really don't want like super super bad

is if your data is both imprecise

meaning it's very scattered and it's

inaccurate all right hopefully that

helps you to understand the position

accuracy and precision so how do we

classify these things if being accurate

means being correct then you can do a

measurement spell favor

okay so error is a measurement

measurement of accuracy there's absolute

error which is just the difference

between the obtained results this is the

one that you actually measure right here

that's the expected result usually

people will instead use percent error

where you're taking the difference


Taine's result in the expected result

and hopefully that would be small you

want to minimize that difference and

then you're dividing it as a proportion

of the expected true result mostly

languages so low values for error are


but how do we know what is true accepted

or expected well you have to get

something like a certified reference

material which an agency like the

National Institute standards NIST has

been lending measurements on different

techniques basic physical principles and

tells you this is true okay

but you need to have true value enough

to know all right so percent error

absolutely error from a standard and

gives you a commission Rhino directors

made precision because it's a

measurement of spread we rely on

standard deviation and friends so the

pressure here standard deviation is the

individual sample so that little marking

right there is X sub I for individual

measurements difference from the mean

which is your typical average square all

those differences in addemup okay and

then a note minus 1 remember that the

number of times it's not a hashtag it's

number two I am NOT 12 numbers minus one

and then you can also do a percent

relative standard deviation which is

abbreviated percent RSC some people call

this coefficient of variation or CV so

if you're looking at older analytical

methods you should know that these are

the same thing simply take your standard

deviation divided by the average value

multiplied by a hundred percent gives

your proportion I love that one's very

helpful and then lastly you can also do

variance which is just the standard

deviation squared

okay so what causes these things we have

two types of error one is systematic

error one is random error they have

alternative names determinant is

systematic in determinant is random have

to do with whether you can find and is

determine the cause determinate error

that has an actual cause systematically

is what affects accuracy where is random

error affects precision usually your

systematic error is coming from some

sort of flaw in your equipment or

experimental design and your random

error is coming from an uncontrolled

variable the thing is it helps you

identify these is that systematic error

is going to be reproducibly positive

every time you do it it'll be offset a

little bit always mean a little bit high

or every time you do it it'll be often

the different direction it will be a

little bit low okay or maybe a lot of it

you never know but it's reproducibly

wrong in the same direction systematise

sir and that affects accuracy

random error is equally likely to be

positively negative and so these tend to

cancel each other out a little bit over

time you cannot fully eliminate random

error you always have some systematic

error if you are lucky and careful you

can find with causing it and you can

eliminate the cause and that means you

can have an accurate measurement

examples here miss calibrate equipment

are really common ways to get systematic

error and there's a whole bunch of

random error in Oasis and stuff like

that I'm going to get into that more

right now remember there's always Randy

okay so more on the causes we'll start

with systematic these are things you can

find one of the first and foremost

issues is if you have a bad sample okay

if your sample is not representative

whatever you took of it isn't really

representative of what you're trying to

measure doesn't matter what else you do

from that point on that sample bad

results there's going to be another

topic of sampling

method error which is maybe something

like you don't have a blink that is

counting for all faster than your sample

or you made some sort of a function like

maybe you're weighing a precipitate and

you're assuming pure but it's not that

kind of thing

measurement error every single thing

that you use equipment flash balances

will have some error in it like they'll

say it's 100 ml flask but maybe it's

somewhere between ninety-nine point

eight and 100 point two and so you need

to know what's the likelihood is going

to be shifted from the label and by how


so those are labels you can get those

tolerances and there's personal error

this means reproducible bias that you've

introduced for example you personally

fail to calibrate it's not the

instruments fall balance that you weight

stuff on is labeled to a certain

tolerance but maybe you forgot to pair

it okay so that's a personal error

that's going to cause an offset that's

going to be there there's also a matter

of like reading a scale so we know that

if you're looking for liquid you've got

the meniscus maybe set a line on a flask

the blackberries you Heinen the blue is

your water you want to be reading the

bottom and so if you're holding this

laughing you're looking at it straight

on right straight on you might get the

line right but if you're always looking

down maybe you get the line slightly

wrong if you're always looking down

religiously you're putting a personal

error bias on there random error these

are things that really have to do with

your precision right so one of the

terminologies here is repeatability this

is your best case scenario usually it

means one person one day same solutions

same insurance same equipment so nothing

changes how close could you get if you

did it exactly the same way every single

time then there is reproducibility and

there's a bunch of other versions of

this and this have to do with changing

those conditions like maybe it's a

totally different labs with different

equipment you're just following the same

procedure that is often called like a

round-robin studies based on the same

samples to a whole buncha labs

I asked or maybe it's the matter of how

reproduce will argue between your

measurement this week and next week for

between Jim and Sally on two different

spectrometers okay what is enveloped in

all of this random error is the fact

that when you have random error it is

going to include the fact that you can't

do something the same way every single

time you've got some inconsistency where

you're sometimes high and sometimes low

say sample preparation like cleaning or

in reading the scale the other thing is

that your instrumentation that you're

using can have some variations due to

the electronic noise or from variations

due to heat okay

all right got your graph here what you

want a good fashioned smile here right

here is to be both accurate and precise

okay accuracy means correct this is

governed by determinant or systematic

errors and could in theory fix these

like a few finds that you didn't calorie

Earth event you can calibrate it and

that will be gone you're going to

measure a known sample okay and you're

going to calculate the percent error

from this but you always have to

remember that truth in annals chemistry

really means the most trusted value that

we have so somebody has to do that and

usually you want to trust a certified

lab then there's precision which is your

measurement of spread that is governed

by indeterminate or random errors

sometimes high sometimes low that we

described by standard deviation and

variations that are else and the thing

is to remember that you always have some

sort of random error which you can

minimize by taking more samples or to

simply try to do things the same way

every single time so you want precise

you want accurate precise means true and

correct okay huh see how easy just mess

it up on I almost planet accurate means

true and correct precise me reproducible

you got at the same at right angle time

but I like to remember in order to keep

this correct is that the word correct is

almost inside the word accurate all

right good luck and peace