Accuracy and Precision

What do people usually mean when they say…? Her analysis of the stock market trends was very accurate.

What do people usually mean when they say…? His engineering work is always precise.

accuracy precision In science, accuracy and precision have specific meanings.

ACCURACY is a measure of how close a series of measurements is to the ACCEPTED or “true” value.

PRECISION how closeindicates how close a series of measurements are to each other. agreementindicates how closely a series of measurements are in agreement. consistencyindicates the degree of consistency in a series of measurements

A series of measurements can be accurate but not precise. Our data can be centered around the correct value … but spread out.

This archer is fairly accurate but not very precise.

A series of measurement can be precise but not very accurate! It is not unusual for a group of repeated measurements to “cluster” together. But that does not always mean the data are accurate! If the instrumentation used in taking the measurements is “off” you will not get accurate results.

This archer is fairly precise, but not very accurate.

Being precise but not accurate can be very misleading. It’s quite impressive when you generate data that is very consistent. But, your data may not be accurate – it may not “hit the bull’s eye.” CALIBRATE For this reason, we must CALIBRATE scientific instruments to ensure that the data we collect are accurate.

We CALIBRATE scientific equipment by testing with a STANDARD of known value. We calibrate a pH meter by testing the meter with solutions of known pH value. If our meter is “off” there are ways to adjust it so that it gives accurate readings.

standards The National Institute of Standards and Technology and various international scientific bodies have standards for such measurements as: LengthLength Mass/weightMass/weight TimeTime Musical pitchMusical pitch VoltageVoltage TemperatureTemperature

This is the standard metre established in Paris in 1791.

The current definition of a meter: “The distance traversed in vacuum by light in 1/ of a second.”

The Handbook of Chemistry and Physics is the “bible of chemistry.” It is full of all kinds of standard reference data about chemical elements and compounds..

This archer is both precise and accurate!

Sloppy lab work Sloppy lab work – neither precise nor accurate.

This archer is neither precise nor accurate!

Look at these data for repeated measurement of the pH of the same soil sample. pH = 7.5 Test #pHTest #pH

pH = 7.5 Accurate? Precise? Test #pHTest #pH

The numbers are close together. So there is good agreement and consistency. The data are precise. However the values cluster around a pH value of 6.1 or 6.2. The true pH value for the soil sample is 7.5. So the data are not accurate!

How might we correct the situation so we get more accurate data?

Look at these data for repeated measurement of the pH of the same soil sample. pH = 7.5 Test #pHTest #pH

pH = 7.5 Accurate? Precise? Test #pHTest #pH

The data appear to be accurate but not precise – the values are centered around the correct pH value of 7.5. How might we correct a problem like this?

Look at these data for repeated measurement of the pH of the same soil sample. pH = 7.5 Test #pHTest #pH

pH = 7.5 Accurate? Precise? Test #pHTest #pH

These results are both accurate and precise! The results are centered around the correct value and are consistent.

An upscale way to look at it…

Error Error is (the absolute value of) the difference between the measured value you obtained and the correct or accepted value. If you weigh a sample and say that it weighs 24.5 grams, but it actually measures 24.1 grams, you have an error of 0.4 grams.

Percent error All measurements are vulnerable to error. We estimate the extent of this error with the percent error statistic. % error = | error | accepted value % error = | accepted value - my value | accepted value

Percent error % error| error | % error = | error | accepted value absolute value Notice that percent error uses the absolute value of the difference between your result and the measurement you should have obtained. Therefore percent error is always a positive number.

A percent error calculation 7.8 g/ml 7.1 g/mL I do a test to determine the density of a sample of zinc. I determine that the density of zinc is 7.8 g/ml. The actual density of zinc is 7.1 g/mL. What is the percent error?

7.8 g/ml 7.1 g/mLpercent error I do a test to determine the density of a sample of zinc. I determine that the density of zinc is 7.8 g/ml. The actual density of zinc is 7.1 g/mL. What is the percent error? % error = | accepted value - my value | accepted value % error = | 7.1 g/mL – 7.8 g/mL| 7.1 g/mL = 9.8% error = 9.8%

Did William live to Tell?

Let’s do the sponge accuracy exercise!