Accuracy and Precision

Much of science has to do with the Much of science has to do with the collection and manipulation of quantitative collection and manipulation of quantitative or numerical data.or numerical data.

The value of computations using numerical The value of computations using numerical data is greatly dependent on the accuracy data is greatly dependent on the accuracy and precision of that data.and precision of that data.

Accuracy and Precision

There is always some degree of ERROR in There is always some degree of ERROR in a measurement. This is due to:a measurement. This is due to: Precision of the EquipmentPrecision of the Equipment Accuracy of the MeasurementAccuracy of the Measurement

Accuracy and Precision

Accuracy and precision can not be Accuracy and precision can not be considered independentlyconsidered independently

A number can be accurate and not preciseA number can be accurate and not precise A number can be precise and not accurateA number can be precise and not accurate The use of the number determines the The use of the number determines the

relative need for accuracy and precisionrelative need for accuracy and precision

ACCURACY

Accuracy can be defined as how close a Accuracy can be defined as how close a number is to what it should be.number is to what it should be.

Accuracy is determined by comparing a Accuracy is determined by comparing a number to a known or accepted value.number to a known or accepted value.

PRECISION

The number of decimal places assigned to The number of decimal places assigned to the measured number the measured number

It is sometimes defined as reproducibilityIt is sometimes defined as reproducibility

Example 1:

How old are you?How old are you? I am 16 years oldI am 16 years old I am 15 years and 8 months oldI am 15 years and 8 months old I am 15years, 8 months, and 5 days oldI am 15years, 8 months, and 5 days old I am 15 years, 8 months, 5 days, and 10 I am 15 years, 8 months, 5 days, and 10

hours oldhours old

Accuracy vs. Precision for Example 1

Each of these statements is more accurate Each of these statements is more accurate and more precise than the one before it.and more precise than the one before it.

Statement two is more accurate and more Statement two is more accurate and more precise that statement one.precise that statement one.

Statement three is more accurate and more Statement three is more accurate and more precise than statement two.precise than statement two.

Example 2:

How long is a piece of string?How long is a piece of string? Johnny measures the string at 2.63 cm.Johnny measures the string at 2.63 cm. Using the same ruler, Fred measures the Using the same ruler, Fred measures the

string at 1.98 cm. string at 1.98 cm. Who is most precise?Who is most precise? Who is most accurate?Who is most accurate?

The actual measurement is 2.65 cm.The actual measurement is 2.65 cm.

Accuracy vs. Precision for Example 2

Johnny is fairly accurate and also very Johnny is fairly accurate and also very precise.precise.

Fred is very precise, however, he is not very Fred is very precise, however, he is not very accurate. His lack of accuracy is due to accurate. His lack of accuracy is due to using the ruler incorrectly.using the ruler incorrectly.

Example 3

Using a centigram balance, Using a centigram balance, Mary measured a sample at 3 g.Mary measured a sample at 3 g. Ashley measured the same sample at Ashley measured the same sample at

3.00 g.3.00 g. Who is most precise?Who is most precise? Who is most accurate?Who is most accurate?

The actual measurement is 3.01 g.The actual measurement is 3.01 g.

Accuracy vs. Precision for Example 3 Mary is reasonably accurate. She was not Mary is reasonably accurate. She was not

very precise because the balance was very precise because the balance was capable of measuring to two decimal places.capable of measuring to two decimal places.

Ashley is much more accurate because of Ashley is much more accurate because of the precision of her measurement the precision of her measurement andand closeness of her value to the actual value.closeness of her value to the actual value.

ACCURACY/PRECISION

You can tell the precision of a number You can tell the precision of a number simply by looking at it. The number of simply by looking at it. The number of decimal places gives the precision.decimal places gives the precision.

Accuracy on the other hand, depends on Accuracy on the other hand, depends on comparing a number to a known value. comparing a number to a known value. Therefore, you cannot simply look at a Therefore, you cannot simply look at a number and tell if it is accuratenumber and tell if it is accurate

In Conclusion

In science we depend upon both the In science we depend upon both the accuracy and precision of the numbers we accuracy and precision of the numbers we use.use.

The need for accuracy and precision varies The need for accuracy and precision varies with the circumstance and other with the circumstance and other measurements being used.measurements being used.

Measurements

Length: metersLength: meters Volume (space occupied by an object): Volume (space occupied by an object):

metermeter3 3 – OR - liter– OR - liter Mass (measured by comparing mass of Mass (measured by comparing mass of

object to standard mass of 1kg): gramobject to standard mass of 1kg): gram Density (ratio of mass of an object to its Density (ratio of mass of an object to its

volume volume d=m/vd=m/v): g/m): g/m33 –or- g/l –or- g/l Temperature: Temperature: °C or K°C or K

More on TemperatureFreezing PointFreezing Point

OfOf

WaterWater

00°C°C 273 K (Kelvin)273 K (Kelvin)

Boiling Point Boiling Point

of of

WaterWater

100100°C°C 373 K (Kelvin)373 K (Kelvin)

*The zero point on the Kelvin scale, 0 K, or absolute zero, is -273°C°C

*A change of 1°C is the same as 1 K*A change of 1°C is the same as 1 K

K= °C + 273K= °C + 273 -or--or- °C= K - 273 °C= K - 273

Evaluating Measurements

Accepted Value: Accepted Value: true or correct value true or correct value based onbased on reliable referencesreliable references

Experimental value: the Experimental value: the measured valuemeasured value determined in the determined in the experiment or labexperiment or lab

Error: Error: differencedifference between the between the accepted and accepted and experimental valuesexperimental values Percent error:Percent error: |error||error| x x 100% 100%

accepted valueaccepted value