Accuracy and Precision in the Laboratory

Precision and Accuracy Errors in Scientific Measurements

Precision - Refers to reproducibility or “How close the

measurements are to each other.”

Accuracy - Refers to how close a measurement is to the

real or true value.

Systematic error - produces values that are either all higher

or all lower than the actual value.

Random Error - in the absence of systematic error, produces

some values that are higher and some that

are lower than the actual value.

Good accuracy

Good precision

Poor accuracy

Good precision

Good accuracy

Poor precision

Poor accuracy

Poor precision

“True” Value

Other Possibilities…

Graduated Cylinder

Correct way to read a graduated cylinder

Estimate the volume in the

graduated cylinder…

Most would read between

19.1 to 19.3 mL

No one would properly

read the volume as high as

19.5 mL or as low as 19.0

mL. No one could

reasonably read the volume

to the 1/100s digit.

Graduated Cylinder

Incorrect way to read a graduated cylinder

Burette

What is the best readable

precision of an linearly-

calibrated analog device? ? 1/10 of the finest calibration mark.

Spectronic-20

Estimate the reading on the upper scale…

Most would read between 35.4 to 35.6 %T

No one would properly read the scale as high as 36 or as low as 35 %T.

Review A linearly-calibrated analog instrument

can usually be read to 1 digit more

precision than the engraved calibration

Balances

±0.1 mg precision

Accuracy determined by calibration

Significant Digit Rules

and Conventions A significant figure (also called a significant digit) in a measurement is one

which is known to some level of precision. The rules presented here are

simplifications of a more complete statistical analysis and should be used to

imply a certain confidence in a written numerical value. These rules are not

infallible.

To avoid round-off errors when making multiple-step calculations, carry one

or two extra significant figures in the intermediate calculations. Round off

the answer to the appropriate number of significant figures at the very end.

Rules: All nonzero digits in a reported value are significant.

422 g has 3 significant figures (SFs)

Zeroes between nonzero digits are significant.

2003 miles has 4 SFs

Trailing zeroes after the decimal point are significant.

-2.10 J has 3 SFs 0.110 g has 3 SFs

Leading zeroes after the decimal point are not significant.

0.00214 g has 3 SFs

Trailing zeroes in a number without a decimal point lead to ambiguity

and are usually assumed not to be significant. Eliminate the

ambiguity by converting to scientific notation (exponential notation).

96,500 C (3, 4, or 5 SFs) might be 9.650 x 104 C (4 SFs)

Handling Significant Figure in Calculations

Addition/Subtraction:

The number of decimal digits in the final answer is the same as the

minimum number of decimal digits in any measurement.

(2 decimal digits)

(1 decimal digit)

(1 decimal digit)

2.01 g

12.1 g

14.11 g

14.1 g

+

Multiplication/Division:

The total number of significant figures in the final answer is equal to

the minimum number of significant figures in any measurement.

Area = Length x Width

Length = 12.5 cm Width = 2.0 cm

2

2

(3 SFs)

(2 SFs)

(2 SFs)

12.5 cm

2.0 cm

25.0 cm

25 cm

X

Review

• Precision refers to the reproducibility of multiple measurements

• Accuracy refers to how close an average of measurements is to the true value.

• Errors can be – systematic (unidirectional and can be eliminated) or

– random (bidirectional and normal)

• A linearly calibrated instrument can usually be read to 1 digit more precision than the engraved calibration

• Presenting measurements and calculated results with appropriate significant digits is a way to display the estimated precision of the values.

• The rules of significant figure calculations are merely approximations of a much more rigorous statistical analysis and must be used carefully to avoid introducing unexpected and, possibly, undetected errors.