Experimental Design & Practice 1 (Error Analysis)

Question 1

The process of “quantifying” or
“measuring” brings concepts such as…

Answer 1

precision, accuracy, uncertainty and error.

Question 2

Experimental Error (4)

Answer 2

• Errors cannot be completely eliminated.
• Other engineers and scientists must be able
  to reproduce your results.
• Reproducibility is only possible if your data
  is reliable. You must be able to effectively
  communicate the limitations of your
  measurements.

Reliable ≠ precise

Question 3

A quantity or number is meaningless without what?

Answer 3

A quantity (or a number) is
meaningless without units and uncertainty.

Question 4

Random Error

Answer 4

Arises from repeated
measurements of the same quantity, property, or
variable. These include statistical and “reading”
errors.

Question 5

Systematic Error

Answer 5

is an uncertainty that affects
all measurements equally. This includes
calibration error.

Question 6

Random Error is usually a result of what?

Answer 6

Commonly from limitations of an instrument, which prevents us from receiving repeatable results

Question 7

Random Errors include: (6)

Answer 7

– Operating at the measurement limits of
instruments (noise floor).
– A poorly controlled experimental parameter.
– Unmonitored fluctuations in the environment (e.g.
temperature, humidity, wind speed).
– Misreading the scale or a display, or a ruler.
– Alignment fluctuations of measuring device
relative to experiment.
– Quantum fluctuations!

Question 8

Purely random errors have a … distribution

Answer 8

Purely random errors have a Gaussian (Normal) distribution

Question 9

How to work out the standard uncertainty?

Answer 9

The standard uncertainty, δx, is calculated as the
standard error of the mean

δx = σ / square root n
where n is the number of measurements

Question 10

How can we reduce the uncertainty on the quantity being measured for imprecise measurements?

Answer 10

For imprecise measurements we can increase the
number of measurements to reduce the uncertainty on the
quantity being measured.

Note:
Increasing the number of measurements does not reduce
systematic errors.

Question 11

Systematic errors can arise due to what?

Answer 11

Can arise from poor calibration. We all
depend on our instruments following a
standard; the standard is usually a
universal constant (such as the speed of
light, or the standard 1-meter rod in Paris).

Unless a calibration is available during
measurements, systematic error are
difficult to identify and quantify.

Question 12

Systematic errors are impossible to
eliminate without…

Answer 12

a calibration or better
equipment. Comparing results taken by
different instruments (or methods) help
us to identify systematic errors.