Measurements
Review of Basic Concepts
 Accuracy & Precision
 Types of Errors
Measurements
Accuracy – how close a measurement is to the
true value
Precision – how close a set of measurements
are to each other
Measurements
Measurements
Estimating the accuracy and precision
of experimental data is extremely
important whenever we collect
laboratory results because data of
unknown quality are worthless.
Measure of Accuracy
1. Absolute Error
E = xi - xT
where
xi = experimental value
xT = true value or accepted value
(literature value)
Measure of Accuracy
2. Percent Relative Error
% RE =
xi - x T
xT
x 100
Measure of Precision
1. Range
R = xH - xL
where
xH = highest experimental value
xL = lowest experimental value
Measure of Precision
2. Standard Deviation
where
x = experimental value
x = mean
n = number of replicates / trials
Measure of Precision
2. Standard Deviation
• A low standard deviation means that
the data is very closely related to the
average, thus very reliable.
• A high standard deviation means
that there is a large variance
between the data and the statistical
average, thus not as reliable.
Types of errors
Three general types of errors occur in lab
measurements:
1. Random error
2. Systematic error, and
3. Gross errors
Random or Indeterminate Errors
• Random (or indeterminate) errors are
caused by uncontrollable fluctuations in
variables that affect experimental results
• This type of error causes data to be
scattered more or less symmetrically
around a mean value.
• Can be corrected or minimized by doing
replicates or multiple trials
• Random error in a measurement is reflected
by its precision.
Systematic or Determinate Errors
The errors that affect the accuracy of a result. This type
of error causes the mean of a set of data to differ from
the accepted value. A systematic error caused the
results in a series of replicate measurements to be all
high (+ bias) or all low (- bias).
Bias has a definite value, an assignable cause and are
about the same magnitude for replicate measurements.
Bias affects all the data in a set in the same way.
How do Systematic Errors Arise?
There are three types of systematic errors:
1. Instrumental errors are caused by the
imperfections in measuring devices and
instabilities in their components.
2. Method errors arise from non-ideal chemical
or physical behavior of analytical systems.
3. Personal errors results from the carelessness,
inattention, or personal limitations of the
experimenter.
Instrumental Errors
All measuring devices are potential sources of systematic
errors.
• Calibrated glasswares
 using glasswares at a temperature that differs
significantly from the calibration temperature
 distortions in container walls due to heating
• Electronic instruments are also subject to systematic
errors
 errors may emerge as the voltage of a batteryoperated power supply decreases with use
 Errors can also occur if instruments are not
calibrated frequently or if they are calibrated
incorrectly
Method Errors
These are errors arising from the following sources
• Chemical reagents – ex. wrong choice of chemical
indicator in an acid-base titration, non-specific
reagent
• Chemical reaction – reaction is too slow, incomplete,
or side reactions are happening
• Experimental procedure – ex. correct reagents, but
wrong concentration of reagent specified in the
procedure
Personal Errors
Many measurements require personal judgements,
judgements of this type are often subject to systematic,
unidirectional errors
• Estimating the position of a pointer between two
scale divisions: consistently low
• Determining the color change at the end point of a
titration: less sensitive to color change
• Reading the level of a liquid with respect to a
graduation in a pipet or buret: consistently high
• Activating a timer: consistently slow
Personal Error – Parallax Error
Parallax Error
– error from
incorrect reading
of volume
Effects of Systematic Errors
• Constant Errors: Constant Errors does not depend on
the size of the quantity measured
• Proportional Errors: Proportional errors decrease or
increase in proportion to the size of the sample taken
for analysis. A common cause of proportional errors is
the presence of interfering contaminants in the
sample.
Detecting Systematic Errors
• Systematic instrument errors are usually
corrected by calibration. Periodic calibration of
equipment is always desirable.
• Personal errors can be minimized by care and
self-discipline. Errors that result from a known
physical disability can usually be avoided by
carefully choosing the method.
• Method errors or bias of an analytical method is
estimated by analyzing standard reference
materials.
Gross Errors
• Gross errors are caused by experimenter
carelessness or equipment failure. They
occur only occasionally.
• Gross error leads to outliers. This error
causes one result to differ significantly from
the rest of the results (either too large or
small)
• Often discarded when assessing data