Chapter 10 - Precision and Accuracy of Chemical Analyses Flashcards
Measurements always contain ____ and ______
- errors
- uncertainties
Measurement data can only give us an _______ of the “true” value
estimate
Why is estimating the reliability of experimental data is extremely important whenever we collect laboratory results?
because data of unknown quality are worthless
Results that might not seem especially accurate may be of considerable value…
if the limits of uncertainty are known
It is the best estimate of the true value
central value for the set
It is done in order to improve the reliability and to obtain information about the variability of results
Replicates
The most widely used measure of central value
mean
mean is also called as
arithmetic mean or average
Mean is obtained by
by dividing the sum of replicate measurements by the number of measurements in the set
∑xi means
to add all of the values xi for the replicates
Formula of Mean
x̄ = add all values for replicates / number of replicates
It is the middle result when replicate data are arranged in increasing or decreasing order
Median
How can you determine the median for an odd number of results?
by arranging the results in order and locating the middle result
How can you determine the median for an even number of results?
the average value of the middle pair is used
It indicates the closeness of the measurement to the true or accepted value
Accuracy
Accuracy is expressed by the ____
error
It is a measure of how close a series of measurements are to one another
Precision
Precision describes the ________ of measurements - in other words, …
- reproducibility
- the closeness of resuts that have been obtained in exactly the same way
Three terms used to describe the precision of a set of replicate data:
- Standard deviation
- Variance
- Coeffcient of variation
These three are functions of
how much an individual result xi differs from the mean, called the ________
deviation from the mean di
Deviation from the mean di formula
di = |xi - x̄|
What must be comapred to evaluate the accuracy of a measurement?
The measured value must be compared to the correct value
What must be comapred to evaluate the precision of a measurement?
You must compare the values of two or more repeated measurements
The difference between the experimental value and the accepted value
Error
Formula of Error
Error = experimental value - accepted value
It is the correct value based on reliable references
Accepted value
It is the value measured in the lab
Experimental value
How can we determine precision?
just by measuring replicate samples
Why is accuracy often more difficult to determine?
because the true value is usually unknown
What must be used instead to determone accuracy?
Accepted value
Accuracy is expressen in term of, what?
either absolute or relatice error
Formula for Absolute Error
E = xi - xt
xi in Absolute error is…
a measurement of the quantity
xt in Absolute error is…
the true or accepted value of the quantity
often a more useful quantity than the absolute error
Relative Error
Formula of Relative Error
Er = xi - xt / xt x 100%
Relative error is also expressed in
parts per thousands (ppt)
Results can be _____ without being _____ and ____ without being _____
- precise, accurate
- accurate, precise
Types of Errors in Experimental Data
- Random (or indeterminate)
- Systematic (or determinate)
- Gross Error
It causes data to be scattered more or less symmetrically around a mean value; usually small in values and not avoidable
Random (or indeterminate) error
Random error
- observational error
- environmental error
It causes the mean of a data set to differ from the accepted value
Systematic (or determinate) error
In general, a systematic error in a series of replicate measurements…
causes all the results to be too high or too low
Example of Systematic error
The loss of a volatile analyte while heating a sample
Systematic error
- Instrumental error
- Environmental error
- Observational error
Systematic error other examples
- Miscalibration of pH meter
- Miscalibration of analytical balance
- Evaporation of liquids
- Spattering chemical
- third tye of error
- usually occur only occasionally, are often large, and may cause a result to be either high or low
Gross error
Gross error is often a product of ____ ___
Human error
Gross errors lead to ____
outliers
Systematic errors have a ____ ___
definite value
Systematic errors have an ____ ___
assignable cause
Systematic errors are of the same magnitude for replicate measurements made in the same way, leading to _____ in measurement results
bias
Bias in measurement results affects, what?
- all the data in a set in the same way
- it carries a sign
Systematic errors may be either ________ or ________
- constant
- proportional
Magnitude of a _____ ___ stays essentially the same as the size of the quantity measured is varied
Constant error
With constant errors, the ____ ____ is _____ with sample size, but the ____ ____ ____ when the sample size is changed
- absolute error is constant
- relative error varies
It increase or decrease according to the size of the sample taken for analysis
Proportional errors
With proportional errors, the ______ ____ ____ with sample size, but the _____ ____ stays _____ when the sample size is changed
- absolute error varies
- relative error stays constant
It is always desirable because the response of most instruments changes with time as a result of component aging, corrosion, or mistreatment
Periodic calibration of equipment
Most personal errors can be minimized by
- careful
- disciplined laboratory work
materials that contain one or more analytes at known concentration levels
Analysis of Standard Samples (or Standard Reference Materials, SRMs)
SRMs can be prepared by
- synthesis
- purchased from a number of governmental and industrial sources
It contains the reagents and solvents used in a determination but no analyte
Blank
Many of the sample constituents are added to simulate the analyte environment, which is called the _____ ____
Sample matrix
As the size of a measurement ______, the effect of a constant error ______
- increases
- decreases
