Chapter 10: Precision and Accuracy of Chemical Analyses Flashcards
Measurements always contain __ and __.
errors
- uncertainties
Frequent __, __, and __ of known samples can sometimes be used to lessen all but the random errors and uncertainties.
- calibrations
- standardizations
- analyses
Measurement data can only give us an __ of the “true” value
estimate
Estimating the reliability of experimental data is extremely important whenever we collect laboratory results because data of unknown quality are __.
worthless
To improve the reliability and to obtain information about the variability of results, several (often __ to __) portions (__) of a sample are usually carried through an entire analytical procedure.
- 2-5
- replications
The best estimate of the true value is the __.
central value for the set
The most widely used measure of central value
mean
The __, also called the __ or the __, is obtained by dividing the sum of replicate measurements by the number of measurements in the set: (formula?)
- mean
- arithmetic mean
- average
N
x̄= ∑ xi / N
i =1
the middle result when replicate data are arranged in increasing or decreasing order
median
__ indicates the closeness of the measurement to the true or accepted value and is expressed by the __.
- accuracy
- error
a measure of how close a series of measurements are to one another
precision
describes the reproducibility of measurements—in other words, the closeness of results that have been obtained in exactly the same way.
precision
Three terms that are widely used to describe the precision of a set of replicate data:
- standard deviation
- variance
- coefficient of variation.
deviation from the mean formula
di = | xi-x̄ |
To evaluate the __ of a measurement, the measured value must be compared to the correct value.
accuracy
To evaluate the __ of a measurement, you must compare the values of two or more repeated measurements.
precision
the difference between the experimental value and the accepted value.
Error
The __ is the correct value based on reliable references.
accepted value
The __ is the value measured in the lab.
experimental value
formula of error
Error = experimental value - accepted value
Accuracy is expressed in terms of either __ __ or __ __
- absolute error
- relative error
We can determine precision just by measuring __ __
replicate samples
Absolute error formula
E = xi - xt
where xi is a measurement of the quantity and xt is the true or accepted value of the quantity
formula of Relative Error
Er = xi - xt / xt * 100%
often a more useful quantity and also expressed in parts per thousand (ppt)
relative error
Types of Errors in Experimental Data
- Random (or indeterminate) error
- Systematic (or determinate) error
a type of error that causes data to be scattered more or less symmetrically around a mean value; usually small in values and not avoidable
Random (or indeterminate) error
A student repeatedly weights a beaker with a solution and gets different measurements every time. What example is this?
Random (or indeterminate) error - Observational error
When getting a pressure reading, students were entering and exiting the lab, causing the pressure to be lower.
Random (or indeterminate) error - Environmental error
a type of error that causes the mean of a data set to differ from the accepted value.
Systematic (determinate) error
in a series of replicate measurements, causes all the results to be too high or too low. (what type of error)
Systematic (determinate) error
examples of Systematic (determinate) error
- Miscalibration of pH meter
- Miscalibration of analytical balance
- Evaporation of liquids
- Spattering chemicals
A third type of error is __ . They usually occur only occasionally, are often large, and may cause a result to be either high or low. They are often the product of __.
- gross error
- human errors
Gross errors lead to __, results that appear to differ markedly from all other data in a set of replicate measurements.
outliers
- have a definite value
- Have an assignable cause
- are of the same magnitude for replicate measurements made in the same way, leading to bias in measurement results. Note that bias affects all the data in a set in the same way and that it carries a sign.
Systematic (determinate) error
Systematic errors may be either __or __.
- constant
- proportional
The magnitude of a __ __ stays essentially the same as the size of the quantity measured is varied. With __ __, the __ __ is constant with sample size, but the __ __ varies when the sample size is changed.
- constant error
- constant error
- absolute error
- relative error
__ __ increase or decrease according to the size of the sample taken for analysis. With __ __, the __ __varies with
sample size, but the __ __ stays constant when the sample size is
changed.
- Proportional errors
- proportional errors
- absolute error
- relative error
What type of error?
if you measured the amount of water in a bucket by filling a beaker N times. The error on your final measured bucket volume is not just the error of the beaker, but scales with the error of the beaker and the number of times it was used. Note this applies to a __ __ in the beaker vs “real truth” in the actual volume of the beaker vs the volume readings on the side of the beaker. If the beaker is 5% smaller than it supposedly is, your final bucket volume will be off by 5%.
- proportional error
Detection of Systematic Instrument and Personal: __ __ __ __ 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
Detection of Systematic Instrument and Personal: Most personal errors can be minimized by __, ___ ___ ___. It is a good habit to check instrument readings, notebook entries, and calculations systematically. Errors due to limitations of the experimenter can usually be avoided by carefully choosing the analytical method or using an automated procedure.
careful, disciplined laboratory work
Detection of Systematic Method Errors (3)
▪ Analysis of Standard Samples (or Standard Reference Materials, SRMs)
▪ Blank Determinations
▪ Variation of Sample Size
Detection of Systematic Method Errors:
__ in an analytical method is particularly difficult to detect. One or more of the following steps can be taken to recognize and adjust for a systematic error in an analytical method.
Bias
Detection of Systematic Method Errors:
- materials that contain one or more analytes at a known concentration levels
- can sometimes be prepared by synthesis or purchased from a number of governmental and industrial sources.
Standard Samples (or Standard Reference Materials, SRMs)
Detection of Systematic Method Errors:
An example of where we can purchase SRMs and how many do they offer
National Institute of Standards and Technology (NIST)
- 1300 SRMs
Detection of Systematic Method Errors:
___ __
A __ contains the reagents and solvents used in a determination
but no analyte. Often, many of the sample constituents are added to simulate the analyte environment, which is called the __ __.
- blank determinations
- blank
- sample matrix
Detection of Systematic Method Errors:
In a __ __, all steps of the analysis are performed on the __ material. The results are then applied as a correction to the sample measurements. They reveal errors due to interfering contaminants from the reagents and vessels employed in the analysis
- blank determination
- blank
Detection of Systematic Method Errors:
__ _ __ __
As the size of a __ increases, the effect of a __ __ decreases. Thus, __ __ can often be detected by varying the __ __.
Variation of Sample Size
- measurement
- constant error
- constant errors
- sample size
Use the __ or __ of replicates as a measure of central value of data.
- mean
- median
It is often more difficult to determine the __ of results than the __ because the true value is seldom known.
- accuracy
- precision
arise from experimental variables that cannot be controlled or determined. Such errors affect precision
Random, or indeterminate, errors
occur when instruments or measuring devices are uncalibrated or are calibrated improperly. They have the same effect on all samples.
Systematic, or determinate, errors
caused by nonideal instrument behavior, by faulty calibrations, or by use under inappropriate conditions.
Instrumental errors
arise from nonideal chemical or physical behavior of analytical systems.
Method errors
result from the carelessness, inattention, or personal limitations of the experimenter.
Personal errors
independent of the size of the sample being analyzed.
Constant errors
decrease or increase in proportion to the size of the sample.
Proportional errors
What type of error?
- random fluctuations in electrical noise
- random inconsistencies in measurement readings
- random changes in the laboratory temperature
Random (indeterminate) error
an error that affects the precision of the results
Random (indeterminate) error
an error that affects the accuracy of the results
Systematic (determinate) error
the substance being determined
analyte
What type of error? you mistakenly read 9 as 4
Gross error
determines the relationship between a measured quantity and the analyte concentration.
calibration
of the three types of systematic error, __ is the most difficult to identify and correct.
method errors
