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 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…?
limits of uncertainty are known
in order to improve reliability to obtain information about the variability of results, what is carried
replicates
best estimate of true value
central value for the set
most widely used measure of central value
mean
mean is also called as
- arithmetic mean or
- average
mean formula
x̄ = add all values for replicates / number of replicates
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
accuracy
accuracy is expressed by what
error
measure of how close a series of measurements are to one another
precision
what does precision describe
closeness of results that have been obtained in exactly the same way
Three terms used to describe the precision
- standard deviation
- variance
- coefficient of variation
how much an individual results xi differs from the mean
deviation from the mean
deviation from the mean formula
di = |xi - x̄ |
Evaluate accuracy
measured value compared to correct value
Evaluate precision
compare values of two or more repeated measurements
difference between experimental value and the accepted value
error
correct value based on reliable references
accepted value
value measured in the lab
experimental value
often more difficult to determine because the true value is usually unknown
accuracy
Terms used to express accuracy
- absolute error or
- relative error
xi
measurement of the quantity
xt
true or accepted value of the quantity
absolute error formula
E = xi - xt
- foten a more useful quantity than the absolute error
- also expressed in parts per thousand (ppt)
relative error
relative error formula
Er = (xi - xt/xt) x 100%
Types of Errors in Experimental Data
- Random error
- Systematic error
- Gross error
causes data to be scattered more or less symmetrically around a mean value; usually small in values and not avoidable
random error
random error or __
indeterminate error
Example of Random Error
- observational error
- environmental error
student repeatedly weights a beaker with solution and gets different measurement every time
observational error (random)
when getting a pressure reading, students were entering and exiting the lab, causing the pressure to be lower
environmental error (random)
causes the mean of a data set to differ from the accepted value
systematic error
systematic error or __
determinate error
in general, a systematic error in a series of replicate measurements causes what?
all results to be too high or too low
Examples of Systematic Error
- Instrumental error
- Environmental error
- Observational error
scale is improperly calibrated so it reads 2mg even with nothing on it
Instrumental error (systematic)
The Geiger counter shows the radiation, however, when a cell phone is near the Geiger counter, the radiation is read as greater than what is actually is because the cell pone is radiating RF waves which disrupts the reading
Environmental error (systematic)
observer looks at the beaker from above eye level and write down the volume as 40 mL, when in reality when looked at eye level you can see the liquid has a volume of about 42 mL
Observational error (systematic)
- often the product of human errors
- usually occur only occasionally
- may cause a result to be either too high or low
Gross error
Gross errors lead to __
outliers
results that appear to differ markedly from all other adta in a set of replicate measurements
outliers
- systematic error leads to __ in measurement results
- affects all the data in a set in the same way and that it carries a sign
bias
Systematic errors may be either __ or __
- Constant
- Proportional
magnitude stays essentially the same as the size of the quantity measured is varied
constant error
With constant errors, the __ error is constant with sample size, but the __ error varies when sample is changed
- absolute error (constant)
- relative error (varies)
increase or decrease according to the size of the sample taken for analysis
Proportional errors
With proportional errors, the __ error varies with sample size, but the __ stays constant when the sample size is changed
- absolute error (varies)
- relative error (constant)
always desirable because the response of most instruments changes with time as a result of component aging, corrosion, or mistreatment
periodic calibration of equipment
Examples of methods used to recognize and adjust for a systematic error in an analytical method
- Analysis of Standard Samples (or Standard Reference Materials, SRMs)
- Blank Determinations
- Variation of Sample Size
materials that contain one or more analytes at known concentration levels
Standard Reference Materials (SRMs)
contains reagents and solvents used in a determination but no analyte
blank
sample constituents to simulate the analyte environment
sample matrix
as the size of measurement __, the effect of a constant error __
- increases (size)
- decreases (constant error)
