Analytical Chemistry

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Objectives
 Togain an understanding in some
concepts of statistical analysis
Errors in  Apply statistical concepts in analytical
Chemical chemistry
Analyses
Wilbert Morales
Error in Chemical Analysis Basic Statistical Concepts
 Error can be referred as  Replicates
 Difference between a measured value and  Samples of about the same size that are
the “true” or “known” value. carried through an analysis in exactly same
way
 Uncertainty in a measurement or
 Population
experiment
 Infinite number of results that could be
collected over an infinite period of time
 Sample
 Subset of a population data
Population vs. Sample Basic Statistical Concepts
 Mean
Group
1  Average value of two or more
measurements
Pop 𝑋=
𝑁
𝑖=1
𝑁
𝑋𝑖
Group
2
1

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Example Basic Statistical Concepts
SAMPLE DATA 1  Median
Det. Of Fe(II) conc Mean:
19.4+19.5+19.6+19.8+20.1+20.3 %𝑝𝑝𝑚  Middle value in a data that has been
19.4 ppm 𝑋= arranged in a numerical order
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19.5 ppm  Can be used if data contain some outliers
19.6 ppm 𝑋 = 19.8 𝑝𝑝𝑚 𝐹𝑒  If set contains even no. of measurements,
19.8 ppm median is the average of central pair
20.1 ppm
20.3 ppm
Basic Statistical Concepts
 Precision
 Describes the reproducibility of
measurements
 Measures the closeness of results obtained
 Accuracy
 Indicates the closeness of the measurement
to the true or accepted value
Types of Error in Experimental Three types of Systematic
Data Errors
 Systematic Errors  Instrumental Errors
 Generally arise from identifiable sources  Substandard volumetric glassware
causing measured value to differ from true  Faulty or worn chemical components
or accepted value  Incorrect electrical signals
 The key feature of this is that the error is
reproducible.
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Three types of Systematic Three types of Systematic
Errors Errors
 Method Errors  Personal Errors
 Inadequate method validation  Carelessness
 Nonideal chemical or physical behavior of  Insufficient training
analytical system  Illness or disability
Accuracy Accuracy
 Absolute Error  Relative Error
𝐸 = 𝑥𝑖 − 𝑥 𝑡 𝑥𝑖 − 𝑥 𝑡
𝐸𝑟 = 𝑥 100%
𝑥𝑡
 Tells whether the value in question is high or
low
Types of Error in Experimental
Data Standard Deviation
 Random Errors  shows
how much dispersion exists from the
 Cause the data to be scattered around the average.
mean value
 It affects the precision of measurements 𝑛
𝑖=1(𝑥 𝑖− 𝑋 )2
𝑠=
𝑛−1
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Range or spread Example
 It
is the difference between the largest Determination of glucose level of diabetic patient
value and smallest value in the set. Data 1 Data 2 Data 3 Data 4
Glucose Conc Glucose Conc Glucose Conc Glucose
(mg/L) (mg/L) (mg/L) Conc (mg/L)
1108 992 788 799
1122 975 805 745
1075 1022 779 750
1099 1001 822 774
1115 991 800 777
1083 800
1100 758
SEATWORK
 Consider
the following sets of replicate QUESTION???
measurements:
 Next meeting
Set A Set B Set C
3.5 0.812 70.65  Review of Significant Figures
3.1 0.792 70.63
3.1 0.794 70.64
3.3 0.900 70.21
2.5
 Foreach set, calculate
(a) Mean (c) range
(b) Median (d) standard deviation
Assignment
 Perform the following operations and
observe proper significant figure.
A) 30.5 ml + 16.75 ml - 0.576 ml + 2.0 ml
B) 1.632x105 g + 4.107x103 g + 0.948x106 g
C) (3.26x10-5 L )*(1.78 L)
D) log 339
E) Antilog (-3.42)
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