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8/13/2019 Ssck 1203 Data Analysis 090214 Students 01
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DATA ANALYSIS
Assoc. Prof. Dr. Azli SulaimanDepartment of Chemistry
Universiti Teknologi Malaysia
81310 UTM Johor Bahru
Johor Darul [email protected]
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LECTURE OUTLINES
Errors in Chemical Analysis Descriptive Statistics Precision and Accuracy
Types of Error Significant Figures Statistics in Data Evaluation
Calibration Curve Method of Validation
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Why do we need statistics in
analytical chemistry?
Scientists need a standard formatto communicatesignificance of experimental numerical data.
Objective mathematical data analysis methodsneeded to get the most information from finite datasets.
To provide a basis for optimal experimentaldesign.
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ERRORS IN CHEMICAL ANALYSIS
It is impossibleto perform a chemical analysis that iserror freeor without uncertainty. Our goals are to minimize errorsand to calculate the
size of the errors.
Normal phrases in describing results of an analysis
pretty sure
very sure
most likely
improbable Replaced by using mathematical statistical tests.
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ERRORS IN CHEMICAL ANALYSIS
Is there such a thing as
ERROR FREE ANALYSIS ?
- Impossibleto eliminate errors.
- Can only be minimized.
- Can only be approximatedto anacceptable precision.
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TO OVERCOME ERRORS
Carry out replicate measurements. Analyse accurately known standards (SRM).
Perform statistical testson data.
How reliable are our data?
Data of unknown quality are useless.
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DESCRIPTIVE STATISTICS
Mean/Average Median
Range Standard Deviation, s or Relative Standard Deviation (RSD)
Varian, V
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MEAN/AVERAGE
Sum of measurements divided by the numberof measurements
Where xi= individual values of x
N = number of replicate measurements
x
x
N
i
N
=i = 1
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MEDIAN
Data in the middle if the number is odd,arranged in ascending order.
The average of two data in the middle if thenumber is even arranged in ascending order.
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RANGE
The different between the highest and lowestresult.
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STANDARD DEVIATION
Measure of the precision of a population ofdata.
Small Sample Size
Population
1
)(
2
=
N
xx
s i
i
N
xx
i
i =
2)(
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RELATIVE STANDARD DEVIATION
Standard deviation divided by the mean
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VARIAN
The square of standard deviation.For sample, V = s2
For population, V = 2
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EXAMPLE 1
10.08 10.11 10.09 10.10 10.12
For the given data above, calculate:
Mean/Average Median Range Standard Deviation
Relative Standard Deviation (RSD) Varian, V
http://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example1.xlshttp://sscc%202243%20space/SSC%202243%20201112%20I/CHAPTER_2/Example1.xls8/13/2019 Ssck 1203 Data Analysis 090214 Students 01
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PRECISION
Relates to reproducibilityor repeatabilityof aresult.
How similarare values obtained in exactly thesame way?
Useful for measuring deviation from themean.
d x xi i
=
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ACCURACY
Measurement of agreementbetweenexperimental mean and true value
(which may not be known!).
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ACCURACY vs PRECISION
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SMART Student A Student B Student C Student D
DATA
10.00
10.00
10.00
10.00
10.00
10.10
10.08
10.09
10.07
10.08
9.65
9.75
9.78
10.07
10.24
9.97
9.98
10.02
10.03
10.05
9.80
9.89
10.01
10.13
10.22
MEAN 10.00 10.10 9.90 10.01 10.01
STD DEV 0.00 0.01 0.25 0.03 0.17
ACCURACY and PRECISION
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TYPES OF ERROR
Gross Error Random Error
Systematic Error
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GROSS ERROR
Seriousbut very seldom occur in analysis. Usually obvious- give outlierreadings. Detectableby carrying out sufficient replicate
measurements.
Experiments must be repeated. Examples:
- Instrument faulty- Contaminate reagent
- Accidentally discarding crucial sample
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RANDOM ERROR Indeterminateerror. Data scatteredapproximately symmetrically
about a mean value.
Affects precision, can only be controlled.Dealt with statistically.
Cannot eliminate but minimise.
Examples:- Physical and chemical variables
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SOURCES OF SYSTEMATIC ERROR
Instrument Error Method Error
Personal Error
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INSTRUMENT ERROR
Need frequent calibration- for apparatussuch as volumetric flasks,
burettes etc.
- for electronicdevices such as balances,
spectrometers.
Examples:
Temperature changes Fluctuation in power supply Worn out
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METHOD ERROR
Due to inadequaciesin physical or chemicalbehaviour of reagents or reactions (e.g. slowor incomplete reactions).
Difficult to detectand the most serioussystematic error.
Example:
Small excess of reagent required causing anindicator to undergo colour change that signalthe completion of a reaction.
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PERSONAL ERROR
Sources:Physical handicap, prejudice, notcompetence.
Examples: Insensitivity to colour changes Tendency to estimate scale readings to
improve precision
Preconceived idea of true value.
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MINIMIZE SYSTEMATIC ERROR
Instrument errorsby careful recalibration and goodmaintenance of equipment.
Method errors- most difficult. True value may not
be known. Three approaches to minimise:- Analysis of certified standards (SRM)
- Use 2 or more independent methods
- Analysis of blanks
Personal errorsby care and self-discipline.
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SIGNIFICANT FIGURES
Minimum number of digits written in scientificnotation without a loss in accuracy.
The digits in measured quantity, including alldigits known exactly and one digit (the last)whose quantity is uncertain.
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SIGNIFICANT FIGURES
Rules for the determining the number of
signif icant figures: Disregard all initial zeros. Disregard all final zeros unless they follow a decimal
point.
All remaining digits, including zeros between non-zero digits, are significant.
Rules for counting significant figures:
Initial zeros or that set the decimal point are notsignificant.
0.00004213 (4 SF) and 470,000 (2 SF)
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Zero is significant only when:
- It occurs in the middle of a number
401 - 3 significant figures
6.0015 - 5 significant figures- It is the last number to the right of thedecimal point.
3.00 - 3 significant figures
6.00 102 - 3 significant figures
0.0500 - 3 significant figures
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SIGNIFICANT FIGURES IN
ARITHMETIC
Addition-Subtraction
Use the same number of decimal places as
the number with the fewest decimal places.
12.2 + 0.365 + 1.04 = 13.605 = 13.6
(1 dp) (3 dp) (2 dp) (1 dp)
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Multiplication - Division
Use the same number of digits as the number
with the fewest number of digits.
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Rules of rounding off
Do not retain any digit beyond the first uncertain one. If the digit beyond the uncertain one is less than 5,
leave the figure as it is.
If it is equal or greater than 6, add one to the lastretained digit. If the next digit is equal to 5, round up to the nearest
even digit (2,4,6,8,0). This will prevent us fromintroducing a bias by always rounding up or down.
Example: rounding 12.450 to nearest tenth gives 12.4but rounding 12.550 to the nearest tenth gives 12.6.
ROUNDING OFF