Ssck 1203 Data Analysis 090214 Students 01

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.xls


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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

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Ssck 1203 Data Analysis 090214 Students 01