Kesalahan dalam pengukuranSumber kesalahanRambatan kesalahan

Experimental Errors

Errors → noise in measured values

Three shooters with three arrows each to shoot.

Can you hit the bull's-eye?Can you hit the bull's-eye?

Both accurate and precise

Precise but not accurate

Neither accurate nor precise

How do they compare?

Measure the diameter of the ball

Using a metric stick, Using a metric stick, determine the diameter determine the diameter of the ball provided.of the ball provided.

Compare your results Compare your results with another group.with another group.

Any problems with your Any problems with your measurement?measurement?

Can all errors be controlled? Can all errors be controlled?

What are some possible things What are some possible things that can be done to minimize that can be done to minimize errors?errors?

Types of (experimental) Errors Systematic ErrorSystematic Error

Result of an experimental “mistake” Result of an experimental “mistake”

Sometimes called Sometimes called biasbias due to error in due to error in one direction- high or lowone direction- high or low

Penyebabnya diketahui (known cause)Penyebabnya diketahui (known cause)OperatorOperatorCalibration of glassware, sensor, or Calibration of glassware, sensor, or instrument, etc.instrument, etc.

Systematic ErrorSystematic Error This error can be corrected/ controlled This error can be corrected/ controlled

when causes of error are determined, when causes of error are determined, i.e :i.e :

(a) calibrating all experimental tools and/(a) calibrating all experimental tools and/

or instruments or instruments

(b) controlling skill of experimenter, (b) controlling skill of experimenter,

operator etc.operator etc.

(c) Cleaning all glassware, bottles, etc (c) Cleaning all glassware, bottles, etc

before doing experimentsbefore doing experiments

(d) etc… ????? (d) etc… ?????

Types of (experimental) Errors

Types of (experimental) Errors Systematic ErrorSystematic Error

Typically produce Typically produce constant constant or or proportionalproportional nature (slowly varying bias) nature (slowly varying bias)

Constant error influences the intercept.

Proportional error influences the slope.

y = ax + b

Types of (experimental) Errors Random errorRandom error

Unpredictable, non-deterministicUnpredictable, non-deterministic Unbiased → equal probability of increasing Unbiased → equal probability of increasing

or decreasing measured valueor decreasing measured value Result ofResult of

Limitations of measuring toolLimitations of measuring tool Random processes within systemRandom processes within system Environmental effect (?), etcEnvironmental effect (?), etc

Typically cannot be controlledTypically cannot be controlled Use statistical tools to characterize and Use statistical tools to characterize and

quantifyquantify

Multiple trialsMultiple trials help to minimize help to minimize

sampling

preparation

analysis

Representativesample

homogeneousvs.

heterogeneousLoss

Contamination(unwanted addition)

Measurement of Analyte

Calibration of Instrument orStandardsolutions

Example:

Example: Quantization → Random error

1 13

141

Quantization error

Timer resolution Timer resolution

→ → quantization errorquantization error Repeated measurements Repeated measurements

X X ± ± ΔΔ

Completely unpredictableCompletely unpredictable

A Model of Errors

Error Measured value

Probability

-E x – E ½

+E x + E ½

A Model of Errors

Error 1 Error 2 Measured value

Probability

-E -E x – 2E ¼

-E+E x ¼

+E -E x ¼

+E +E x + 2E ¼

A Model of Errors

Probability

0

0.1

0.2

0.3

0.4

0.5

0.6

x-E x x+E

Measured value

Systematic errors Systematic errors → → accuracyaccuracy How close mean of measured values is to How close mean of measured values is to

true valuetrue value Random errors Random errors → → precisionprecision

Repeatability/reproducibility of Repeatability/reproducibility of measurementsmeasurements

Characteristics of tools Characteristics of tools → → resolutionresolution Smallest increment between measured Smallest increment between measured

valuesvalues

Graphical methods

Scatter plotsScatter plots

0

1

2

3

4

5

6

0 1 2 3 4 5analyst or different methods or measuring devices

true value

Most accurate and precise

Worst precision

Systematic error?

Two students analyzing two different CaCO3 antacid tablets

Student 1 Student 2

Label value

500 mg 750 mg

Mean 463 mg 761 mg

Std. dev. 20 mg 28 mg

Which student has the more accurate results?Which student has the greater precision?

True value

quantity Student 1 Student 2

% Relative standard deviation asses the precision

%Error asses the accuracy

How are we going to address these questions?

Always remember to… Make all measurements Make all measurements carefullycarefully and and

check your results or readings a check your results or readings a second time.second time.

Read all devices to as many places Read all devices to as many places as possible (significant figures): as possible (significant figures): calibration marks + one more placecalibration marks + one more place

A buret, which is calibrated to 0.1 mL, can be A buret, which is calibrated to 0.1 mL, can be read to 0.01 mL.read to 0.01 mL.

A thermometer marked every degree can be A thermometer marked every degree can be read to 0.1 degreeread to 0.1 degree

Kandungan rhodamin dalam sampel

Metode ESIMetode

SpektrofotometriUlangan Ulangan

1 2 3 1 2 3Saos A 0.11 0.25 0.15 0.15 0.10 0.17Saos B 0.22 0.34 0.32 0.25 0.22 0.38

1. Berapakah konsentrasi rhodamin pada saos A dan B yang terukur dengan metode ESI dan spektrofotometri?

2. Berapakah ketelitian dan ketepatan pengukuran rhodamin dengan kedua metode jika konsentrasi rhodamin sebenarnya dalam saos A 0.18 ppm dan saos B 0.24 ppm?

3. Apa saja sumber systematic dan random errors dalam pengukuran tersebut?