The document discusses error analysis and minimization, defining accuracy and precision, and classifying errors into determinate and indeterminate types. It outlines methods to minimize errors, such as calibration and parallel determinations, as well as statistical tools for data rejection and confidence limits. Additionally, it covers significant figures, characteristics of replicate measurements, and tests like Dixon's q test and the t-test for comparing results.

1. Error Analysis and
Minimisation
Abhiram Mullapudi
CB.EN.U4CIE11038
08-09-2014 Seminar CHY 259 1

2. INTRODUCTION
DATA
Design
Analysis
Study
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3. • Error
True value(accepted value)- Measured value
• Accuracy
• Precision
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4. Expressing Accuracy
• Absolute Error
Measured value – True value
• Relative Error
퐴푏푠표푙푢푡푒 퐸푟푟표푟
푇푟푢푒 푉푎푙푢푒
× 100
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5. Classification of Error
• Determinate or Systematic Error
• Indeterminate or Accidental Errors
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6. Minimization of Error
• Calibration of apparatus and application of
corrections
• Running a control determination
• Use of independent methods of analysis
• Running parallel determinations
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7. Significant figures
• The significant figures of a number are those digits
that carry meaning contributing to its precision
1. All non-zero numbers (1,2,3,4,5,6,7,8,9) are always
significant.
2. All zeroes between non-zero numbers are always
significant.
3. All zeroes which are simultaneously to the right of the
decimal point and at the end of the number are always
significant.
4. All zeroes which are to the left of a written decimal point
and are in a number >= 10 are always significant.
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8. 08-09-2014 Seminar CHY 259 8

9. Characteristics of Replicate
Measurements
• Range
푅푎푛푔푒 ∝
1
푃푟푒푐푖푠푖표푛
• Mean
• Median
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10. Deviation
• Mean Deviation
• Standard Deviation
It measures the amount of variation or dispersion from the
average
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11. Rejection of Data
• Average Deviation
1. Omit the doubtful value
2. Determine Mean and Avg.Deviation
3. Check for
푥 ≥ 4 × 퐴푣푒푟푎푔푒 푑푒푣푖푎푡푖표푛
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12. Standard Deviation
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13. Dixon’s Q test
• Arrange the data in order of increasing values
• Calculate Q
푄 =
퐺푎푝
푅푎푛푔푒
• If Q > Qtable, where Qtable is a reference value
corresponding to the sample size and confidence
level, then reject the questionable point
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14. Confidence Limits
퐶표푛푓푖푑푒푛푐푒 퐿푖푚푖푡 = 푥 ±
(푁 − 1)푠
푁
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15. Comparison of Results
• Students t test
푡 =
푥 − 휇 √푁
푆
Compare the t value with the value in the table.
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16. • F test
퐹 =
푆푎2
푆푏2
Compare the values to the table.
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17. Thank you.
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