Error analysis

Error Analysis and Minimisation

Abhiram MullapudiCB.EN.U4CIE11038

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INTRODUCTION

DATA

Design

Analysis

Study

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• Error

True value(accepted value)- Measured value

• Accuracy

• Precision

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Expressing Accuracy

• Absolute Error

Measured value – True value

• Relative Error

𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐸𝑟𝑟𝑜𝑟

𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒× 100

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Classification of Error

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• Determinate or Systematic Error

• Indeterminate or Accidental Errors

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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Significant figures• The significant figures of a number are those digits

that carry meaning contributing to its precision

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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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Characteristics of Replicate Measurements

• Range

𝑅𝑎𝑛𝑔𝑒 ∝1

𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛• Mean

• Median

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Deviation

• Mean Deviation

• Standard Deviation

It measures the amount of variation or dispersion from the average

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Rejection of Data

• Average Deviation

1. Omit the doubtful value

2. Determine Mean and Avg.Deviation

3. Check for

𝑥 ≥ 4 × 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛

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Standard Deviation

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Dixon’s Q test

• Arrange the data in order of increasing values

• Calculate Q

𝑄 =𝐺𝑎𝑝

𝑅𝑎𝑛𝑔𝑒

• 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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Confidence Limits

𝐶𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒 𝐿𝑖𝑚𝑖𝑡 = 𝑥 ±(𝑁 − 1)𝑠

𝑁

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Comparison of Results

• Students t test

𝑡 =𝑥 − 𝜇 √𝑁

𝑆

Compare the t value with the value in the table.

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• F test

𝐹 =𝑆𝑎2

𝑆𝑏2

Compare the values to the table.

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Thank you.

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