Chapter 5: Errors in Chemical Analysis

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Chapter 5 Errors in Chemical Analysis

• CHE 321 Quantitative Chemical Analysis
• Dr. Jerome Williams, Ph.D.
• Saint Leo University

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Overview

• Mean Median
• Accuracy Precision
• Types of Errors in Data
• Random Errors
• Systematic Errors
• A Mean Calculation Using Excel

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Mean Median

• Mean is arithmetic average of data set evaluated
  as follows
• Mean S Xi / N
• Median is the middle value of a data set when the
  data are arranged according to increasing or
  decreasing value
• Odd numbered Data Set Median easily picked
• Even numbered Data Set Take mean of middle pair
• Review Example 5.1

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Fig 5-1, p.91
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Accuracy Precision

• Accuracy is the closeness of a measured value Xi
  to the true or accepted value Xt
• Often expressed as either absolute error or
  relative error (percent, parts per thousand, or
  parts per million)
• Absolute Error (E) Xi - Xt
• Relative Error (Er) ((Xi - Xt ) / Xt ) 100

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Accuracy Precision

• Precision describes the reproducibility of
  measurements (closeness of results to others)
  obtained in exactly the same way.
• Three terms widely used to describe precision
  include standard deviation, variance, and
  coefficient of variation. All are functions of
  deviation from the mean.
• Deviation from Mean (di) Xi Mean

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Fig 5-2, p.93
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Fig 5-3, p.94
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p86
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p86
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Types of Errors in Data

• Random Errors (Indeterminate Errors) affect
  measurement of precision.
• Systematic Errors (Determinate Errors) affect
  accuracy of results.
• Gross Errors occur as a result of human error and
  often lead to outliers (results that differ
  markedly from all other data in a set of
  replicate measurements.

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Types of Errors in Data

• Systematic Errors have a definite value and an
  assignable cause, and are of the same magnitude
  for replicate measurements made in the same way.
• Systematic errors lead to bias in measurement
  results. Bias can be negative or positive in sign.

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Types of Errors in Data

• Three Types of Systematic Errors
• Instrument errors
• Method errors
• Personal errors

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Types of Errors in Data

• Systematic Errors may be either constant or
  proportional.
• Constant errors are independent of the size of
  the sample being analyzed.
• Proportional errors decrease or increase in
  proportion to the sample size.

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Types of Errors in Data

• Detection of Systematic Errors
• Instrument errors resolved through calibration of
  equipment.
• Personal errors minimized by exercising care and
  self-discipline.
• Method errors are the hardest to overcome some
  ideas to overcome this one include using standard
  reference materials, independent analysis,
  running blank determinations, etc.

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p91
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Excel Exercise 3 A Mean Calculation

• Construct the following in Microsoft Excel

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p.100
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p.101
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p.102
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p.102
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Suggested Exercises

• HW Set 4 5.1, 5.5, 5.8, 5.12