Chapter 5: Errors in Chemical Analysis

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

Mean & Median Mean is arithmetic average of data set; evaluated as follows: Mean = Σ 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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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%

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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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.

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.

Types of Errors in Data Three Types of Systematic Errors Instrument errors Method errors Personal errors

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.

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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Excel Exercise 3: A Mean Calculation Construct the following in Microsoft Excel

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Suggested Exercises HW Set 4: 5.1, 5.5, 5.8, 5.12