Chapter 3: Experimental Errors doc

Chapter 3: Experimental Errors Chapter 4: Statistics Steps in a Typical Quantitative Analysis ¾Data of unknown quality are useless! ¾All laboratory measurements contain experimental error. ¾It is necessary to determine the magnitude of the accuracy and reliability in your measurements. ¾Then you can make a judgment about their usefulness. Replicates - two or more determinations on the same sample Example 3-1: One student measures Fe (III) concentrations six times. The results are listed below: 19.4, 19.5, 19. 6, 19.8, 20.1, 20.3 ppm (parts per million) 6 replicates = 6 measurements The "middle" or "central" value for a group of results: ¾ Mean: average or arithmetic mean ¾ Median: the middle value of replicate data ¾ If an odd number of replicates, the middle value of replicate data ¾ If an even number of replicates, the middle two values are averaged to obtain the median N N 1i i ∑ = = x x Terms & Definitions Example 3-2: measurements of Fe (III) concentrations: 19.4, 19.5, 19. 6, 19.8, 20.1, 20.3 ppm (parts per million) What are the mean and median of these measurements Mean = = 19.78 ppm = 19.8 ppm 6 replicates An even number of replicates !!! Median = = 19.7 ppm Calculation: Mean and Median 6 20.320.119.819.619.519.4 +++++ 2 19.819.6 + Calculation: Mean and Median Example 3-3: measurements of Fe (III) concentrations: 19.4, 19.5, 19. 6, 19.8, 20.1 ppm (parts per million) What are the mean and median of these measurements Mean = = 19.68 ppm = 19.7 ppm 5 replicates An odd number of replicates !!! Median = 19.6 ppm 5 20.119.819.619.519.4 ++++ Any Questions??? ¾ Precision - describes the reproducibility of measurements. How close are results which have been obtained in exactly the same way? The reproducibility is derived from the deviation from the mean: Deviation from the mean = d i = |x i -| ¾ Standard deviation ¾ Variance ¾ Coefficient of variation Terms & Definitions X ¾ Accuracy - the closeness of the measurement to the true or accepted value. This "closeness" called as the error: absolute or relative error of a result to its true value. Terms & Definitions ¾absolute error ¾relative error ¾ Outlier - Occasional error that obviously differs significantly from the rest of the results. Terms & Definitions [...]... Questions??? Types of Errors Systematic or determinate errors affect accuracy! Random or indeterminate errors affect precision! Gross errors or blunders Lead to outlier’s and require statistical techniques to be rejected Systematic or Determinate Errors 1 Instrument errors - failure to calibrate, degradation of parts in the instrument, power fluctuations, etc 2 Method errors - errors due to no ideal... problems 3 Personal errors - occur where measurements require judgment, result from prejudice, color acuity problems Systematic or determinate errors Potential Instrument Errors Variation in temperature Contamination of the equipment Power fluctuations Component failure All of these can be corrected by calibration or proper instrumentation maintenance Systematic or determinate errors Method Errors Slow or...Precision & Accuracy Mean & True Value Mean : X Xt = true value Absolute and Relative Errors Absolute Error (E) - the difference between the experimental value and the true value Has a sign and experimental units: E = xi − xt Experimental value – true (acceptable) value Relative Error (Er) - the absolute error corrected for the size of the measurement or... development Systematic or determinate errors Personal Errors Misreading of data Improper calibration Poor technique/sample preparation Personal bias Improper calculation of results These are blunders that can be minimized or eliminated with proper training and experience The Effect of Systematic Error - normally "biased" and often very "reproducible" 1 Constant errors - Es is of the same magnitude,... Error Gross errors cause an experimental value to be discarded Lead to outlier’s and require statistical techniques to be rejected Examples of gross error are an obviously "overrun end point" (titration), instrument breakdown, loss of a crucial sample, and discovery that a "pure" reagent was actually contaminated We do NOT use data obtained when gross error has occurred during collection Random Errors. .. Constant eg Solubility loss in gravimetric analysis eg Reading a buret 2 Proportional errors - Es increases or decreases with increasing or decreasing sample size, respectively In other words, the relative error remains constant Proportional Typically a contaminant or interference in the sample Detection of Systematic Method Errors 1 Analysis of standard samples 2 Independent Analysis: Analysis using a "Reference... parts per hundred (pph) = Er x100 parts per thousand (ppt) = Er x1000 Calculation: Absolute and Relative Errors Example 3-4: measurements of Fe concentrations: 19.4, 19.5, 19 6, 19.8, 20.1, 20.3 ppm Assumed we already knew the true value of Fe (III) concentration at 20.0ppm What are absolute and relative errors of each measurement? E = 19.4 - 20.0 = -0.6 ppm Er =(-0.6/20)x100% = - 3% E = 19.5 - 20.0 = -0.5... be defined The accumulated effect causes replicate measurements to fluctuate randomly around the mean Random errors give rise to a normal or gaussian curve Results can be evaluated using statistics Usually statistical analysis assumes a normal distribution Term & Definition The Nature of Random Errors – also called "indeterminate" and follow a predictable pattern Error is the deviation from the "true . Chapter 3: Experimental Errors Chapter 4: Statistics Steps in a Typical Quantitative Analysis ¾Data of unknown quality are useless! ¾All laboratory measurements contain experimental. true value Absolute and Relative Errors ¾ Absolute Error (E) - the difference between the experimental value and the true value. Has a sign and experimental units: Experimental value – true (acceptable). determinate errors affect accuracy! ¾ Random or indeterminate errors affect precision! ¾ Gross errors or blunders Lead to outlier’s and require statistical techniques to be rejected. Types of Errors 1.