Lecture 2 - Exercise Basic Considerations for Selecting...

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1 Exercise: Basic Considerations for Selecting Analytical Methods – How reproducible? – … Analytical figures of merit Analytical figures of merit (2) Accuracy/Bias How close to true value? (3) Sensitivity How small a difference can be measured? (4) Detection limit Whether an analyte is there? (5) Concentration/dynamic range What range of amounts? (6) Selectivity How much interference? (1) Precision How reproducible? (1) Precision/scatter Precision/scatter Indeterminate/Random errors Precision Accuracy First, we need a certain number of repeated measurements: N Average/mean of signals: = N x N x x i as : note μ Deviation from the mean: x x d i i - = agreement of final result with ‘true’ value ability to reproduce a given result for replicate analyses
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2 Standard deviation: 1 ) ( 1 2 2 - - = - = N x x N d s i i N d i = 2 σ N as s : Note σ % Relative standard deviation: % 100 % × = x s RSD A measure of precision!!! Use when N > 30… s is an “estimate” of σ valid for small data sets Also know as Coefficient of Variance (CV) another measure of precision!!! 2 Variance s = Together, mean and standard deviation identify a range s x - s x x % RSD x RSD x s x ± ± ± Confidence interval/range Probability, likelihood, level of confidence, chance, etc. that the true value μ will fall in this range. Gaussian distribution: 68% chance that μ is comprised within ± s 95.5% chance that μ is within ± 2 s of the mean 99.7% chance that μ is within ± 3 s of the mean value true - = i x Error % 100 value true value true % × - = x Error The only way to assess the accuracy is by analyzing a known, certified standard (NIST, commercial, in-house). Case 1) Perform a single measurement Case 2) Perform repeated measurements value true - = x Error (2) Accuracy, bias, error (2) Accuracy, bias, error - Determinate errors (Operator, Method, Instrumental) Determinate errors (Operator, Method, Instrumental) (Systematic errors) (Systematic errors)
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3 Case 3) Perform many measurements!!! value true - = μ Error N x as μ bias value) (true ) population of mean ( - = bias μ orightshadow statistical true value orightshadow take care of the indetermined error If there is no determined error orightshadow μ ≡ true value However, we know the real true value. Subtract the known true value from μ orightshadow only contribution of determinate error orightshadow bias !!! ( 3) Sensitivity 3) Sensitivity Ability of a method to discriminate between small differences in analyte concentration Limiting factors: i) slope of calibration curve orightshadow the steeper the better ii) precision orightshadow the more precise (lower scatter) the better a) Calibration sensitivity y = mx +q S = mC +S blank Does not take in account the variability between individual measurements b) Analytical sensitivity γ = m/s S m = slope s S = std. dev. of signals Advantages - insensitive to amplification orightshadow if m × 5, then s S also increases ~5 - independent from the units of s S Disadvantages - concentration dependent: in low concentration ranges, s s
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