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Lecture 3 - Together mean and standard deviation identify a...

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1 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) (Systematic errors) (Systematic errors) 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 !!!
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2 ( 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 increases with decrease in concentration What’s the relationship between sensitivity and precision? ( 4) Detection limit 4) Detection limit The minimum concentration or mass of analyte, which can be detected at a known confidence level. Detection limit Signal magnitude Statistical fluctuations of blank signal Signal to noise ratio (S/N) BL BL M s k S S + = Minimum analytically distinguishable signal Mean blank Std. dev. blank BL s k S M S BL S BL s BL S N S k = 3 Minimum distinguishable S/N = 3 at 95% confidence level Where does 95% come from? Blank measurements may not strictly follow normal distribution of random events.
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3 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 ± 3s 3s of the mean Experimentally, the blank is run 20~30 times orightshadow BL BL s S ± Then, the analyte is determined and a calibration curve is constructed.
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