Laboratory Statistics. Handbook of Formulas and Terms by Anders Kallner
By Anders Kallner
Laboratory records: guide of formulation and Terms provides universal innovations for evaluating and comparing numerical laboratory info. specifically, the textual content bargains with the kind of facts and difficulties that laboratory scientists and scholars in analytical chemistry, scientific chemistry, epidemiology, and scientific examine face every day. This e-book takes the secret out of information and gives basic, hands-on directions within the layout of daily formulation. so far as attainable, spreadsheet shortcuts and capabilities are incorporated, in addition to many easy labored examples. This e-book is a must-have advisor to utilized records within the lab that would lead to more desirable experimental layout and analysis.
- Comprehensive assurance of straightforward statistical suggestions familiarizes the reader with formatted statistical expression
- Simple, labored examples make formulation effortless to take advantage of in actual life
- Spreadsheet capabilities reveal how to define instant suggestions to universal problems
- In-depth indexing and widespread use of synonyms facilitate the short situation of acceptable procedures
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Extra info for Laboratory Statistics. Handbook of Formulas and Terms
Quant A (Expected) Quant B (Found) “Positive” “Negative” Total “Positive” “Negative” Total Diseased 37 13 50 35 15 50 Nondiseased 63 387 450 105 345 450 Sum 100 400 500 140 360 500 Since the comparison was made using the same patient group, the number of diseased and nondiseased is the same in both trials. 05,1), and therefore, the null hypothesis is accepted and it is not likely that there is a difference between the methods. 47. The difference can be explained by rounding errors: p ¼ 0:06 CHIDISTð3:47;1Þ 45 ROBUST ESTIMATORS The w2 test for small numbers of observations can be improved by Yates’ continuity correction, which gives smaller values of w2: w2 ¼ Xn ðjfi À Fi j À 0:5Þ2 ; i¼1 Fi df ¼ 1 ð93Þ Example A w2 ¼ ð35 À 37 À 0:5Þ2 ð15 À 13 À 0:5Þ2 ð105 À 90 À 0:5Þ2 þ þ 37 13 90 þ ðj345 À 360j À 0:5Þ2 ¼ 3:25; 360 df ¼ 1 The corrected value is smaller than the uncorrected, but the difference is usually small enough not to change the conclusion.
If the mean (16) of the observations and their standard deviation (20) are ð xÞ and (s), respectively and the Xn systematic deviation x À x ð Þ ¼ d then, since ð x À x0 Þ 2 ¼ 0 i i¼1 Xn ðx À xÞ2 þ nð x À x0 Þ2 (29) can be rewritten as i¼1 i D¼ sX ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ i¼n ðx À x0 Þ2 i¼1 i n rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ ðn À 1Þs2 2 þd n ¼ sX ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ i¼n ðx À xÞ2 þ nðx À x0 Þ2 i¼1 i n Standard deviation, relative (coefficient of variation): s CV ¼ x ¼ ð30Þ ð31Þ Standard deviation, relative, percent: %CV ¼ 100 Â s x ð32Þ The coefficient of variation, percent, is often abbreviated %CV.
Normal or Student’s distribution). Note The relative uncertainty is always calculated from the combined standard uncertainty, not the expanded uncertainty (cf. the Note to Equation 32). ROBUST ESTIMATORS 39 Reference Change Value and Minimal Difference As an example of error propagation, consider estimating the least significant difference between two results, in clinical chemistry known as “minimum difference,” MD. Example If the results of two measurements are A and B with the uncertainties u(A) and u(B) a significant difference (D) must be larger than the uncertainty of the difference u(D).