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Unformatted text preview: Practical Applications of Statistical Methods in the Clinical Laboratory Roger L. Bertholf, Ph.D., DABCC Associate Professor of Pathology Director of Clinical Chemistry & Toxicology UF Health Science Center/Jacksonville “[Statistics are] the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of Man.” [Sir] Francis Galton (18221911) “There are three kinds of lies: Lies, damned lies, and statistics” Benjamin Disraeli (18041881) What are statistics, and what are they used for? • Descriptive statistics are used to characterize data • Statistical analysis is used to distinguish between random and meaningful variations • In the laboratory, we use statistics to monitor and verify method performance, and interpret the results of clinical laboratory tests “ “ Do not worry about your Do not worry about your difficulties in mathematics, I assure difficulties in mathematics, I assure you that mine are greater” you that mine are greater” Albert Einstein (18791955) “ “ I don't believe in I don't believe in mathematics” mathematics” Albert Einstein Summation function N N i i x x x x x 3 2 1 1 + + = ∑ = Product function x x x x x i i N N = ∏ = ⋅ ⋅ 1 1 2 3 The Mean (average) The mean is a measure of the centrality of a set of data. Mean (arithmetical) x N x i i N = = ∑ 1 1 Mean (geometric) x x x x x x g N N i i N N = ⋅ ⋅ = = ∏ 1 2 3 1 Use of the Geometric mean: The geometric mean is primarily used to average ratios or rates of change. Mean (harmonic) x N x x x x N x h N i i N = + + + + = = ∑ 1 1 1 1 1 1 2 3 1 Example of the use of Harmonic mean: Suppose you spend $6 on pills costing 30 cents per dozen, and $6 on pills costing 20 cents per dozen. What was the average price of the pills you bought? Example of the use of Harmonic mean: You spent $12 on 50 dozen pills, so the average cost is 12/50=0.24, or 24 cents. This also happens to be the harmonic mean of 20 and 30: 2 1 30 1 20 24 + = Root mean square (RMS) x x x x x N N x rms N i i N = + + + + = = ∑ 1 2 2 2 3 2 2 2 1 1 For the data set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10: Arithmetic mean 5.50 Geometric mean 4.53 Harmonic mean 3.41 Root mean square 6.20 The Weighted Mean x x w w w i i i N i i N = ⋅ = = ∑ ∑ 1 1 Other measures of centrality • Mode The Mode The mode is the value that occurs most often Other measures of centrality • Mode • Midrange The Midrange The midrange is the mean of the highest and lowest values Other measures of centrality • Mode • Midrange • Median The Median The median is the value for which half of the remaining values are above and half are below it. I.e. , in an ordered array of 15 values, the 8th value is the median. If the array has 16 values, the median is the mean of the 8th and 9th values. Example of the use of median vs....
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 Summer '11
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 Normal Distribution, Standard Deviation

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