This document discusses various statistical concepts and their applications in clinical laboratories. It defines descriptive statistics, statistical analysis, measures of central tendency (mean, median, mode), measures of variation (variance, standard deviation), probability distributions (binomial, Gaussian, Poisson), and statistical tests (t-test, chi-square, F-test). It provides examples of how these statistical methods are used to monitor laboratory test performance, interpret results, and compare different laboratory instruments and methods.

1. 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

2. “ [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 (1822-1911)

3. “ There are three kinds of lies: Lies, damned lies, and statistics” Benjamin Disraeli (1804-1881)

5. “ Do not worry about your difficulties in mathematics, I assure you that mine are greater” Albert Einstein (1879-1955)

6. “ I don't believe in mathematics” Albert Einstein

7. Summation function

8. Product function

10. Mean (arithmetical)

11. Mean (geometric)

13. Mean (harmonic)

16. Root mean square (RMS)

17. For the data set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10:

18. The Weighted Mean

28. The Variance

30. The Variance

32. The Standard Deviation

34. The Standard Deviation In what units is the standard deviation? Is that a problem?

45. “ Sir, I have found you an argument. I am not obliged to find you an understanding.” Samuel Johnson (1709-1784)

46. Population vs. Sample standard deviation

52. Solution

54. “ God does arithmetic” Karl Friedrich Gauss (1777-1855)

56. 63 81 36 12 28 7 79 52 96 17 22 4 61 85 etc.

58. 63 81 36 12 28 7 79 52 96 17 22 4 61 85 22 73 54 33 99 5 61 28 58 24 16 77 43 8 + 85 152 90 45 127 12 140 70 154 41 38 81 104 93 =

60. . . . etc.

61. Probability x

64. “ Like the ski resort full of girls hunting for husbands and husbands hunting for girls, the situation is not as symmetrical as it might seem.” Alan Lindsay Mackay (1926- )

67. Gaussian probability distribution Probability µ µ+  µ+2  µ+3  µ-  µ-2  µ-3  .67 .95

69. Some useful Gaussian probabilities Range Probability Odds +/- 1.00  68.3% 1 in 3 +/- 1.64  90.0% 1 in 10 +/- 1.96  95.0% 1 in 20 +/- 2.58  99.0% 1 in 100

70. Example This That

71. [On the Gaussian curve] “Experimentalists think that it is a mathematical theorem while the mathematicians believe it to be an experimental fact.” Gabriel Lippman (1845-1921 )

73. "Life is good for only two things, discovering mathematics and teaching mathematics" Siméon Poisson (1781-1840)

76. A very useful property of the Poisson distribution

78. Answer

84. Gaussian probability distribution Probability 0 1 2 3 -1 -2 -3 .95 z .67

93. Statistical Tables

113. Data

125. Log transform Probability x Probability log x

131. “ Everything should be made as simple as possible, but not simpler.” Albert Einstein

136. “‘ Obvious’ is the most dangerous word in mathematics.” Eric Temple Bell (1883-1960)

139. The Monte Carlo method x y

140. The Monte Carlo method Reference population mean, SD mean, SD mean, SD mean, SD N N N N

144. Correlation 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50

146. Correlation 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 y = 1.031 x - 0.024

150. The Correlation Coefficient

152. Correlation 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 y = 1.031 x - 0.024  = 0.9986

153. Correlation 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 y = 1.031 x - 0.024  = 0.9894

156. Correlation 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 y = 1.031 x - 0.024  = 0.9986 s y/x =1.83

157. Correlation 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 y = 1.031 x - 0.024  = 0.9894 s y/x = 5.32

165. Signal time Signal/Noise threshold

171. Signal Concentration

174. Signal Concentration

181. Signal Concentration

186. “ If your experiment needs statistics, you ought to have done a better experiment.” Ernest Rutherford (1871-1937)

195. Marker concentration - + Disease

197. Receiver Operating Characteristic True positive rate (sensitivity) False positive rate 1-specificity

208. Efficiency of our Addison screen

209. “ To call in the statistician after the experiment is done may be no more than asking him to perform a postmortem examination: he may be able to say what the experiment died of.” Ronald Aylmer Fisher (1890 - 1962)

211. “ He uses statistics as a drunken man uses lamp posts -- for support rather than illumination.” Andrew Lang (1844-1912)

213. Some examples mean +1sd +2sd +3sd -1sd -2sd -3sd

214. Some examples mean +1sd +2sd +3sd -1sd -2sd -3sd

215. Some examples mean +1sd +2sd +3sd -1sd -2sd -3sd

216. Some examples mean +1sd +2sd +3sd -1sd -2sd -3sd

217. “ In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite.” Paul Adrien Maurice Dirac (1902- 1984)