1、Description of Measurement Data Chapter 2Content1.Frequency distribution 2.Descriptions of central tendency 3.Measures of dispersion 4.Normal distribution 5.Range of reference value Section 1 Frequency Distribution 1、Frequency table：Example 2-1 To acquire the values of total cholesterol in serum of
2、101 healthy female adults as below,and to work out the frequency table.2.35 4.21 3.32 5.35 4.17 4.13 2.78 4.26 3.58 4.34 4.84 4.41 4.78 3.95 3.92 3.58 3.66 4.28 3.26 3.50 2.70 4.61 4.75 2.91 3.91 4.59 4.19 2.68 4.52 4.91 3.18 3.68 4.83 3.87 3.95 3.91 4.15 4.55 4.80 3.41 4.12 3.95 5.08 4.53 3.92 3.58
3、 5.35 3.84 3.60 3.51 4.06 3.07 3.55 4.23 3.57 4.83 3.52 3.84 4.50 3.96 4.50 3.27 4.52 3.19 4.59 3.75 3.98 4.13 4.26 3.63 3.87 5.71 3.30 4.73 4.17 5.13 3.78 4.57 3.80 3.93 3.78 3.99 4.48 4.28 4.06 5.26 5.25 3.98 5.03 3.51 3.86 3.02 3.70 4.33 3.29 3.25 4.15 4.36 4.95 3.00 3.26 Approach：(1).Range:The d
4、ifference between the maximum and the minimum,R.。5.712.353.36(mmol/L)R(2)Class Interval(i):Usually divided into 10-15 groups(3)Group：Lower limit（L）：the beginning of every groupUpper limit（U）：the end of every group3.36/100.3360.30i Group 2.30 2.60 2.90 3.20 5.605.90 2.302.60(4)Grouping and Counting F
5、requencies LXU2.302.602、Graph of frequency distribution3、Use of frequency table and graph of frequency distribution1Describing the type of frequencies distribution（1）Symmetric distribution：（2）Skewed to the right distribution/Positively skewed distribution (3)Skewed to the left distribution/negativel
6、y skewed distribution2Describing the characteristic of frequencies distribution3.Finding shadiness value4.Convenient for next statistical analysis and managementSection 2 Descriptions of Central Tendency Average in common use:Mean Geometric mean Median1、MeanA descriptive statistic used as a measure
7、of central tendency.All scores in a set of scores are added together and divided by the number of subjects.(1)、Calculate MethodDirect Account:Formula：12nXXXXXnnExample 2-2 To calculate mean of the values of total cholesterol in serum of 100 healthy female adults in direct method.2.35 4.21 3.32 5.35
8、4.17 4.13 2.78 4.26 3.58 4.34 4.84 4.41 4.78 3.95 3.92 3.58 3.66 4.28 3.26 3.50 2.70 4.61 4.75 2.91 3.91 4.59 4.19 2.68 4.52 4.91 3.18 3.68 4.83 3.87 3.95 3.91 4.15 4.55 4.80 3.41 4.12 3.95 5.08 4.53 3.92 3.58 5.35 3.84 3.60 3.51 4.06 3.07 3.55 4.23 3.57 4.83 3.52 3.84 4.50 3.96 4.50 3.27 4.52 3.19
9、4.59 3.75 3.98 4.13 4.26 3.63 3.87 5.71 3.30 4.73 4.17 5.13 3.78 4.57 3.80 3.93 3.78 3.99 4.48 4.28 4.06 5.26 5.25 3.98 5.03 3.51 3.86 3.02 3.70 4.33 3.29 3.25 4.15 4.36 4.95 3.00 3.26 2.354.783.914.03(mmol/L)101XWeighting Method：Formula：112233123kkkfXf Xf Xf Xf XXfffffExample 2-3 Calculate the mean
10、 of values in table 2-1 by weighting methodGroup Frequencies(1)(2)2.30 1 2.60 3 2.90 6 3.20 8 3.50 17 3.80 20 4.10 17 4.40 12 4.70 9 5.00 5 5.30 2 5.605.90 1 Total 101 1 2.45 3 2.751 5.75409.754.06(mmol/L)1 31101X (2)、Application Adapt to describe Symmetric distribution，specially of normal distribut
11、ion data.2、Geometric meanThe geometric mean is simply the average of symmetric values after logarithm transition.(1)、Calculate MethodDirect method Formula：or12nnGX XX1lglg()XGnExample 2-4 To acquire reciprocal titer of sera as below,calculate the geometric mean.10，20，40，40,160510 20 40 40 16034.8G 1
12、1lglg10lg20lg40lg40lg160lg()lg()34.85XGnWeighting methodFormula：1lglg()fXGf(2)、Application：Adapt to data of geometric progression growth，especially of logarithm normal distribution.3、Median and Percentile(1)Median The median is the score/value that is exactly in the middle of a distribution.Formula:
13、n-odd numbern-even number 1()2nMX()(1)2212nnMXXExample 2-5 Calculate the medium of latent period of 7 patients as below.2,3,4,5,6,9,16Example 2-6 Calculate the medium of latent period of 8 patients as below.1,2,2,3,5,8,15,24Application1、All kinds of data2、Data of skewed distribution and those of no
14、exact value in one end or two（2）PercentilePercentile is a kind of position index.Direct method -decimal fraction：-integer：%nXtrunc(%)1XnXPX%nX(%)(%1)12XnXnXPXXExample 2-7 Calculate no.5 and no.99 percentile as below.Patients：Days in hospital：n=120，120X5%=6：1 2 3 4 5 6 7 8 9 117 118 119 120 1 2 2 2 3
15、 3 4 4 5 40 40 42 455(6)(7)11(34)3.5()22PXX天Weighting method Formula：(%)XXXLXiPLnXff Section 3 Measures of Dispersion RangeQuartileVariance and Standard DeviationCoefficient of Variation 1、Range The difference between the maximum and the minimum,R.2、QuartileQR=Lower QuartileUpper Quartile2575PP 25LQ
16、P75UQP3、Variance and Standard DeviationVariance:A measure of dispersion or variability(spread),calculated by squaring the value of the standard deviation.Sample variance:22()XN2SPopulation standard deviation Sample standard deviation2()XN2()1XXSn Sample standard deviation can also be calculated as b
17、elow：22()1XXnSnExample2-8 Calculate the standard deviation of values in table 2-12101,409.75,1705.09ffXfX 2(409.75)1705.091010.654(mmol/L)101 1S4、Coefficient of Variation CVSX100%Unit 4 Normal DistributionFig.2-3.Frequencies Distribution Approaches ti Normal Distribution1、ConceptMathematic function
18、expression:22()21()2Xf XeX2、CharacteristicBell Curve The normal curve was developed mathematically in 1733.Gauss used the normal curve to analyze astronomical data in 1809.The normal curve is often called the Gaussian distribution.The term bell-shaped curve is often used in everyday usage.Two Parame
19、ters The normal distribution is characterized by two parameters:the mean and the standard deviation sigma.The mean is a measure of location or center and the standard deviation is a measure of scale or spread.The mean can be any value between infinity and the standard deviation must be positive.Each
20、 possible value of and sigma define a specific normal distribution and collectively all possible normal distributions define the normal family.Fig.2-4 Position Transform of Normal Distribution00.10.20.30.40.5-4-3-2-101234 Fig.2-5 Illustration for the changing of normal distribution 00.10.20.30.40.50
21、.60.70.80.9-6-5-4-3-2-10123456=0.5=1=2 Distribution characteristics of ProportionFig.2-6.Proportion Rule of Normal Distribution 3、Standard Normal DistributionThe standard(or canonical)normal distribution is a special member of the normal family that has a mean of 0 and a standard deviation of 1.The
22、standard normal distribution is important since the probabilities and percentiles of any normal distribution can be computed from the standard normal distributionif and sigma are known.Unit 5 Medical Reference Range1、Concept The reference range is derived mathematically by taking the average value f
23、or the mass normal population and allowing for natural variation around that value.One-sided/Two-sidedMedical reference range include 、And is in common use 90%95%99%95%2、Calculate Medical Reference Range 1、Normal Distribution Method 2、Percentile MethodFormulaNormal Distribution MethodTwo-sided refer
24、ence range:One-sided reference range:or1a1 a/2aXs1 aaXsaXsaXsaXsTable 2-2 uCritical V alues Reference range（%）One-sided Two-sided 80 90 95 99 0.84 1.28 1.64 2.33 1.28 1.64 1.96 2.58 Example2-9 Evaluate the 95%reference range of values in example 2-1.Lower limitUpper limit aXs4.06 1.96 0.6542.78(/)mmol L4.06 1.96 0.6542.78(/)mmol LaXs4.06 1.96 0.6545.34(/)mmol LPercentile MethodTwo-sided reference range:One-sided reference range:2/1001002/100PP100P或100 100P 1 a1 aTHANK YOU!
