生物统计学学习笔记(1)描述性统计变量.docx

生物统计学学习笔记（1）描述性统计Descriptive Statistics位置测度法 measure of locationOne type of measure useful for summarizing data defines the center, or middle, of the sample. This type of measure is a measure of location.算术平均数：arithmetic meanThe arithmetic mean is the sum of all the observations divided by the number of observations. It is written in statistical terms as算术平均是的缺点是对极端是太敏感了。在这种情况下他不能代表样本的绝大多数。The arithmetic mean is, in general, a very natural measure of location. One of its main limitations, however, is that it is oversensitive to extreme values. In this instance, it may not be representative of the location of the great majority of sample points.中位数 medianSuppose there are n observations in a sample. If these observations are orderedfrom smallest to largest, then the median is defined as follows:1. The（ n+12）th largest observation if n is odd2. The average of the（ n2）th and （ n2+1）th largest observations if n is even众数modeThe mode is the most frequently occurring value among all the observations in a sample.几何平均数The Geometric MeanThe geometric mean is the antilogarithm of log x, where离散性测度 Measure s of Spread极差range一个样本中最大值和最小值之间的差异The range is the difference between the largest and smallest observations in a sample分位数The pth percentile is defined by(1) The (k + 1)th largest sample point if np/100 is not an integer (where k is the largest integer less than np/100).(2) The average of the (np/100)th and (np/100 + 1)th largest observations if np/100 is an integer.Percentiles are also sometimes called quantiles.R可以如下求解 quantile(pzcz$BornAlive) 0% 25% 50% 75% 100% 0 8 10 12 20 quantile(pzcz$BornAlive,probs=c(0.1,0.9),na.rm = TRUE,type = 2)10% 90% 6 13 quantile(pzcz$BornAlive,probs=c(0.1,0.25,0.5,0.75,0.9),na.rm = TRUE,type = 2)10% 25% 50% 75% 90% 6 8 10 12 13 方差与标准差The Variance and Standard DeviationThe sample variance, or variance, is defined as follows:S2=i=1n(xi-x)n-1A rationale for using n 1 in the denominator rather than n is presented in the discussion of estimation in Chapter 6.The sample standard deviation, or standard deviation, is defined as follows:S=i=1n(xi-x)n-1 =sample variance分组数据 Grouped DataA frequency distribution is an ordered display of each value in a data set together with its frequency, that is, the number of times that value occurs in the data set. In addition, the percentage of sample points that take on a particular value is also typically given.x=table(pzcz$BornAlive);x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 107 23 56 129 222 386 541 806 1034 1233 1421 1402 1169 758 452 235 90 31 14 2 20 1 as.data.frame(x,responseName = Frequency) Var1 Frequency1 0 1072 1 233 2 564 3 1295 4 2226 5 3867 6 5418 7 8069 8 103410 9 123311 10 142112 11 140213 12 116914 13 75815 14 45216 15 23517 16 9018 17 3119 18 1420 19 221 20 1 as.data.frame(x,responseName = Frequency) Var1 Frequency1 0 1072 1 233 2 564 3 1295 4 2226 5 3867 6 5418 7 8069 8 103410 9 123311 10 142112 11 140213 12 116914 13 75815 14 45216 15 23517 16 9018 17 3119 18 1420 19 221 20 1 as.data.frame(x/sum(x),responseName = Percent) Var1 Percent1 0 1.058149e-022 1 2.274525e-033 2 5.537975e-034 3 1.275712e-025 4 2.195411e-026 5 3.817247e-027 6 5.350079e-028 7 7.970728e-029 8 1.022547e-0110 9 1.219343e-0111 10 1.405261e-0112 11 1.386472e-0113 12 1.156052e-0114 13 7.496044e-0215 14 4.469937e-0216 15 2.323972e-0217 16 8.900316e-0318 17 3.065665e-0319 18 1.384494e-0320 19 1.977848e-0421 20 9.889241e-05l Minitab 统计 表格 单变量计数用于显示每个指定变量的计数、累积计数、百分比和累积百分比。对话框项 变量：输入要计数的列。显示 计数：选中此项以显示每个可区分值出现的次数。百分比：选中此项以显示每个类别的百分比贡献。累积计数：选中此项以显示每个类别的累积计数。累积百分比：选中此项以显示每个类别的累积百分比 。存储结果：选中此项以将所选结果存储在工作表中 TotalVariable Count N N* CumN Percent CumPct Mean SE Mean TrMean StDevBornAlive 10112 10112 0 10112 100 100 9.6164 0.0300 9.7023 3.0136Variable Variance CoefVar Sum Sum of Squares Minimum Q1 Median Q3BornAlive 9.0817 31.34 97241.0000 1.02693E+06 0.0000 8.0000 10.0000 12.0000 N forVariable Maximum Range IQR Mode Mode Skewness Kurtosis MSSDBornAlive 20.0000 20.0000 4.0000 10 1421 -0.45 0.43 8.6802An outlying value is a value x such that either(1) x upper quartile + 1.5 (upper quartile lower quartile) or(2) x upper quartile + 3.0 (upper quartile lower quartile) or(2) x lower quartile 3.0 (upper quartile lower quartile)The box plot is then completed by(1) Drawing a vertical bar from the upper quartile to the largest nonoutlying value in the samp