第二章 统计数据的描述2014

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Bar chart from FARS data
4-Runner Bronco/Bronco II/Explorer Cherokee Chevrolet C, K, R, V E-Series Van/Econoline F-Series pickup Large Truck Ranger S-10 Blazer 0
4M Example: Rolling over
• Motivation : state the question Authorities enter a description of every fatal automobile accident into the Fatality Analysis Reporting System(FARS). FARS became well known when reporters from New York Times discovered something unusual. Their tools: a question, some data and a bar chart. The question arose anecdotally. Numerous accidents seemed associated with vehicles rolling over: Were these reports coincidental, or was something systematic and dangerous happening on the highways? We will use data for the year 2000 because that’s when this issue came to the public’s attention. News reports suggested some types of cars were more prone to rolling over accidents than others. Most of the reported incidents involved SUVs, but are all SUVs dangerous? If some types of cars are more prone to these dangerous
3.5 3.1 3.9 2.4 2.5 2.1 4.6 3.3 11.9
5 10 mean of percentage
15
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4M Example • The explanation of the bar chart came several years later and brought with a bitter dispute between Ford and Bridgestone, maker of the Firestone tires that were standard equipment on Ford Broncos and Explorers. Ford claimed that the Firestone tires caused the problem, not the vehicle. The dispute led to a massive recall of more than 13 million Firestone tires.
GPS Market Share
19%
10%
47%
7%
17%
Garmin Mio TomTom
Magellan Other
面积原则
• 数据的展示必须服从一个基本原则：面积 原则。此原则要求表现数据的某部分图形 所占据的面积应该与数据的数量成比例。 在条形图中，每个条形的面积应与此条形 所代表的类别的频数成比例。由于每个条 形的宽度一样，面积原则要求条形的高度 应与频数成比例。违反面积原则是利用统 计让人误导的一种常见方式。
第一节 图表展示分布
数据集包含2600个数据，最小值为0.85%， 最大值为15.76%。一般采用等距分组 确定合适的组距，组距过大或过小都不能很 好反映数据的分布。确定组距为2% 从最小值开始进行分组： 0.00≤rate＜2.00, 2.00≤rate＜4.00 ……………………, 14.00≤rate＜16.00 统计各组的次数或百分比，编制次数分布表
Mechanics: do the analysis
FARS reports 1024 fatal accidents on interstates in which the primary event was a roll-over. The accidents include 189 different types of cars. Of course, 180 models were involved in fewer than 20 accidents each. We will combine these into a category called Other. Here are the frequency table and the bar chart.
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Message : summarize the results
• Data from FARS in 2000 show that Ford Broncos (and the comparable Explorer) were involved in more fatal roll-over accidents on interstate highways than any other model. Ford Broncos were involved in more than twice as many roll-over as the nextclosest model(the Ford F-series truck) and more than three times as many as the similar Chevy Blazer. Be honest about any caveats or assumptions you have made. These results could also be explained by popularity. Perhaps more Broncos show up in rollover accidents simply because there are more Broncos being driven on interstate highways. Perhaps Broncos are driven more aggressively. We cannot resolve these questions from the data in FARS alone, but this bar chart begs for an explanation.

资料来源：David S.Mroore著《统计 学世界》
本章内容安排
第一节 图表展示分布 第二节 数字描述分布 第三节 研究分类变量关系 第四节 研究数值变量关系
第一节 图表展示分布
数据分布的图表展示基本步骤： 1.根据数据的取值特点和反映对象的特征， 将数据分成若干类或组，把数据分配到每 个类或组中，计算各类或组包含数据的次 数或比重，编制次数分布表（Frequency Distribution Tabels）。 2.用合适的图形展示次数分布表 3.根据描述数据分布的图表概括数据的分布 特征
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第一节 图表展示分布
2.1.2 数值变量：频数分布、直方图与茎叶图 数值变量可取许多个不同的数值，需要将若干个相 邻的值合并成一个组来反映数据的分布，各组用 取值区间来表示。一般采用等距分组，也可异距 分组。分组后统计落入各组的次数或百分比，形 成次数分布表 例2.3 美国国债（Treasury Bills）的利率分布 数据tbillrates包含美国国债1958年12月12日到2008 年10月3日期间国债的利率，共2600个数据。 数值变量的分组首先需要对数据有一个初步的了解， 如数据个数、最小值、最大值等 Stata的命令：summarize Rate
第一节 图表展示分布
tabulate Company [fweight = MarketShare]
第一节 图表展示分布
从中可看出，美国市场Garmin占支配性地位， 占有几乎一半的市场分额征： 条形图：GPS市场份额
graph bar (mean) MarketShare, over(Company)
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Method: describe the data and select an approach
Identify the data and come up with a plan for how you will use the data. For this example, we will extract from FARS those accidents for which the primary cause was a roll-over. We will also stick to accidents on interstate highways. Once we have the data, we plan to use a frequency tables that includes percentages and a bar chart to show the results.
第一节 图表展示分布
2.1.1 分类变量：条形图（bar graphs）和饼形图 （pie charts） 分类变量的取值就是类别的标签，分类数据直接表 示个体所在的类别，分类变量的分布就是列出各 个类别并给出落在每一类别的次数（count）或百 分比（percent），形成次数分布表。 例2.1 GPS市场份额 Excel数据gps给出美国市场上主要GPS接收器品牌 的市场份额次数分布表。将数据导入Stata软件， 做出次数分布表：