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Statistics

統計學

【資料圖】

There were two widely divergent influences on the early development of statistical methods. Statistics had a mother who was dedicated to keeping orderly records of governmental units (states and statistics come from the same Latin root status) and a gentlemanly gambling father who relied on mathematics to increase his skill at playing the odds in games of chance. The influence of the mother on the offspring, statistics, is represented by counting, measuring, describing, tabulating, ordering, and the taking of censuses-all of which led to modern descriptive statistics. From the influence of the father came modern inferential statistics, which is based squarely on theories of probability.

統計方法的早期發展受到兩種截然不同的影響。統計學有一個“母親”，她致力于井井有條地記錄政府機構的文件(國家和統計學這兩個詞源于同一個拉丁語詞根，status)，還有一個有紳士般的賭博“父親”，他依靠數學來提高賭技，以便在幾率的游戲中取勝。“母親”對其子女統計學的影響表現在計數、測量、描述、制表、歸類和人口普查。所有這些導致了現代描述統計學的誕生。由于“父親”的影響則產生了完全基于概率論原理的現代推理統計學。

Descriptive statistics involves tabulating, depicting and describing collections of data. These data may be quantitative such as measures of height, intelligence or grade level -- variables that are characterized by an underlying continuum -- or the data may represent qualitative variables, such as sex, college major or personality type. Large masses of data must generally undergo a process of summarization or reduction before they are comprehensible. Descriptive statistics is a tool for describing or summarizing or reducing to comprehensible form the properties of an otherwise unwieldy mass of data.

描述統計學涉及對所收集數據的制表、制圖和描述。這些數據可以是數量性的數據，如高度、智商、或者是層級性的數據——具有連續性的變量——或數據也可以代表性質變量，如性別、大學專業或性格類型等等。數量龐大的數據通常必須經過概括或刪減的程序才能為人所理解。描述統計學就是這樣一個工具，它對極其龐雜的數據進行描述、概括或刪減，使其變成能為人理解的東西。

Inferential statistics is a formalized body of methods for solving another class of problems that present great difficulties for the unaided human mind. This general class of problems characteristically involve attempts to make predictions using a sample of observations. For example, a school superintendent wishes to determine the proportion of children in a large school system who come to school without breakfast, have been vaccinated for flu, or whatever. Having a little knowledge of statistics, the superintendent would know that it is unnecessary and inefficient to question each child: the proportion for the entire district could be estimated fairly accurately from a sample of as few as 100 children. Thus, the purpose of inferential statistics is to predict or estimate characteristics of a population from a knowledge of the characteristics of only a sample of the population.

推理統計學是一套已定形了的方法體系，它解決的是光憑人腦極難解決的另一類問題。這類問題的顯著特點是試圖通過取樣調查來作出預測。例如，有一位教育督察想知道在一個龐大的學校系統中，不吃早飯就上學的學生、已經做過防感冒免疫的學生，或其它任何類型的學生占多大比例。若具備一些統計學的知識，這位督察應明白，詢問每個孩子是沒有必要而且沒有效率的，只要用100個孩子為樣本，他就可以相當精確地得出這些孩子占整個學區的比例了。因此，推理統計學的目的就是通過了解一個群體中一些樣本的特性，從而對整個群體的特性進行推測和估算。

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