重学Statistics，Cha1 Data and Statistics

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**学什么？这一章主要是Nominal, Ordinal, Interval, Ratio Scale的区别

I. 表格的各种表示

Elements are the entities on which data are collected。

A variable is a characteristic of interest for the elements.

The set of measurements obtained for a particular element is called an observation.

II. Nominal, Ordinal, Interval, Ratio Scale

When the data for a variable consist of labels or names used to identify an attribute of the element, the scale of measurement is considered a nominal scale.

男女是nominal scale

The scale of measurement for a variable is called an ordinal scale if the data exhibit the properties of nominal data and the order or rank of the data is meaningful.

1星到5星是 ordinal scale，因为是分类的，类别的顺序有意义。

The scale of measurement for a variable is an interval scale if the data have all the properties of ordinal data and the interval between values is expressed in terms of a fixed
unit of measure. Interval data are always numeric.

考试的分数是 Interval data，数据可以加减乘除

The scale of measurement for a variable is a ratio scale if the data have all the properties of interval data and the ratio of two values is meaningful.

距离，身高，体重，时间都是 ratio scale. 有固定的原点。 因此，在等比量表中，我们可以标识对象，将对象进行分类、排序， 并比较不同对象某一变量测量值的差别。

问： ordinal scale 与 interval data 有什么分别？

定距型数据是数字型变量，可以求加减平均值等，但不存在基准0值，即当变量值为0时不是表示没有，如温度变量，当温度为0时，并不是表示没有温度，这样温度就为定距变量，而不是定比变量。(因为温度的刻度是人决定的，0代表水结冰的温度)  -- 来自百度百科

III. 一些定义

Data that can be grouped by specific categories are referred to as categorical data. Categorical data use either the nominal or ordinal scale of measurement. Data that use numeric values to indicate how much or how many are referred to as quantitative data. Quantitative data are obtained using either the interval or ratio scale of measurement. A categorical variable is a variable with categorical data, and a quantitative variable is a variable with quantitative data.

Cross-Sectional Data (data collected at the same time)

Time Series Data (data collected over several time periods)

Experimental Study ：控制变量实验

Observational Study：Survey

Descriptive data: summaries of data, which may be tabular, graphical, or numerical

Population: A population is the set of all elements of interest in a particular study.

SAMPLE: A sample is a subset of the population.

The process of conducting a survey to collect data for the entire population is called a census. The process of conducting a survey to collect data for a sample is called a sample survey. Statistical Inference is 用sample 估计population

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