=====变量的测度等级 Scale of Variable=====

收集数据需要我们对所观察的现象进行测量，包括定性测量和定量测量。即，我们用**变量**来量化地描述概念。\\ 
  * Collecting data requires us to measure the observed phenomena, including qualitative and quantitative measurements. That is, we use **variables** to quantify the description concept.\\
不同的变量能够被量化的程度有所不同，变量的**测度等级**按照这种被量化的程度可以分为以下四类((这是我们提供的通俗阐释， [[scalesinAPA|点此查看]]《APA统计与研究方法词典》(APA Dictionary of Statistics and Research Methods)的定义。))： \\
  * The degree to which different variables can be quantized varies, and the **scale levels of variables** can be divided into the following four categories according to the degree of quantization:\\
 \\
 **命名测度**(nominal scale)：也称名义测度等级，是最低的一种测度等级，由一系列具有不同名称的类型组成。命名测度对观察结果进行标定和分类，但数据没有大小之分。命名测度等级也可以用数字表示，不过这些数字仅可定性，并不反映定量信息，也不可比较，如样本代号和数字、编码等。命名数据不支持四则运算，仅支持等于或不等于、是或不是。
   * **Nominal scale**,also known as the nominal measurement grade, it is the lowest measurement grade and consists of a series of types with different names. Named measures calibrate and classify observations, but there is no difference in size of the data. Named measure grades can also be expressed as numbers, but these numbers are only qualitative and do not reflect quantitative information, and are not comparable,such as sample codes and numbers, codes, etc.Nominal data does not support any form of arithmetic computation,and the only kind of mathematical opration it supports is equal to or not equal to, yes or no. 
 **顺序测度**(ordinal scale)：量化水平高于命名测度等级，由一系列按顺序排列的范畴组成。将观察所得结果按其大小或数量排定秩次(rank)，可以提供不同个体之间的顺序差异。顺序数据点之间可进行大小比较，但其本质依旧是定性而非定量的，因此不支持四则运算，也无法体现数据点之间差异的大小及程度。
   * **Ordinal scale** has a higher quantification level than nominal scale, and consists of a series of sequential categories. Ranking the observations by their size or number can provide sequential differences between different individuals. Sequential data points can be compared in size, but they are still qualitative rather than quantitative, so it does not support any form of arithmetic computation as well, and the magnitude and extent of the differences between data points cannot be reflected.
 **等距测度**(interval scale)：也称间距测度等级，沿数字刻度测量，拥有更高的量化水平。相较于顺序测度，规定每两个相邻范畴之间距离相等。一般是采用一定单位的实际测量值，可以用加减运算得到数值之间的差或和，反映大小差距。但缺少物理意义上的绝对零点，因此乘除运算没有意义。一些心理量表，如里科特5点等级量表和是/否的两点量表就是常见的等距量表。
   * **Interval scale**，also known as the spacing measurement grade,has a higher quantification level than ordinal scale. It is measured along a numerical scale.In contrast to the sequential measure, the distance between every two adjacent categories is equal. Generally used the actual measured value in a certain unit, and the difference or sum between the values can be obtained by addition and subtraction operations to reflect the size difference. But the true 0 point in the physical sense is missing, so multiplication and division is meaningless. Some psychological scales, such as the Ricott 5-point scale and the yes/no two-point scale, are common isometric scales.
**比例测度**(ratio scale)：是最高的测度等级，除等距测度的特征外，还拥有绝对零点,可以表示差异的比率。可以进行乘除运算，反映数量间的比例关系。
   * **Ratio scale** is the highest measurement grade.In addition to the characteristics of equidistant measurements, it also has an true 0 point,and the ratios of differences can be expressed. Multiplication and division operations can be performed to reflect the proportional relationship between quantities.
====特征表 Feature table====
^  测度等级(scale level)         ^   变量(variable)类型        ^    单位(unit)      ^    零点(zero)      ^    可采用的数学运算      ^    是否等距     ^   变量是否可比较     ^       
^  命名测度(nominal scale)      |  离散型(discrete)               |     不相等            |  /  |  =,≠  |  /  |  不可以(No)  |
^  顺序测度(ordinal scale)      |  离散型              |      不相等      |  /    |  ＞,＜  |  否(No)  |  可以(Yes)  |
^  等距测度(interval scale)      |  可以是连续型(continuous)               |    相等           |  相对(relative)零点  |  +,－  |  是(Yes)   |  可以(Yes)  |
^  比例测度(ratio scale)      |  可以是连续型   |  相等   |  绝对(true)零点      |  +,－,×,÷  |  是(Yes)  |  可以(Yes)  |

====例子 Examples====
  * **命名测度**：性别、血型、职业、十二星座、各种人格、不同颜色；
    * Gender, blood type, occupation, 12 constellations, various personalities, different colors. 
  * 血型（ABO分类）：每个样本都具有A、B、O、AB四种标签中的某一种，既不能没有血型，也不能拥有两种及以上的血型。不同被试之间只可以比较血型的相同和不同。

  * **顺序测度**：游戏段位、（病情等）轻/中/重、（绩效评定）优/良/及格/不及格、学历、Likert 5等级量表（不同程度之间不等距）；
    * Game Rank, (illness, etc.) light/medium/heavy, (performance evaluation) excellent/good/pass/fail, educational background, Likert 5 rating scale (unequal distance between different degrees). 
  * 游戏段位：每个样本都具有特定的、互不相容的段位，段位之间有高低之分，但不同段位的差别不相等，也不能从某几个段位通过加减运算得到另一个段位。

  * **等距测度**：IQ/意愿倾向/能力分数等等距量表、疼痛程度、温度（摄氏或华氏温标）；
    * IQ/propensity/ability, etc. score, pain degree, temperature (Celsius or Fahrenheit). 
  * IQ（离差智商）：每个样本具有特定的IQ得分，IQ之间有高低之分，每两个相邻IQ值之间的差别相等，但IQ为0不表示不存在IQ。

  * **比例测度**：长度、距离、质量（体重）、心率、收入、年龄、温度（热力学温标）。
    * Length, distance, mass (weight), heart rate, income, age, temperature (Kelvin).
  * 长度：每个样本具有特定的长度，长度有大小之分，可以连续、均匀地变化，长度为0表示长度不存在。

====统计方法的选择 Selection of Statistical Methods====
各种测量类型的局限性直接关系到统计分析方法的选取，因此在开始收集实验数据之前，应格外注意。

The limitations of the various measurement types are directly related to the selection of statistical analysis methods, and therefore extra care should be taken before starting to collect experimental data.
=== 命名测度 Nominal Scale ===
  * **描述统计**：可以使用频率分布和模式、百分比、次数、众数等；
    *Descriptive statistics: frequency distributions and modes, percentages, counts, plurality, etc. can be used; 
  * **假设检验**：可以进行非参数的统计检验，如[[卡方独立性检验]]和Fisher检验。
    *Hypothesis testing: non-parametric statistical tests such as [[卡方独立性检验|chi-square independence test]] and Fisher's test can be performed.
  * **绘图**：条形图、饼状图。
    *Charting Graphing: bar charts, pie charts.
=== 顺序测度 Ordinal Scale ===
  * **描述统计**：可以使用频率分布和模式、中位数、序列、百分位数、[[spearman相关|等级相关]]系数等；
    *Descriptive statistics: frequency distributions and modes, medians, ranges, percentiles, [[spearman相关|Spearman correlation]] coefficients, etc. can be used;
  * **假设检验**：可以进行非参数的统计检验，如卡方检验和Fisher检验，[[kendall和谐系数|肯德尔和谐系数]]检验。
    *Hypothesis testing: non-parametric statistical tests such as chi-square and Fisher's tests, [[kendall和谐系数|Kendall's coefficient of concordance]] tests can be performed.
  * **绘图**：条形图、饼状图、折线图，此外可以使用数据的四分位数（上四分位数、下四分位数）、中位数、最值绘制箱型图。
    *Charting Graphing: bar graphs, pie charts, line graphs, in addition box plots can be drawn using quartiles (upper quartile, lower quartile), medians, and maximum values of the data.
=== 等距测度 Interval Scale ===
  * **描述统计**：可以使用频率分布和模式、中位数、平均数、序列、标准差、方差、等级相关、[[Pearson相关|积差相关]]。
    * Descriptive statistics: frequency distributions and modes, medians, means, ranges, standard deviations, variances, rank correlations, [[Pearson相关|product-moment correlation]] can be used.
  * **假设检验**：可以进行参数的统计检验，如[[t检验]]、F检验，以及线性[[Regression|回归]]。
    * Hypothesis testing: Statistical tests of parameters such as [[t检验|t-test]], F-test, and linear [[Regression]] can be performed.
  * **绘图**：条形图、饼状图、折线图、直方图、箱型图、散点图。
    * Charting Graphing: bar charts, pie charts, line graphs, histograms, boxplots, scatter plots.
=== 比例测度 Ratio Scale ===
  * **描述统计**：可以使用频率分布和模式、中位数、平均数、序列、标准差、方差、几何平均数、变异系数等；
    * Descriptive statistics: frequency distributions and modes, medians, means, ranges, standard deviations, variances, geometric means, coefficients of variation, etc. can be used;
  * **假设检验**：可以进行参数的统计检验，如[[ANOVA|方差分析]]、线性回归，以及其他等距量表可以使用的方法。
    * Hypothesis testing: statistical tests of parameters can be performed, such as [[ANOVA]], linear regression, and other methods that can be used with interval scales.
  * **绘图**：条形图、饼状图、折线图、直方图、箱型图、散点图、小提琴图、山脊图等。
    * Charting Graphing: bar charts, pie charts, line graphs, histograms, boxplots, scatter plots, violin plots, ridge plots, and so on.