======Level of measurement======

Collecting data requires us to measure the observed phenomena, including qualitative and quantitative measurements. That is, we use **variables** to quantify the description concept.

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((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。))：

   * **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. 
   * **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.
   * **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.
   * **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.

=====Feature table=====
^  Scale level  ^  变量(variable)类型  ^  Unit  ^  零点(zero)  ^  可采用的数学运算  ^  是否等距  ^  变量是否可比较  ^       
^  Nominal scale  |  离散型(discrete)  |  不相等  |  /  |  =,≠  |  /  |  No  |
^  Ordinal scale  |  离散型  |  不相等  |  /  |  ＞,＜  |  No  |  Yes  |
^  Interval scale  |  可以是连续型(continuous)  |  相等  |  相对(relative)零点  |  +,−  |  Yes  |  Yes  |
^  Ratio scale  |  可以是连续型  |  相等  |  绝对(true)零点  |  +,−,×,÷  |  Yes  |  Yes  |

=====Examples=====

  * **Nominal scale**: 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。

  * **Ordinal scale**: 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。

  * **Interval scale**: 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。

  * **Ratio scale**: 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。

=====Selection of statistical methods=====

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.

==== Nominal scale ====

  * **Descriptive statistics**: frequency distributions and modes, percentages, counts, plurality, etc. can be used; 
  * **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.
  * **Charting Graphing**: bar charts, pie charts.

==== Ordinal Scale ====

  * **Descriptive statistics**: frequency distributions and modes, medians, ranges, percentiles, [[spearman相关|Spearman correlation]] coefficients, etc. can be used. 
  * **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.
  * **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.

==== Interval Scale ====

  * **Descriptive statistics**: frequency distributions and modes, medians, means, ranges, standard deviations, variances, rank correlations, [[Pearson相关|product-moment correlation]] can be used.
  * **Hypothesis testing**: Statistical tests of parameters such as [[t检验|t-test]], F-test, and linear [[Regression]] can be performed.
  * **Charting Graphing**: bar charts, pie charts, line graphs, histograms, boxplots, scatter plots.

==== Ratio Scale ====

  * **Descriptive statistics**: frequency distributions and modes, medians, means, ranges, standard deviations, variances, geometric means, coefficients of variation, etc. can be used;
  * **Hypothesis testing**: statistical tests of parameters can be performed, such as [[ANOVA]], linear regression, and other methods that can be used with interval scales.
  * **Charting Graphing**: bar charts, pie charts, line graphs, histograms, boxplots, scatter plots, violin plots, ridge plots, and so on.