📚 Categoric Variables | 分类变量
In experimental physics, every investigation begins with identifying the variables involved. A variable is any quantity, factor or condition that can change during an experiment. To design a valid experiment, you must distinguish between the independent variable (the quantity you deliberately change), the dependent variable (the quantity you measure in response) and the control variables (quantities kept constant to ensure a fair test). While many variables are numerical, some take the form of labels or names rather than numbers. These are called categoric variables, and they are a recurring theme in AQA A-Level Physics practical work and examinations.
在实验物理学中，每一项研究都始于识别所涉及的变量。变量是实验中任何可以改变的量、因素或条件。要设计一个有效的实验，你必须区分自变量（你有意改变的量）、因变量（你测量响应的量）和控制变量（保持恒定的量以确保公平测试）。虽然许多变量是数值型的，但有些变量以标签或名称而非数字的形式出现。这些变量被称为分类变量（categoric variables），它们是 AQA A-Level 物理实践操作和考试中反复出现的主题。
1. What Are Categoric Variables? | 什么是分类变量？
A categoric variable is a qualitative variable whose values are labels, names or categories. These values cannot be measured on a numerical scale, nor can they be arranged in a meaningful order. For example, in an experiment investigating how the type of metal affects resistivity, the metal itself — copper, aluminium, iron — is a categoric variable. The resistivity values measured are the dependent continuous variable, but the material is simply a category.
分类变量是一种定性变量，其取值为标签、名称或类别。这些值不能以数值尺度测量，也不能按有意义的顺序排列。例如，在研究金属类型如何影响电阻率的实验中，金属本身——铜、铝、铁——就是一个分类变量。所测量的电阻率值是因变量（连续变量），但材料仅仅是类别。
Common examples of categoric variables in physics include: the material of a wire or block, the type of surface (rough, smooth, polished), the state of matter (solid, liquid, gas), the type of radiation (alpha, beta, gamma), the colour of a filter, and the shape of an object.
物理中常见的分类变量包括：导线或块体的材料、表面类型（粗糙、光滑、抛光）、物质状态（固态、液态、气态）、辐射类型（α、β、γ）、滤光片的颜色以及物体的形状。
The word “categoric” (rather than “categorical”) is the standard spelling used in AQA A-Level Physics specifications and textbooks. This is an important spelling to recognise in exam questions, where you may be asked to “identify the categoric variable” in a described experiment.
“Categoric”（而非”categorical”）是 AQA A-Level 物理大纲和教科书中的标准拼写。这是考试问题中需要识别的关键拼写，例如可能会要求你”识别所描述实验中的分类变量”。
2. The Four Types of Variables in Physics | 物理中的四类变量
AQA A-Level Physics distinguishes between four types of variables: categoric, ordered, discrete and continuous. Each type dictates how data should be recorded, processed and displayed. Categoric variables are qualitative labels with no order; for instance, “wood” and “metal” have no natural ranking. Ordered (ordinal) variables are categories with a natural sequence, such as “low”, “medium” and “high” energy levels — the order exists but the intervals between the categories are not numerically defined.
AQA A-Level 物理区分四类变量：分类变量、有序变量、离散变量和连续变量。每种类型决定了数据应如何记录、处理和显示。分类变量是无顺序的定性标签；例如，”木材”和”金属”没有自然的排序。有序（定序）变量是具有自然序列的类别，如”低”、”中”和”高”能级——顺序存在，但类别之间的间隔没有数值定义。
Discrete variables are numerical variables that take only whole-number values, such as the number of oscillations in a pendulum or the number of coils in a spring. Continuous variables can take any value within a given range — for example, the time taken for 20 oscillations, the extension of a spring, or the temperature of a gas. The distinction between these types underpins your choice of graph and analysis.
离散变量是只取整数值的数值变量，例如钟摆振荡的次数或弹簧的圈数。连续变量可以在给定范围内取任意值——例如，20 次振荡所需的时间、弹簧的伸长量或气体的温度。这些类型之间的区别支撑着你对图表和分析方法的选择。
| Variable type | Nature | Example | Suitable graph |
| Categoric | Qualitative labels, no order | Material of a wire | Bar chart |
| Ordered | Qualitative with natural order | Surface roughness: low, medium, high | Bar chart |
| Discrete | Numerical, whole-number values | Number of particles | Bar chart or line graph |
| Continuous | Numerical, any value in a range | Time, length, voltage | Line graph |
3. Categoric vs. Discrete vs. Continuous | 分类变量与离散变量、连续变量的区别
One of the most common errors in A-Level Physics is confusing categoric variables with discrete variables. The key distinction is that discrete variables are numerical — they are counts, such as 3 oscillations or 7 coils — whereas categoric variables are non-numerical descriptors. You can perform arithmetic on discrete values (for example, calculating the mean number of oscillations per second), but you cannot perform arithmetic on category names. What is the sum of “copper” and “steel”? The question itself shows that categoric variables do not support mathematical operations.
A-Level 物理中最常见的错误之一是将分类变量与离散变量混淆。关键区别在于，离散变量是数值型的——它们是计数，如 3 次振荡或 7 圈——而分类变量是非数值的描述符。你可以对离散值进行算术运算（例如，计算每秒平均振荡次数），但不能对类别名称进行算术运算。”铜”加”钢”等于什么？这个问题本身就表明分类变量不支持数学运算。
Continuous variables differ from both in that they arise from measurement rather than counting or naming. A ruler reading of 12.4 mm for a wire diameter is a continuous value; the material of the wire is categoric. When a question asks you to identify the nature of a variable, always ask: did we measure this, count this, or name this? If the answer is “name”, it is categoric.
连续变量与两者的区别在于，它们来源于测量而非计数或命名。用尺子测得导线直径 12.4 mm 是连续值；导线的材料则是分类变量。当问题要求你识别变量的性质时，务必问自己：我们是在测量它、计数它，还是命名它？如果答案是”命名”，那它就是分类变量。
4. Identifying Categoric Variables in Experiments | 在实验中识别分类变量
When planning an experiment for AQA A-Level Physics, the first step is to classify the independent variable. If the independent variable is a property that can be changed continuously, such as the angle of inclination or the concentration of a solution, it is continuous. If it is a choice between different types, kinds or conditions, it is categoric.
在为 AQA A-Level 物理规划实验时，第一步是对自变量进行分类。如果自变量是可连续变化的性质，如倾斜角度或溶液浓度，它就是连续变量。如果它是对不同类型、种类或条件的选择，它就是分类变量。
A practical way to test for a categoric variable is to ask whether the “values” of the variable can be placed on a measuring instrument. You cannot place “concrete” or “glass” on a ruler, a balance or a voltmeter. Likewise, you cannot set a material to “2.5 times more plastic than rubber” — the categories are fixed and indivisible. In an exam, underline the words that describe the variable; if they are nouns (material, surface, shape, colour), the variable is categoric.
检验分类变量的一种实用方法是，问自己该变量的”值”是否能放在测量仪器上。你不能把”混凝土”或”玻璃”放在尺子、天平或电压表上。同样，你也不能将一种材料设置为”比橡胶塑料 2.5 倍”——类别是固定且不可分割的。在考试中，划出描述该变量的关键词；如果它们是名词（材料、表面、形状、颜色），那么该变量就是分类变量。
5. Data Collection and Recording | 数据收集与记录
For an experiment with a categoric independent variable, data are recorded by grouping repeated measurements under each category name. Suppose you are investigating how different materials affect the rate of cooling of hot water. The categories — glass beaker, polystyrene cup, copper cup — are listed in separate rows of a table. For each category, you take multiple readings of temperature drop over a fixed time, calculate a mean, and record the result.
对于自变量为分类变量的实验，数据的记录方式是将重复测量值归入每个类别名称之下。假设你在研究不同材料如何影响热水冷却速率。类别——玻璃烧杯、聚苯乙烯杯、铜杯——在表格中分行列出。对每个类别，你测量固定时间内多个温度下降的读数，计算平均值并记录结果。
When recording repeated data for categoric variables, the precision and uncertainty analysis remains the same as for continuous variables. The mean value for each category should be stated with an appropriate uncertainty, calculated from the range of repeated readings. However, note that the uncertainty applies to the measured dependent variable, not to the category itself — a category name has no uncertainty associated with it.
在记录分类变量的重复数据时，精度和不确定度分析与连续变量相同。每个类别的平均值应以适当的不确定度表示，该不确定度由重复读数的极差计算。然而，请注意，不确定度适用于所测量的因变量，而非类别本身——类别名称没有相关的不确定度。
Table layout for a categoric experiment:
分类实验的表格布局示例：
| Material (categoric) | Reading 1 / °C | Reading 2 / °C | Reading 3 / °C | Mean / °C |
| Glass | 12.2 | 12.5 | 12.4 | 12.4 ± 0.2 |
| Polystyrene | 7.8 | 8.1 | 7.9 | 7.9 ± 0.2 |
| Copper | 15.5 | 15.3 | 15.6 | 15.5 ± 0.2 |
6. Presenting Categoric Data: Bar Charts | 呈现分类数据：条形图
The correct method of presenting categoric data is a bar chart. On the x-axis, plot the category labels with equal spacing — the gaps between bars are essential because they communicate that the variable is not continuous. On the y-axis, plot the mean value of the dependent variable, with error bars drawn from the calculated uncertainty. Each bar has the same width, and its height represents the measured value for that category.
呈现分类数据的正确方法是条形图。在 x 轴上，以相等间距放置类别标签——条形之间的间隙至关重要，因为它们传达出该变量不是连续的。在 y 轴上，绘制因变量的平均值，并画出由计算不确定度得到的误差线。每个条形宽度相同，其高度代表该类别的测量值。
It is never appropriate to draw a line graph through categoric data points. A line graph implies that an intermediate value can be interpolated between two data points — but there is no value between “glass” and “polystyrene”. Similarly, the concept of a gradient or a line of best fit is meaningless for categoric data, because the x-axis has no numerical scale. If you see an exam question presenting a line graph drawn for categoric data, you should identify it as an error.
在分类数据点上绘制折线图是永远不合适的。折线图暗示可以在两个数据点之间内插一个中间值——但”玻璃”和”聚苯乙烯”之间没有值。同样，梯度或最佳拟合线的概念对分类数据没有意义，因为 x 轴没有数值刻度。如果你在考试中看到为分类数据绘制的折线图，应当将其识别为错误。
7. Categoric Variables in AQA Required Practicals | AQA 必做实验中的分类变量
AQA A-Level Physics includes twelve required practicals, and several of these can involve categoric variables. In Required Practical 6 (determination of the Young modulus), if you choose to compare different materials — such as copper wire and steel wire — the material is a categoric variable. The extension of the wire under increasing load is the continuous dependent variable, while the load itself is also continuous.
AQA A-Level 物理包含十二个必做实验，其中几项可能涉及分类变量。在必做实验 6（测定杨氏模量）中，如果你选择比较不同的材料——如铜丝和钢丝——那么材料就是分类变量。导线在不断增加载荷下的伸长量是连续的因变量，而载荷本身也是连续的。
In Required Practical 11 (investigation of how the rate of decay of a radioactive source is affected by different absorbers), the absorber material — paper, aluminium, lead — is a categoric variable. The count rate measured with a Geiger-Müller tube is the continuous dependent variable. In Required Practical 4 (determination of the resistivity of a wire), the wire material is categoric if different metals are tested, while the wire length and diameter are continuous variables.
在必做实验 11（研究不同吸收体如何影响放射源衰变速率）中，吸收体材料——纸、铝、铅——是分类变量。用盖革-米勒管测量的计数率是连续的因变量。在必做实验 4（测定导线的电阻率）中，如果测试不同金属，导线材料就是分类变量，而导线长度和直径是连续变量。
Another example arises in Required Practical 1 (stationary waves on a string). The harmonic number being investigated can be treated as a discrete variable rather than categoric, because harmonics are countable integers. This distinction is subtle but important: a numeric count such as the number of antinodes is discrete
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