📚 Categoric Variables in A-Level Physics | A-Level物理中的分类变量
In AQA A-level Physics, variables are the quantities or factors you change, measure, or control in an experiment. One of the most common exam misconceptions is how to classify a variable whose values are not numbers. This article focuses on the categoric variable, giving clear definitions, examples, graph rules, and mark scheme tips.
在AQA A-Level物理中，变量是你在实验中改变、测量或控制的量或因素。考试中最常见的误解之一，是如何对取值不是数字的变量进行分类。本文聚焦于分类变量，给出清晰的定义、示例、作图规则和评分技巧。
1. What Is a Categoric Variable? | 什么是分类变量？
A categoric variable is a variable whose values are descriptive labels, names, or categories instead of numbers. For example, if you investigate how the type of metal wire affects resistance, the independent variable 'type of metal' is categoric because copper, nichrome, and constantan are labels, not numerical measurements.
分类变量是取值为描述性标签、名称或类别而非数字的变量。例如，如果你研究金属丝的类型如何影响电阻，自变量就是分类变量，因为铜、镍铬合金和康铜是标签，而不是数值测量结果。
Other physics examples include the shape of an object, the colour of a light filter, the state of matter, or the type of circuit component such as a diode, resistor, or thermistor. Categoric variables cannot usually be put in a meaningful numerical order unless you add extra information.
其他物理示例包括物体的形状、滤光片的颜色、物质的状态，或电路元件的类型，如二极管、电阻器或热敏电阻。分类变量通常无法按有意义的数值顺序排列，除非加入额外信息。
2. Categoric vs Continuous Variables | 分类变量与连续变量
A continuous variable can take any numerical value within a range, usually through measurement. Examples include length, time, current, potential difference, and temperature. In contrast, a categoric variable is not measured on a numerical scale, so you cannot calculate a meaningful difference or average by adding the labels.
连续变量可以在一个范围内取任意数值，通常通过测量获得。例子包括长度、时间、电流、电势差和温度。相反，分类变量不是用数值尺度测量的，因此你不能通过将标签相加来计算有意义的差值或平均值。
| Feature | Categoric variable | Continuous variable |
|---|---|---|
| Values | Words or labels | Numbers from measurement |
| Example | Type of material | Length in metres |
| Graph type | Bar chart | Line graph or scatter graph |
中文对照：特征是取值、示例和图表类型。分类变量取值是文字或标签，示例为材料类型，图表使用条形图；连续变量取值是测量数字，示例为以米为单位的长度，图表使用折线图或散点图。
3. Categoric vs Discrete Variables | 分类变量与离散变量
Discrete variables are numerical but can only take certain values, usually whole numbers. For example, the number of slits in a diffraction grating or the number of complete oscillations is discrete. Although discrete values are not continuous, they are still numbers, so they are not categoric.
离散变量是数值变量，但只能取某些特定值，通常是整数。例如，衍射光栅的狭缝数或完整振动的次数是离散变量。虽然离散值不是连续的，但它们仍然是数字，因此不是分类变量。
A common error is to label a 'number of...' variable as categoric just because it changes in steps. In AQA mark schemes, 'number of springs in parallel' is discrete, while 'spring arrangement: series or parallel' is categoric.
一个常见错误是，仅仅因为变量按阶梯变化，就把“某某的数量”标记为分类变量。在AQA评分标准中，“并联弹簧的数量”是离散变量，而“弹簧连接方式：串联或并联”是分类变量。
4. Why Variables Matter in AQA Physics | 为何AQA物理重视变量
AQA practical questions often ask you to state the independent, dependent, and control variables, then identify whether the independent variable is categoric, continuous, or discrete. This links to Working Scientifically skills and can appear in both required practical questions and unfamiliar contexts.
AQA实验题经常要求你陈述自变量、因变量和控制变量，然后判断自变量是分类变量、连续变量还是离散变量。这与科学工作技能相关，可能出现在必修实验题和陌生情境题中。
You may also be asked to justify a choice of graph. If the independent variable is categoric, you must choose a bar chart. If you choose a line graph, you may lose marks because the categories have no numerical scale.
你还可能被要求说明选择某种图表的理由。如果自变量是分类变量，你必须选择条形图。如果选择折线图，则可能失分，因为类别没有数值刻度。
5. Identifying Categoric Variables in Required Practicals | 在必修实验中识别分类变量
In AQA A-level Physics required practicals, many independent variables are continuous because you vary length, mass, or resistance. Categoric variables appear when you compare different types of something, such as different materials, components, or conditions.
在AQA A-Level物理必修实验中，许多自变量是连续变量，因为你改变的是长度、质量或电阻。当你比较不同类型的材料、元件或条件时，分类变量就会出现。
For example, if you investigate how the type of wire affects resistivity, the type of wire is categoric. If you investigate how the type of surface affects the coefficient of friction, the surface type is categoric. In each case, the dependent variable is usually continuous.
例如，如果你研究导线的类型如何影响电阻率，导线的类型就是分类变量。如果你研究表面的类型如何影响摩擦系数，表面类型就是分类变量。在每种情况下，因变量通常是连续变量。
6. Categoric Variables and Graphs | 分类变量与图表
When the independent variable is categoric, plot a bar chart. Each category sits on the horizontal axis with equal spacing, and the dependent continuous variable is plotted on the vertical axis. You should not draw a line of best fit because a line suggests a continuous relationship between numbers.
当自变量是分类变量时，应绘制条形图。每个类别以等间距放在横轴上，连续的因变量绘制在纵轴上。不应绘制最佳拟合线，因为拟合线意味着数字之间存在连续关系。
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