Cross-subject methods
Know which rule the calculator is using
The same word—“uncertainty”—can refer to different ideas. These tools keep school-lab propagation rules separate from SD, SE, confidence intervals and formal statistical models.
Uncertainty propagation used in the toolkit
| Operation | Physics | Chemistry | Biology |
|---|---|---|---|
| Add / subtract | Add absolute uncertainties when using the school-lab worst-case rule. | Add absolute uncertainties for the school-lab rule used by the calculator. | Use only when the biological calculation is being treated as a measurement-propagation problem; do not substitute this for SD/SE. |
| Multiply / divide | Add fractional or percentage uncertainties as a first-order school-lab approximation. | Add percentage uncertainties in the toolkit’s course-level calculator. | When appropriate to a measurement calculation, use the stated propagation convention; biological variation still needs its own statistical treatment. |
| Power xⁿ | Multiply fractional uncertainty by |n| as a first-order estimate. | The toolkit marks power propagation as HL-only; follow the current course/teacher convention for your task. | Not treated as a general substitute for statistical uncertainty; use only when the task explicitly calls for measurement propagation. |
These linear school-lab rules are not the same as combining independent standard uncertainties in quadrature. Each subject About page explains its own assumptions in more detail.
Reporting and rounding
- Keep extra digits in intermediate calculations.
- Report a final uncertainty to one or two significant figures unless your task specifies otherwise.
- Round the measured value to the same decimal place as its final absolute uncertainty.
- Chemistry tools distinguish an unrounded calculated value from a suggested report value where appropriate.
- Units and model assumptions matter as much as the arithmetic.
Regression and graphs
Ordinary least squares, r and R² describe the selected numerical model; they do not prove causation, physical validity or absence of systematic error. Error bars must be identified as uncertainty, SD, SE or another quantity before interpretation.
Subject method pages
Physics calculation methods · Chemistry calculation methods · Biology statistics and methods
跨学科方法约定
先知道计算器使用的到底是哪一种规则
“不确定度”在不同场景中可能指不同概念。本工具把课内实验常见的传播规则，与 SD、SE、置信区间和正式统计模型区分开。
本工具使用的不确定度传播
| 运算 | 物理 | 化学 | 生物 |
|---|---|---|---|
| 加 / 减 | 按课内实验的保守规则，相加绝对不确定度。 | 本工具的课内实验规则同样相加绝对不确定度。 | 只有在题目把生物量当作测量传播问题处理时才使用；不能拿它代替 SD/SE。 |
| 乘 / 除 | 一阶近似下相加相对或百分比不确定度。 | 本工具按课程层面的计算规则相加百分比不确定度。 | 若题目确实要求测量传播，可使用明确说明的规则；生物变异仍需单独统计处理。 |
| 乘方 xⁿ | 一阶近似下，相对不确定度乘以 |n|。 | 本工具把乘方传播标记为 HL-only；具体任务仍应以当前课程和老师约定为准。 | 不能作为一般统计不确定度的替代；只有题目明确要求测量传播时使用。 |
这些线性的课内实验规则不同于把独立标准不确定度按平方和开根号组合。三科 About 页面会进一步说明各自假设。
结果报告与舍入
- 中间步骤保留更多数字。
- 最终不确定度通常保留 1–2 位有效数字，除非题目另有要求。
- 测量值与最终绝对不确定度保留到相同小数位。
- 化学工具在适用时会区分未舍入计算值和建议报告值。
- 单位和模型假设与算术本身同样重要。
回归与图像
OLS、r 和 R² 只能描述你选定的数值模型，并不能证明因果关系、物理有效性或不存在系统误差。误差棒必须先说明代表 uncertainty、SD、SE 或其他量，才有意义。