📚 Year 10 WJEC Psychology: Formula & Law Quick Handbook | Year 10 WJEC 心理学：公式定理速查手册
This quick reference handbook brings together the essential mathematical formulas and key psychological laws you need to know for the Year 10 WJEC Psychology course. From descriptive statistics used in research methods to the psychophysical laws and memory principles that explain human behaviour, each entry is presented in clear English with a Chinese translation, so you can revise effectively and build a solid foundation for your exams.
这本速查手册汇编了 Year 10 WJEC 心理学课程中你必须掌握的核心数学公式和关键心理学定律。从研究方法中用到的描述性统计，到解释人类行为的心理物理定律与记忆法则，每个词条都配有清晰的中英文解释，帮助你高效复习，为考试打下扎实基础。
1. Calculating the Mean | 计算平均数
The mean is a measure of central tendency calculated by adding all the scores in a data set and then dividing by the number of scores. It is the most commonly used average in psychological research.
平均数是一种集中趋势的度量，通过将数据集中所有数值相加，再除以数值的个数得出。它是心理学研究中最常用的平均值。
- Add all the values together: Σx (sum of scores).
- 将所有数值相加：Σx（分数之和）。
- Count how many values there are (N).
- 数出有多少个数值（N）。
- Divide the sum by the number of values: Σx ÷ N.
- 用总和除以数值的个数：Σx ÷ N。
Mean = Σx / N
e, if a memory test produces scores of 7, 9, 11, and 13, the mean is (7+9+11+13) ÷ 4 = 10.
例如，一项记忆测试得到分数 7、9、11、13，那么平均数就是 (7+9+11+13) ÷ 4 = 10。
2. Finding the Median | 求中位数
The median is the middle value when all the scores are arranged in order from smallest to largest. It is not affected by extreme scores, making it useful when data are skewed.
中位数是将所有分数从小到大排列后处于中间位置的那个值。它不受极端分数的影响，因此当数据偏斜时很有用。
- Arrange the scores in ascending order.
- 将分数按从小到大的顺序排列。
- If the number of scores (N) is odd, the median is the middle score.
- 如果分数个数（N）是奇数，中位数就是正中间的那个分数。
- If N is even, find the two middle scores and calculate their mean.
- 如果 N 是偶数，找出中间的两个分数并计算它们的平均数。
e 3, 5, 8, the median is 5. With an even set like 2, 4, 6, 8, the median is (4+6) ÷ 2 = 5.
对于奇数数据集如 3, 5, 8，中位数是 5。对于偶数数据集如 2, 4, 6, 8，中位数为 (4+6) ÷ 2 = 5。
3. Identifying the Mode | 确定众数
The mode is the most frequently occurring value in a data set. A set can have one mode (unimodal), two modes (bimodal), or more. The mode is the only measure of central tendency suitable for nominal (categorical) data.
众数是数据集中出现频率最高的值。一组数据可以有一个众数（单峰）、两个众数（双峰）或更多。众数是唯一适用于称名（类别）数据的集中趋势指标。
In a survey on favourite colours, if 'blue' is chosen 15 times, 'red' 8 times, and 'green' 7 times, the mode is blue. No calculation is needed—just identify the highest frequency.
在一项关于最喜欢颜色的调查中，如果“蓝色”被选 15 次，“红色”8 次，“绿色”7 次，那么众数就是蓝色。无需计算，只需找出最高频次即可。
When you report the mode, always mention the frequency count alongside the value to show how common it is.
当你报告众数时，一定要同时提及频次，以显示该值的普遍程度。
4. Measuring the Range | 测量全距（极差）
The range is a simple measure of dispersion that tells you how spread out the scores are. It is found by subtracting the smallest value from the largest value in the set.
全距是一种简单的离散程度度量，告诉你分数的分散程度。它通过从数据集中最大的值减去最小的值得到。
Range = Highest Score – Lowest Score
Although the range is easy to calculate, it can be distorted by a single extreme outlier, so it is often reported alongside the median or interquartile range in more advanced analysis.
尽管全距容易计算，但它可能会被单一的极端异常值扭曲，因此更高级的分析中常与中位数或四分位距一起报告。
For a set of conformity scores like 12, 15, 18, 22, 45, the range is 45 – 12 = 33. The value 45 is clearly much higher than the rest, which inflates the range.
对于一组从众分数，如 12, 15, 18, 22, 45，全距为 45 – 12 = 33。数值 45 显然远高于其他值，从而夸大了全距。
5. Calculating Percentage Change | 计算百分比变化
Percentage change is used in psychology to compare results before and after an intervention, or between two conditions in an experiment. It shows the relative increase or decrease as a proportion of the original value.
百分比变化在心理学中用于比较干预前后的结果，或实验中两种条件之间的差异。它以原始值为基数，显示相对的增加或减少。
Percentage Change = [(New Value – Original Value) / Original Value] × 100
For instance, if recall accuracy increased from 40% to 52%, the percentage change is [(52 – 40) / 40] × 100 = +30%. A negative result indicates a decrease.
例如，如果回忆正确率从 40% 提升到 52%，百分比变化为 [(52 – 40) / 40] × 100 = +30%。负值表示下降。
Always include the '+' or '–' sign to make the direction of change clear. This formula is especially useful when presenting findings from memory or learning experiments.
务必加上“+”或“–”符号以明确变化方向。这个公式在呈现记忆或学习实验的结果时尤其有用。
6. Weber's Law | 韦伯定律
Weber's Law is a classic principle in psychophysics. It states that the just noticeable difference (JND) between two stimuli is proportional to the magnitude of the original stimulus. In other words, the larger the stimulus, the larger the change needed for a person to notice it.
韦伯定律是心理物理学中的经典原理。它指出，人对两个刺激之间的最小可觉差（JND）与原始刺激的强度成正比。换句话说，原始刺激越大，需要更大的变化才能被人察觉到。
ΔI / I = k
Here, ΔI is the difference threshold, I is the original stimulus intensity, and k is the Weber fraction, a constant that varies by sensory modality (e.g., around 0.02 for visual brightness).
这里，ΔI 是差别阈限，I 是原始刺激强度，k 是韦伯分数，一个随感觉通道变化而不同的常数（例如视觉亮度的 k 约为 0.02）。
u would need 20 g extra. This law helps explain thresholds in sensory perception experiments.
如果你手拿 100 克的重物，可能需要增加 2 克才能感到差别（k = 0.02）。若拿 1000 克重物，则需增加 20 克。这一定律有助于解释感觉知觉实验中的阈限。
7. Fechner's Law | 费希纳定律
Building on Weber's work, Fechner's Law describes the relationship between the physical intensity of a stimulus and the perceived sensation magnitude. It proposes that sensation increases as the logarithm of the stimulus intensity.
在韦伯研究的基础上，费希纳定律描述了刺激的物理强度与知觉到的感觉大小之间的关系。它提出，感觉量随刺激强度的对数增长而增加。
S = k log I
S is the sensation magnitude, I is the stimulus intensity, and k is a constant that depends on the type of stimulation. The logarithmic scale means that to double the sensation, the stimulus intensity must be multiplied many times.
S 是感觉量，I 是刺激强度，k 是取决于刺激类型的常数。对数刻度意味着，要使感觉量翻倍，刺激强度必须翻很多倍。
For example, if you light one candle in a dark room, the perceived brightness increases dramatically. Adding a second candle produces a smaller noticeable increase, consistent with Fechner's logarithmic function.
例如，在黑暗的房间里点亮一支蜡烛，感觉到的亮度会大幅增加。再添加第二支蜡烛，能察觉到的亮度增加就变小了，这与费希纳的对数函数吻合。
8. Yerkes-Dodson Law | 耶基斯-多德森定律
The Yerkes-Dodson Law explains the curvilinear relationship between arousal and performance. According to this law, performance improves with increased arousal up to an optimal point, after which further arousal leads to a decline in performance.
耶基斯-多德森定律解释了唤醒水平与表现之间的曲线关系。根据该定律，表现随着唤醒水平的提升而提高，直到达到一个最佳点，此后更高的唤醒反而导致表现下降。
The optimal level of arousal differs depending on the task: for simple or well-learned tasks, a higher arousal is often better, while for complex or novel tasks, a lower arousal tends to produce better results.
最佳唤醒水平因任务不同而有所差异：对于简单或熟练的任务，较高的唤醒通常效果更好；而对于复杂或陌生的任务，较低的唤醒往往能带来更佳表现。
Psychologists often link this law to exam performance. Moderate anxiety can motivate students to revise effectively, but excessive stress may impair memory recall, demonstrating the inverted-U curve.
心理学家常将这一定律与考试表现联系起来。适度的焦虑可以激励学生高效复习，但过度的压力可能损害记忆提取，这正是倒U形曲线的体现。
9. Miller's Law (7±2) | 米勒法则（7±2）
Miller's Law, formulated by George Miller in 1956, proposes that the average capacity of short-term memory is about seven items (plus or minus two). This means most people can hold between five and nine chunks of information in their working memory at any one time.
米勒法则由乔治·米勒于 1956 年提出，认为短时记忆的平均容量约为 7 个项目（加减 2）。这意味着大多数人在任何时刻都可以在工作记忆中保持 5 到 9 个信息组块。
A 'chunk' is a meaningful unit of information. By grouping individual digits or letters into larger chunks, you can remember more. For example, the letters ‘F B I C I A U K’ are easier to recall when grouped as ‘FBI’, ‘CIA’, and ‘UK’.
“组块”是信息的有意义单元。将单个数字或字母组合成更大的组块，你就能记住更多。例如，字母序列‘F B I C I A U K’ 分组为 ‘FBI’，‘CIA’ 和 ‘UK’ 后就更容易回忆。
Miller's Law has practical implications for revision: breaking complex information into smaller chunks can help move material from short-term to long-term memory.
米勒法则对复习有实际意义：将复杂信息分解成较小的组块，有助于将材料从短时记忆转入长时记忆。
10. Serial Position Effect | 系列位置效应
The serial position effect describes how a person's ability to remember information in a list depends on the position of items. It consists of two distinct phenomena: the primacy effect and the recency effect.
系列位置效应描述了人们记忆列表中信息的难易程度取决于项目所处的位置。它包括两种不同的现象：首因效应和近因效应。
The primacy effect refers to better recall of items presented at the beginning of a list. This is thought to occur because early items receive more rehearsal and transfer into long-term memory.
首因效应指的是对列表开头呈现的项目回忆得更好。这被认为是由于早期项目得到了更多的复述，并转入了长时记忆。
The recency effect refers to better recall of items at the end of the list. These items are still held in short-term memory at the time of recall and are therefore easily accessible, unless a distracting task intervenes.
近因效应指的是对列表末尾项目的更好回忆。这些项目在回忆时仍保留在短时记忆中，因此易于提取，除非其间插入了干扰任务。
Understanding this effect helps in designing experiments on memory and can also guide your own study schedule—reviewing key points at the start and end of a session can improve retention.
理解这一效应有助于设计记忆实验，也能指导你的学习计划——在学习阶段的开头和结尾复习关键点，可以提升记忆保持率。
11. Ebbinghaus Forgetting Curve | 艾宾浩斯遗忘曲线
Hermann Ebbinghaus pioneered the experimental study of memory by testing himself with nonsense syllables. His forgetting curve shows that memory loss is most rapid just after learning, and then the rate of forgetting gradually levels off over time.
赫尔曼·艾宾浩斯通过用无意义音节测试自己，开创了记忆的实验研究。他的遗忘曲线表明，记忆损失在学习刚结束时最为迅速，随后遗忘速率随时间逐渐减缓。
Although there is no single simple formula for the curve at Year 10 level, the classic pattern can be described as an exponential decay: retention drops sharply within the first hour and continues to decline slowly over days and weeks if no revision takes place.
虽然在 Year 10 阶段该曲线没有单一的简单公式，但其经典模式可被描述为指数衰减：如果在没有复习的情况下，记忆保持量在第一个小时内急剧下降，并在随后的数天和数周内继续缓慢降低。
The key message of the forgetting curve is that spaced repetition and active recall can greatly reduce forgetting. Reviewing material after a day, a week, and a month helps strengthen long-term memory encoding.
遗忘曲线传递的关键信息是，间隔重复和主动回忆可以极大减少遗忘。在学习后一天、一周和一个月进行复习，有助于加强长时记忆的编码。
12. BPS Ethical Principles | 英国心理学会伦理原则
The British Psychological Society (BPS) sets out ethical guidelines that all psychological researchers must follow to protect participants from harm. While these are not mathematical laws, they are fundamental 'rules' that govern investigative practice in psychology.
英国心理学会（BPS）制定了所有心理学研究者都必须遵守的伦理准则，以保护参与者免受伤害。虽然它们不是数学法则，但却是制约心理学研究实践的基本“规则”。
Researchers must obtain informed consent: participants should know the purpose and nature of the study and agree to take part. If deception is unavoidable, a thorough debrief must be provided afterwards, explaining the true aims and offering the right to withdraw data.
研究者必须获取知情同意：参与者应了解研究的目的和性质并同意参加。如果欺骗不可避免，事后必须提供详尽的解释，说明真实目的，并有权撤回自己的数据。
Participants have the right to withdraw at any time without penalty. Confidentiality must be maintained—identifiable information should not be disclosed. Researchers must also avoid causing physical or psychological distress, and they must protect vulnerable groups.
参与者有权随时退出且不受惩罚。必须保守机密——不应披露可识别的个人信息。研究者还必须避免造成身体或心理上的痛苦，并保护弱势群体。
These ethical principles are assessed in your WJEC exam whenever you evaluate a study or design your own investigation, so memorising them is essential.
在你的 WJEC 考试中，无论是评价一项研究还是设计自己的调查，都会涉及这些伦理原则，因此熟记它们至关重要。
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