📚 Year 10 Edexcel Psychology: Formulas and Theorems Quick Reference | Year 10 Edexcel 心理学：公式定理速查手册
In Year 10 Edexcel Psychology, understanding key numerical laws, model parameters and statistical formulas is essential for exam success. This handbook gathers the most important ‘formulas and theorems’ – from memory store capacities and Weber’s Law to descriptive statistics and Piaget’s age stages – into one quick-reference guide. Each entry pairs a concise English explanation with a Chinese translation, followed by clearly formatted data tables or equations where relevant.
在 Year 10 Edexcel 心理学中，掌握关键的数字定律、模型参数和统计公式是考试成功的关键。本手册将最重要的“公式与定理”——从记忆存储容量、韦伯定律到描述性统计和皮亚杰年龄阶段——汇集成一份速查指南。每个条目均以简洁的英文解释搭配中文译文，并在适当处配有清晰的数据表格或方程。
1. The Multi-Store Model: Capacity, Duration and Encoding | 多存储模型：容量、持续时间与编码
Atkinson & Shiffrin (1968) proposed that memory consists of three separate stores: the sensory register, short-term memory (STM) and long-term memory (LTM). Each store has a distinct capacity, duration, and preferred type of encoding. The sensory register holds a very large amount of information for a few milliseconds, encoded in raw modality-specific form. STM can hold between 5 and 9 items for approximately 18–30 seconds without rehearsal, using mainly acoustic encoding. LTM has unlimited capacity, can store memories for a lifetime and relies primarily on semantic encoding.
Atkinson 和 Shiffrin（1968）提出，记忆由三个独立的存储组成：感觉登记、短时记忆（STM）和长时记忆（LTM）。每个存储都有不同的容量、持续时间和偏好的编码方式。感觉登记可以在几毫秒内持有大量信息，编码为原始的感觉通道形式。短时记忆在没有复述的情况下可容纳5到9个项目，持续时间约为18–30秒，主要采用听觉编码。长时记忆的容量无限，可存储记忆长达一生，主要依赖语义编码。
| Store / 存储 | Capacity / 容量 | Duration / 持续时间 | Encoding / 编码 |
|---|---|---|---|
| Sensory Register / 感觉登记 | Very large / 非常大 | ~250 ms (visual) / 约250毫秒(视觉) | Modality-specific / 感觉通道特定 |
| Short-Term Memory (STM) / 短时记忆 | 7 ± 2 items / 个项目 | 18–30 seconds / 秒 | Mainly acoustic / 主要为听觉 |
| Long-Term Memory (LTM) / 长时记忆 | Unlimited / 无限 | Up to a lifetime / 可长达一生 | Mainly semantic / 主要为语义 |
2. Miller’s Law: STM Capacity 7 ± 2 | 米勒定律：短时记忆容量 7 ± 2
George Miller (1956) famously argued that the capacity of short-term memory is about seven items (or ‘chunks’), plus or minus two. This regularity is often called Miller’s Law and can be written as a simple expression: STM capacity ≈ 7 ± 2 chunks. Chunking allows us to enlarge each unit by grouping separate bits, which is why a string of 12 letters becomes manageable when recoded into smaller groups.
George Miller（1956）著名地提出，短时记忆的容量大约为七个项目（或“组块”），加减两个。这一规律常被称为米勒定律，可以写作：STM 容量 ≈ 7 ± 2 个组块。组块化使我们能够通过将独立信息分组来扩大每个单元，因此一串12个字母在被重新编码为更小的组后变得易于记忆。
Capacity = 7 ± 2 chunks
3. Duration of Short-Term Memory: Peterson & Peterson (1959) | 短时记忆的持续时间：Peterson 与 Peterson (1959)
Peterson and Peterson (1959) tested STM duration by asking participants to remember a nonsense trigram (e.g., CGP) while counting backwards in threes to prevent rehearsal. They found that after 3 seconds recall was around 80%, but after 18 seconds it dropped to about 10%. This demonstrates that without active rehearsal, STM traces decay rapidly within 18–30 seconds. The finding leads to a useful ‘duration theorem’: STM without rehearsal lasts approximately 18 seconds before significant loss occurs.
Peterson 和 Peterson（1959）通过要求被试记住一个无意义的三字母组（如 CGP），同时进行倒减三的干扰任务以防止复述，测试了短时记忆的持续时间。他们发现，3秒后回忆率约为80%，但18秒后下降到约10%。这表明，在没有主动复述的情况下，短时记忆痕迹在18–30秒内迅速消退。这一发现导出了一个有用的“持续时间定理”：无复述的短时记忆约在18秒后出现显著丢失。
STM decay time (no rehearsal) ≈ 18 seconds
4. Long-Term Memory: Unlimited Capacity and Permanence | 长时记忆：无限容量与持久性
Unlike STM, long-term memory is not constrained by a seven-item cap. The multi-store model posits that LTM has an unlimited capacity and can store information for a lifetime. Encoding in LTM is mainly semantic, meaning we remember the meaning of information rather than the exact words or sounds. While LTM forgetting can occur due to interference or retrieval failure, there is no fixed time limit or capacity ceiling – a principle as fundamental to the model as any numerical law.
与短时记忆不同，长时记忆并不受七项的容量限制。多存储模型假设长时记忆具有无限的容量，并且可以终生储存信息。长时记忆的编码主要是语义性的，即我们记住的是信息的意义，而非确切的词语或声音。虽然长时记忆的遗忘可能因干扰或提取失败而发生，但它没有固定的时间限制或容量上限——这是一条与该模型中的任何数字定律同样基础的原则。
5. Weber’s Law in Perception | 感知中的韦伯定律
Weber’s Law, a classic psychophysical principle, states that the just noticeable difference (JND) between two stimuli is a constant proportion of the original stimulus intensity. In mathematical terms, ΔI / I = k, where ΔI is the minimal detectable change in intensity, I is the initial stimulus intensity, and k is the Weber fraction (a constant that varies across sensory modalities). For example, if the Weber fraction for weight is 0.02, you would feel a difference when lifting 102 grams compared to 100 grams. This ‘formula’ underpins our understanding of sensory discrimination thresholds.
韦伯定律是一条经典的心理物理学原理，指出两个刺激之间最小可觉差（JND）与原始刺激强度之比是一个常数。用数学语言表达为 ΔI / I = k，其中 ΔI 是刚能察觉的强度变化，I 是初始刺激强度，k 是韦伯分数（一个随感觉通道而异的常数）。例如，若重量的韦伯分数为0.02，当你提起102克与100克相比时就会感觉到差异。这一“公式”奠定了我们对感觉辨别阈限的理解。
Weber’s Law: ΔI / I = k
6. Absolute Threshold: The 50% Detection Rule | 绝对阈限：50% 检测规则
The absolute threshold is defined as the minimum intensity of a stimulus that can be detected 50% of the time. This operational definition gives researchers a reliable way to measure sensory sensitivity. While it is not a mathematical formula in the strict sense, the 50% criterion functions as a methodological ‘theorem’ in psychophysics – it transforms a subjective experience into quantifiable data. Different senses have different absolute thresholds, e.g., a candle flame seen 30 miles away on a clear dark night, or a watch ticking 20 feet away in quiet conditions.
绝对阈限被定义为有50%的次数能够被检测到的最低刺激强度。这一操作性定义使研究者有了一种可靠的方法来测量感觉敏感度。虽然严格的数学公式，但50%的标准在心理物理学中起着方法学“定理”的作用——它将主观体验转化为可量化的数据。不同感觉通道有不同的绝对阈限，例如在晴朗漆黑的夜晚可看到30英里外的烛光，或在安静的房间里可听到20英尺外手表的嘀嗒声。
7. Piaget’s Stages of Cognitive Development: Age Key | 皮亚杰认知发展阶段：关键年龄
Jean Piaget’s theory of cognitive development proposes four sequential stages, each associated with a characteristic age range. These age bands act as a developmental ‘formula’ to predict the reasoning abilities children are likely to display. Sensorimotor stage (0–2 years): infants learn through senses and motor actions. Preoperational stage (2–7 years): symbolic thinking but lack of conservation. Concrete operational stage (7–11 years): logical reasoning about concrete events. Formal operational stage (11+ years): abstract and hypothetical thinking. Although individual differences exist, these age windows are central to any developmental study in GCSE Psychology.
让·皮亚杰的认知发展理论提出了四个连续的阶段，每个阶段都与特定的年龄范围相联系。这些年龄段如同一种发展“公式”，用来预测儿童可能表现出的推理能力。感知运动阶段（0–2岁）：婴儿通过感觉和动作来学习。前运算阶段（2–7岁）：出现象征性思维但缺乏守恒概念。具体运算阶段（7–11岁）：能够对具体事件进行逻辑推理。形式运算阶段（11岁以上）：进行抽象和假设性思维。尽管存在个体差异，但这些年龄窗口是任何GCSE心理学发展研究中的核心内容。
| Stage / 阶段 | Approximate Age / 大致年龄 | Key Feature / 关键特征 |
|---|---|---|
| Sensorimotor / 感知运动 | 0–2 years / 岁 | Object permanence develops / 客体永久性发展 |
| Preoperational / 前运算 | 2–7 years / 岁 | Egocentrism, lack of conservation / 自我中心，缺乏守恒 |
| Concrete operational / 具体运算 | 7–11 years / 岁 | Conservation, logical thought about concrete events / 守恒，对具体事件的逻辑思维 |
| Formal operational / 形式运算 | 11+ years / 岁 | Abstract reasoning, hypothetical thinking / 抽象推理，假设性思维 |
8. Descriptive Statistics: Mean, Median, Mode and Range | 描述性统计：平均数、中位数、众数与范围
Research methods in Year 10 Edexcel Psychology require the ability to calculate basic descriptive statistics. These formulas are essential ‘tools’ for analysing data from experiments and surveys. The mean is the arithmetic average. The median is the middle value when data are ordered. The mode is the most frequent score. The range measures the spread between the highest and lowest values. Remember to use these measures appropriately – the mean is best for symmetrical data without outliers, while the median is preferred for skewed distributions.
Year 10 Edexcel 心理学的研究方法要求掌握基本的描述性统计计算。这些公式是分析实验和调查数据必不可少的“工具”。平均数是算术平均值。中位数是将数据排序后位于中间的值。众数是出现频次最多的分数。范围衡量最高值与最低值之间的差距。记住要恰当使用这些测量——平均数最适用于没有异常值的对称数据，而中位数在偏态分布中更为可取。
Mean = Σx / N | Median = middle value | Mode = most frequent | Range = max – min
- Steps for mean: Add all raw scores (Σx), divide by number of scores (N).
- 求平均数的步骤：将所有原始分数相加（Σx），除以分数的个数（N）。
- Steps for median: Arrange scores in order; if N is odd, median is the middle score; if N is even, median is the mean of the two middle scores.
- 求中位数的步骤：将分数按顺序排列；若 N 为奇数，中位数是中间的那个分数；若 N 为偶数，中位数是中间两个分数的平均数。
- Mode: Identify the score that appears most often; a data set can have more than one mode or none.
- 众数：找出出现次数最多的分数；一组数据可有多个众数或无众数。
- Range: Subtract the smallest value from the largest value – quick measure of dispersion.
- 范围：最大值减去最小值——一种快速的离散程度测量。
9. Ethical Principles: The BPS Code of Conduct | 伦理原则：英国心理学会行为守则
While not a mathematical formula, the ethical guidelines set by the British Psychological Society (BPS) act as a ‘normative theorem’ that every psychological investigation must satisfy. The key principles can be remembered as a checklist: informed consent (participants should know the aims and agree), avoidance of deception (unless justified and debriefed), right to withdraw (participants can leave at any time), protection from harm (psychological and physical), and confidentiality (data must remain private). Violating these principles can invalidate a study, much like breaking a scientific formula would destroy an experiment’s validity.
虽然并非数学公式，但英国心理学会（BPS）制定的伦理准则充当着每一项心理学调查必须满足的“规范性定理”。关键原则可以记作一份核对清单：知情同意（被试应了解研究目的并表示同意），避免欺骗（除非有正当理由并进行事后解释），退出权利（被试可随时退出），免受伤害（心理和身体上），以及保密（数据必须保持隐私）。违反这些原则可能会使研究无效，就像违反科学公式会破坏实验的效度一样。
- Informed Consent / 知情同意: Give participants full information about the study and obtain their written agreement. / 向被试提供研究的全部信息并取得书面同意。
- Deception / 欺骗: Avoid misleading participants; if unavoidable, debrief thoroughly. / 避免误导被试；如不可避免，必须进行充分的事后解释。
- Right to Withdraw / 退出权利: Participants can stop their involvement at any stage without penalty. / 被试可在任何阶段停止参与，不受惩罚。
- Protection from Harm / 免受伤害: Ensure no physical or psychological harm comes to participants. / 确保被试不遭受身体或心理伤害。
- Confidentiality / 保密: Keep participants’ data anonymous and protected. / 保持被试数据匿名并加以保护。
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