📚 Psychology Formula & Theorem Quick Reference Handbook | 心理学公式定理速查手册
This handbook gathers the essential formulas, hypothesis structures, statistical tools and core psychological theorems you need to master for the Edexcel GCSE (9-1) Psychology course. Each section presents a concept in clear English, immediately followed by its Chinese translation, helping you build accurate knowledge and bilingual fluency. Use it for quick revision, exam preparation and end-of-topic checks.
本手册汇集了 Edexcel GCSE（9-1）心理学课程必须掌握的关键公式、假设结构、统计工具和核心心理学定理。每个部分先用清晰的英文呈现概念，紧接着提供中文翻译，帮助你建立准确的知识体系并提升双语能力。可用于快速复习、备考以及单元主题检查。
1. Research Hypothesis Formulation | 研究假设公式
A hypothesis is a testable, predictive statement about the expected outcome of a study. In Edexcel Psychology you must be able to write both directional (one‑tailed) and non‑directional (two‑tailed) alternative hypotheses. A directional hypothesis states the precise direction of the result: for example, 'Participants who learn a word list in silence will recall significantly more words than participants who learn the list with background noise.' A non‑directional hypothesis simply predicts a difference without specifying the direction: 'There will be a significant difference in recall between silent and noise conditions.' The hypothesis must always mention the independent variable (IV) and the dependent variable (DV).
假设是一个可检验的预测性陈述，说明研究的预期结果。在 Edexcel 心理学中，你必须会写方向性（单尾）和非方向性（双尾）备择假设。方向性假设明确指出结果的方向，例如：“在安静环境中学习单词列表的参与者比在有背景噪音中学习的参与者回忆出的单词显著更多。”非方向性假设只预测存在差异而不指明方向，例如：“安静与噪音条件下的回忆量存在显著差异。”假设必须始终提到自变量 (IV) 和因变量 (DV)。
2. Null Hypothesis Formulation | 零假设公式
The null hypothesis is the default position that any observed effect is due to chance. It always predicts 'no significant difference' (for an experiment) or 'no significant correlation' (for a correlational study). A typical null hypothesis format is: 'There will be no significant difference in [DV] between [IV condition A] and [IV condition B]; any difference found will be due to chance.' For example: 'There will be no significant difference in word recall between the silent and noise conditions; any difference is due to chance.' Every statistical test decision relates back to whether the null hypothesis can be rejected.
零假设是默认立场，认为任何观察到的效应都是由偶然引起的。它总是预测“无显著差异”（对于实验）或“无显著相关”（对于相关研究）。典型的零假设格式是：“在 [IV 条件 A] 和 [IV 条件 B] 之间，[DV] 没有显著差异；发现的任何差异均归因于偶然。”例如：“安静与噪音条件下的单词回忆量没有显著差异；任何差异均归因于偶然。”每个统计检验的决策都与能否拒绝零假设有关。
3. Measures of Central Tendency | 集中趋势测量公式
cores. This can be written as: Mean = Σx ÷ n, where Σx is the total of all scores and n is the number of scores. The median is the middle value when the data are arranged in order; if there is an even number of scores, the median is the average of the two central numbers. The mode is the most frequently occurring score in the data set. Choosing the correct measure depends on the level of measurement and the presence of outliers.
集中趋势的三种主要测量是平均数、中位数和众数。平均数通过将所有分数相加再除以分数的个数来计算，写法为：平均数 = Σx ÷ n，其中 Σx 是所有分数之和，n 是分数的个数。中位数是将数据按顺序排列后的中间值；如果分数个数为偶数，中位数是中间两个数的平均值。众数是数据集中出现次数最多的分数。选择正确的测量方式取决于测量水平和是否存在异常值。
4. Measures of Dispersion | 离散趋势测量公式
s calculated by subtracting the lowest score from the highest score: Range = highest value – hile the range is easy to compute, it can be heavily influenced by outliers. In GCSE Psychology you may also interpret data that shows the interquartile range, but you are not required to calculate it by formula.
极差是最简单的离散趋势测量方式，显示分数的分布宽度。它的计算方式是用最高分减去最低分：极差 = 最高值 − 最低值。例如，如果记忆测试最高分是 18，最低分是 5，极差就是 13。极差越大说明变异性越大。虽然极差容易计算，但它很容易受异常值的影响。在 GCSE 心理学中，你可能会分析显示四分位距的数据，但不要求用公式计算。
5. Percentages, Fractions and Ratios | 百分比、分数与比率
s, fractions or ratios to make comparisons easier. The percentage formula is: Percentage (% out of 50 participants recalled at least 10 words, the percentage is (15 ÷ 50) × 100 = 30% orrect responses could be 7:3. Being able to move between these forms is an essential numeracy skill in psychology.
在报告结果时，心理学家经常将原始频率转换为百分比、分数或比率，以便于比较。百分比公式为：百分比 (%) = (部分 ÷ 整体) × 100。例如，如果 50 名参与者中有 15 人回忆出至少 10 个单词，则百分比为 (15 ÷ 50) × 100 = 30%。分数直接写作部分/整体，例如 3/10。比率比较两个同类量，写作部分 : 部分，例如正确反应与错误反应的比可能是 7:3。能够在这些形式之间切换是心理学中必不可少的数字技能。
6. Correlational Direction | 相关分析方向
A correlation describes the strength and direction of a relationship between two co‑variables. A positive correlation means that as one co‑variable increases, the other also increases (e.g. hours of revision and exam score). A negative correlation means that as one co‑variable increases, the other decreases (e.g. hours spent on social media and concentration score). Zero correlation indicates no linear relationship. In GCSE Psychology you do not calculate a correlation coefficient by formula, but you must be able to plot a scatter graph and draw a line of best fit, then describe the direction. Remember: correlation does not imply causation.
相关描述的是两个协变量之间关系的强度和方向。正相关意味着当一个协变量增加时，另一个也增加（例如复习时间和考试分数）。负相关意味着当一个协变量增加时，另一个减少（例如花在社交媒体上的时间和注意力得分）。零相关表示没有线性关系。在 GCSE 心理学中，不要求用公式计算相关系数，但你必须能够绘制散点图、画一条最佳拟合线，然后描述方向。切记：相关关系不等于因果关系。
7. Multi‑store Model of Memory (Atkinson & Shiffrin, 1968) | 记忆多存储模型定理
model proposes that memory consists of three separate stores: the sensory register, short‑term memory (STM) and long‑ sses to STM, which has a limited capacity (around 7±2 items) and a short duration (about 18– city and duration. Encoding differs across stores: the sensory register encodes in modality‑ encoding. The model is supported by evidence from case studies such as HM and from serial‑position effect experiments, though it has been criticised for over‑simplifying memory processes.
这一有影响力的认知模型提出，记忆由三个分离的存储系统组成：感觉登记器、短时记忆 (STM) 和长时记忆 (LTM)。信息通过感官进入感觉登记器，持续时间不到一秒。如果受到注意，信息便进入 STM，STM 的容量有限（约为 7±2 个项目），持续时间也短（约 18–30 秒），除非进行复述。复述起到维持作用，可以将材料转入 LTM，LTM 的容量和持续时间可能是无限的。各个存储器的编码方式不同：感觉登记器以模态特定形式编码（图像式、声象式），STM 主要使用声学编码，而 LTM 则主要依赖语义编码。该模型得到来自 HM 等的个案研究和系列位置效应实验的支持，但也因过于简化记忆过程而受到批评。
8. Piaget’s Stages of Cognitive Development | 皮亚杰认知发展阶段定理
Jean Piaget’s theory proposes that children’s thinking develops through four invariant, universal stages. The sensorimotor stage (birth to 2 years) is characterised by learning through senses and actions, with the development of object permanence—understanding that objects exist even when not seen. The pre‑operational stage (2 to 7 years) sees the use of symbols and language but thinking is egocentric; children struggle with conservation tasks because they cannot perform logical operations. The concrete operational stage (7 to 11 years) brings logical thinking about concrete events, with mastery of conservation and classification, though abstract reasoning is still difficult. The formal operational stage (11+ years) witnesses the emergence of abstract, systematic reasoning such as hypothesis testing. Piaget’s research, including the three‑mountains task and conservation experiments, provides key evidence, but modern researchers note that development may be more continuous than the stage model implies.
让·皮亚杰的理论提出，儿童的思维发展经历四个不变的、普遍适用的阶段。感知运动阶段（0–2 岁）的特点是通过感官和动作学习，并发展出客体永久性——理解物体即使看不见也依然存在。前运算阶段（2–7 岁）开始使用符号和语言，但思维是自我中心的；儿童难以完成守恒任务，因为他们还不能进行逻辑运算。具体运算阶段（7–11 岁）带来了关于具体事物的逻辑思维，能够掌握守恒和分类，但抽象推理仍然困难。形式运算阶段（11 岁以上）出现了抽象系统性推理，如假设检验。皮亚杰的研究（包括三山实验和守恒实验）提供了关键证据，但现代研究者指出，发展可能比阶段模型所暗示的更具连续性。
9. Asch’s Conformity Theory (1951) | 阿希从众理论
Solomon Asch’s classic line‑judgement experiment demonstrated the power of normative social influence—the desire to fit in with the group. In the study, confederates deliberately gave obviously wrong answers about the length of lines. About 75% of true participants conformed at least once, and the overall conformity rate was around 37%. Factors affecting conformity included group size (conformity increased up to a group of three confederates, then levelled off), unanimity (if one confederate broke the agreement, conformity dropped sharply) and task difficulty (when lines were more similar, conformity rose). Asch’s work remains a core study for the Edexcel social influence topic, illustrating that people may publicly agree with a group while privately disagreeing—a behaviour known as compliance.
所罗门·阿希的经典线条判断实验展示了规范性社会影响的力量——渴望与群体保持一致。在研究中，同谋者故意给出关于线条长度的明显错误答案。大约 75% 的真正参与者至少从众了一次，总体从众率约为 37%。影响从众的因素包括群体规模（从众行为在三个同谋者时达到最高，之后趋于平稳），一致性（如果有一个同谋者打破了全体一致，从众急剧下降）和任务难度（当线条更相似时，从众增加）。阿希的研究仍然是 Edexcel 社会影响专题的核心研究，它说明人们可能会公开同意群体意见，而私下却持不同看法——这种行为被称为顺从。
10. Brain Localisation of Function | 大脑功能定位定理
The theory of localisation argues that specific psychological functions are associated with particular brain areas. Two classic language areas are central: Broca’s area, located in the left frontal lobe, is responsible for speech production; damage results in Broca’s aphasia, where speech becomes slow and lacking in fluency but comprehension is largely intact. Wernicke’s area, in the left temporal lobe, controls language comprehension; damage leads to Wernicke’s aphasia, producing fluent but meaningless speech and poor understanding. Evidence for localisation includes case studies like Phineas Gage, who suffered frontal lobe damage and showed personality changes, and modern brain‑scanning techniques such as fMRI and PET scans. However, critics note that complex functions often involve distributed networks rather than isolated regions, a viewpoint known as the holistic theory of brain function.
功能定位理论认为，特定的心理功能与特定的大脑区域相关。两个经典的语言区至关重要：布罗卡区位于左额叶，负责言语产出；该区受损会导致布罗卡失语症，表现为言语缓慢、不流利，但理解能力基本完好。韦尼克区位于左颞叶，控制语言理解；受损会导致韦尼克失语症，产生流利但无意义的言语，理解力差。支持定位的证据包括像菲尼亚斯·盖奇这样的个案研究（他额叶受损后人格发生变化），以及现代脑成像技术如 fMRI 和 PET 扫描。然而，批评者指出，复杂功能往往涉及分布式网络而非孤立区域，这种观点被称为大脑功能的整体论。
11. Ethical Guidelines as Principles | 心理学伦理准则定理
Ethical guidelines function as a set of core theorems for conducting psychological research responsibly. In the UK, the British Psychological Society (BPS) sets out key principles: informed consent (participants must know the aims and agree to take part), right to withdraw (participants can leave at any time without penalty), deception should be avoided or minimised, and a full debrief must be given afterwards explaining the true nature of the study. Confidentiality must be protected and participants should be shielded from physical or psychological harm. For GCSE examinations, you must be able to apply these principles to hypothetical studies, recognise ethical issues in classic experiments and suggest appropriate improvements. Ethical reasoning is therefore just as systematic as the statistical formulas you learn.
伦理准则好比一套核心定理，用于负责任地开展心理学研究。在英国，英国心理学会 (BPS) 规定了关键原则：知情同意（参与者必须知晓研究目的并同意参与）、退出权（参与者可随时退出而不受惩罚）、应避免或尽量减少欺骗，事后必须进行完整的解释，说明研究的真实性质。必须保护隐私，参与者应免受身体或心理上的伤害。在 GCSE 考试中，你必须能够将这些原则应用于假设的研究情境，识别经典实验中的伦理问题，并提出恰当的改进措施。因此，伦理推理与你所学的统计公式一样具有系统性。
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