📚 GCSE OCR Psychology: Quick Reference Handbook of Formulas and Theorems | GCSE OCR 心理学：公式定理速查手册
This quick reference handbook brings together all the essential formulas, statistical tests, data descriptors and key psychological theorems required for GCSE OCR Psychology. Whether you are analysing quantitative data, running inferential statistics or recalling core theoretical models, this guide serves as your exam-ready cheat sheet. Use it to refresh your memory, check calculations and reinforce your understanding of the research methods strand.
这本速查手册汇集了 GCSE OCR 心理学考试中所有必备的公式、统计检验方法、数据描述指标以及核心的心理学定理。无论你是在分析量化数据、进行推断统计，还是回忆重要的理论模型，这本指南都将成为你备考时的便捷速查表。用它来巩固记忆、核对运算步骤，并加深对研究方法板块的理解。
1. Mean, Median, Mode and Range | 平均数、中位数、众数与全距
The mean is the arithmetic average: add all the values together and divide by the number of values. The median is the middle score when the data are arranged in order; if there is an even number of scores, take the mean of the two middle values. The mode is the most frequently occurring value in the data set. The range tells you how spread out the data are and is calculated as the highest score minus the lowest score.
平均数即算术平均值：把所有数值相加，再除以数值的个数。中位数是将数据按顺序排列后位于最中间的数值；如果有偶数个数据，则取中间两个数的平均数。众数是数据集中出现频率最高的数值。全距反映数据的分散程度，计算方法是最高分减去最低分。
+20+22)÷6 = 17. The median is (15+18)÷2 = 16.5. The mode is 15. The range is 22 − 12 = 10.
示例：对于数据集 12、15、15、18、20、22，平均数为 (12+15+15+18+20+22)÷6 = 17。中位数为 (15+18)÷2 = 16.5。众数是 15。全距为 22 − 12 = 10。
2. Percentages, Ratios and Fractions | 百分比、比率与分数
antities and can be simplified by dividing both sides by common factors, for example 8:4 becomes 2:1. Fractions show a part of a whole with a numerator and a denominator; they can be converted to percentages by multiplying by 100.
百分比用来表示每一百中的比例：百分比 = (部分 ÷ 总体) × 100。比率用于比较两个或更多数量，可以通过两边除以公因数来化简，例如 8:4 可化为 2:1。分数用分子和分母表示整体的一部分，将其乘以 100 即可转化为百分比。
In psychological investigations, you might be asked to report the percentage of participants who showed a particular response, or give a ratio of males to females in a sample. Always present ratios in their simplest form.
在心理学研究中，你可能需要报告出现某种反应的被试百分比，或者给出样本中男性与女性的比率。务必以最简形式呈现比率。
3. Percentage Change | 百分比变化
ginal value) ÷ original value) × 100. If the result is positive, it indicates an increase; a negative result indicates a decrease.
百分比变化用于比较随时间或在条件之间发生的变化大小。公式为：百分比变化 = ((新数值 − 原始数值) ÷ 原始数值) × 100。结果为正表示增加，结果为负表示减少。
For example, if a participant' 28 after a mindfulness intervention, the percentage change is ((28 − 40) ÷ 40) × 100 = −30%, meaning a 30% reduction.
例如，某被试在接受正念干预后，焦虑分数从 40 降至 28，则百分比变化为 ((28 − 40) ÷ 40) × 100 = −30%，即下降了 30%。
4. The Normal Distribution | 正态分布
A normal distribution produces a bell-shaped curve that is symmetrical about the mean. In a perfect normal distribution, the mean, median and mode all have the same value. Most scores cluster around the centre, and the frequency of scores decreases symmetrically towards both tails. The curve is defined by its shape, centre and spread (standard deviation).
正态分布生成一条钟形曲线，关于平均数对称。在理想的正态分布中，平均数、中位数和众数恰好重合。大部分分数聚集在中心附近，向两侧尾部对称递减。曲线由其形状、中心位置和离散程度（标准差）来定义。
GCSE students should recognise that many psychological variables — such as IQ, reaction times in large samples or self-report scores — can approximate a normal distribution. This understanding helps when interpreting statistical tests and assessing the probability of obtaining a particular score.
GCSE 学生应认识到，许多心理学变量——例如智商、大样本中的反应时或自评量表得分——可近似服从正态分布。这一认识有助于理解统计检验以及评估得到特定分数的概率。
5. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s rho (ρ) is a non-parametric inferential test for a correlation or association between two co-variables measured on at least ordinal scales. The formula is:
斯皮尔曼等级相关系数 ρ 是一种非参数推断检验，用于检验两个至少是顺序尺度测量的共变量之间的相关或关联。其公式为：
ρ = 1 − (6∑d²) / (n(n² − 1))
of pairs. Steps: rank each set of data separately (giving 1 to the highest or lowest, consistently), find the difference between the ranks for each pair, square these differences (d²), sum them, and substitute into the formula. The result ranges from +1 (perfect positive correlation) to −1 (perfect negative correlation); 0 indicates no correlation.
其中 d = 每对分数的等级差，n = 数据对的数量。步骤：分别对两组数据进行排序并赋予等级（一致地将最高或最低值定为 1），求出每对等级差 d，将其平方 (d²)，求和，再代入公式。结果范围为 +1（完全正相关）至 −1（完全负相关），0 表示无相关。
0.05). If ρ is greater than or equal to the critical value, the correlation is statistically significant and the null hypothesis can be rejected.
接着将计算所得的 ρ 值与所选显著性水平（通常为 p ≤ 0.05）下的临界值表进行比较。若 ρ 大于或等于临界值，则相关具有统计显著性，可以拒绝零假设。
6. Chi-Square Test of Association | 卡方关联性检验
The chi-square (χ²) test is used to analyse nominal (categorical) data and determines whether there is a significant association between two independent variables. The formula is:
卡方 (χ²) 检验用于分析名称（分类）数据，判断两个自变量之间是否存在显著关联。其公式为：
χ² = ∑((O − E)² / E)
grees of freedom (df) = (number of rows − 1) × (number of columns − 1). After calculating χ², compare it with the critical value from a chi-square table for the appropriate df and significance level (usually p ≤ 0.05).
O = 观察频数，E = 期望频数。每个单元格的期望频数 = (行合计 × 列合计) ÷ 总计。自由度 (df) = (行数 − 1) × (列数 − 1)。计算出 χ² 后，将其与对应自由度和显著性水平（通常为 p ≤ 0.05）的卡方临界值表进行比较。
ificant association and the null hypothesis is rejected. This test is frequently used in observational studies or questionnaire data where counts of participants are placed into categories (e.g. smokers vs non-smokers and whether they exercise).
若 χ² ≥ 临界值，则存在显著关联，拒绝零假设。该检验常用于观察研究或问卷数据，将被试计数放入不同类别中（例如吸烟者与不吸烟者是否锻炼）。
7. Inferential Statistics: Significance, p-value and Critical Value | 推断统计：显著性、p 值与临界值
Inferential tests start with two hypotheses: the null hypothesis (H₀) states there is no effect, no difference or no correlation; the alternative hypothesis (H₁ or Hₐ) states there is an effect or relationship. The p-value is the probability that the observed result (or a more extreme one) occurred by chance if the null hypothesis is true.
推断检验从两个假设开始：零假设 (H₀) 表明无效应、无差异或无相关；备择假设 (H₁ 或 Hₐ) 表明存在效应或关系。p 值是在零假设成立的情况下，观察到当前结果（或更极端结果）由偶然因素造成的概率。
GCSE Psychology, the conventional significance level is p ≤ 0.05. This means there is a 5% e critical value, the result is significant; you reject the null hypothesis. Remember that 'significant' he outcome is unlikely to be due to chance, not that it is necessarily large or important.
在 GCSE 心理学中，常规的显著性水平为 p ≤ 0.05。这意味着做出存在效应的结论、而实际并无效应的风险为 5% 或更低。如果计算所得的检验统计量等于或大于临界值，则结果显著，可以拒绝零假设。请记住，“显著”在统计语境中表示该结果不太可能是偶然造成的，而不一定表示效应很大或重要。
8. Types of Data: Nominal, Ordinal and Interval | 数据类型：定类、定序与定距
Nominal data represent categories with no inherent order (e.g. gender, handedness, eye colour). Ordinal data can be placed in rank order but the intervals between ranks are not necessarily equal (e.g. attitude ratings, class position). Interval data have equal intervals between units but no true zero point; in psychology, many scale scores are treated as interval data (e.g. IQ scores, temperature ratings).
定类数据表示无内在顺序的类别（如性别、利手、眼睛颜色）。定序数据可以排序，但每个等级之间的间距并不一定相等（如态度评分、班级排名）。定距数据具有相等的单位间距，但没有真正的零点；在心理学中，许多量表分数被视为定距数据（如 IQ 分数、温度评分）。
Choosing the correct inferential test depends on the data type. Spearman’s rho is suitable for ordinal data (or when data are converted to ranks). Chi-square is designed for nominal frequency data. Recognising your data level is one of the first steps in a valid statistical analysis.
选择正确的推断检验取决于数据类型。斯皮尔曼 ρ 适用于定序数据（或当数据转换为等级时）。卡方检验专为定类频数数据设计。识别你的数据测量水平是进行有效统计分析的第一步。
9. Ethical Principles | 伦理原则
Although not a formula in the mathematical sense, ethical principles form a set of essential 'theorems' that guide all psychological research. According to the British Psychological Society (BPS) guidelines, researchers must gain informed consent from participants, protect them from physical and psychological harm, offer the right to withdraw at any time, maintain confidentiality of personal data, and debrief participants fully after the study. If deception is necessary, it must be justified and debriefing is mandatory.
虽然在数学意义上算不上公式，但伦理原则构成了一套指导所有心理学研究的核心“定理”。根据英国心理学会 (BPS) 的指南，研究者必须获得被试的知情同意，保护他们免受身心伤害，提供随时退出的权利，对个人信息保密，并在研究结束后给予完整的事后说明。若必须采用欺骗手段，则必须提供合理理由，并且事后的解释说明不可或缺。
These ethical 'rules' are non-negotiable and are tested in GCSE questions about research design and evaluation. You should be ready to spot ethical issues in scenarios and suggest how they could be resolved.
这些伦理“法则”不容商量，并且会在 GCSE 有关研究设计与评估的题目中考查。你应当能够识别情景中的伦理问题，并提出如何加以解决。
10. Key Psychology Theories in Brief | 心理学核心理论速览
Memory: The Multi-Store Model (Atkinson & Shiffrin) proposes three stores — sensory register, short-term memory (STM) and long-term memory (LTM) — linked by attention and rehearsal. The Working Memory Model (Baddeley & Hitch) expands STM into the central executive, phonological loop, visuospatial sketchpad and episodic buffer.
记忆：多存储模型 (Atkinson & Shiffrin) 提出感觉登记、短时记忆和长时记忆三个存储系统，通过注意和复述相联系。工作记忆模型 (Baddeley & Hitch) 将短时记忆扩展为中央执行系统、语音环、视空间模板和情景缓冲器。
Social Influence: Milgram’s Agency Theory suggests people shift between autonomous and agentic states under authority. Situational factors (uniform, location, proximity) and dispositional factors (authoritarian personality) both influence obedience. Conformity is explained by informational and normative social influence.
社会影响：Milgram 的代理人状态理论指出，个体在面对权威时会在自主状态与代理人状态之间切换。情境因素（制服、地点、距离）和个体因素（权威主义人格）都会影响服从。从众行为可由信息性社会影响和规范性社会影响加以解释。
Psychological Problems: Explanations for mental health issues draw on biological (genetics, neurochemistry), psychological (cognitive biases, learning) and social (life events, cultural pressure) perspectives. Treatments range from biological (medication) to psychological (CBT, systematic desensitisation) and social interventions.
心理问题：对心理健康问题的解释涉及生物学（遗传、神经化学）、心理学（认知偏差、学习）和社会角度（生活事件、文化压力）。治疗方式包括生物疗法（药物）、心理疗法（CBT、系统脱敏）以及社会干预。
Criminal Psychology: Eysenck’s PEN theory links criminality to high extraversion, neuroticism and psychoticism. Social Learning Theory proposes criminal behaviour is acquired through observation and reinforcement. Rehabilitation strategies include token economy programmes and cognitive behavioural interventions.
犯罪心理学：Eysenck 的 PEN 理论将犯罪倾向与高外向性、高神经质和高精神质联系在一起。社会学习理论认为犯罪行为通过观察和强化习得。矫治策略包括代币制方案和认知行为干预。
Development: Piaget’s stages outline cognitive development from sensorimotor to formal operations. Vygotsky emphasised the zone of proximal development and scaffolding. Additionally, brain development during adolescence — especially the maturation of the prefrontal cortex — explains risk-taking and identity formation.
发展：Piaget 的阶段论阐述了从感知运动阶段到形式运算阶段的认知发展。Vygotsky 强调最近发展区和支架作用。此外，青春期大脑发育——尤其是前额叶皮质的成熟——可以解释冒险行为和同一性的形成。
The above summaries capture only the skeleton; you are expected to refer to specific studies and details in your exam answers.
上述总结仅为框架；考试答题时你需要引用具体研究并补充细节。
Published by TutorHao | Psychology Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图