📚 IGCSE OCR Psychology: Formula & Theorem Quick Reference | IGCSE OCR 心理学：公式定理速查手册
This quick-reference handbook compiles the essential formulas, statistical tests, and theoretical ‘theorems’ that every IGCSE OCR Psychology student needs to master for the exam. From descriptive statistics to classical conditioning models, each entry is presented as a clear statement or equation with paired English and Chinese explanations.
这本速查手册汇集了每一位 IGCSE OCR 心理学考生必须掌握的核心公式、统计检验和理论”定理”。从描述统计到经典条件反射模型，每一个条目都以清晰的陈述或方程呈现，并配有中英文对照解释。
1. Measures of Central Tendency | 集中趋势测度
The mean is the arithmetic average of a set of scores. It is calculated by summing all the values and dividing by the total number of values.
Mean = Σx ÷ N
平均数是所有分数的算术平均值，用总和除以值的个数。
The median is the middle score when data are arranged in rank order. If there are an even number of scores, take the average of the two middle scores.
中位数是数据按顺序排列后位于中间的分数。如果个数为偶数，则取中间两个分数的平均值。
The mode is the most frequently occurring score in a data set. A set may have more than one mode (bimodal) or no mode at all.
众数是数据集中出现次数最多的分数。一个数据集可能有一个以上的众数（双峰），也可能没有众数。
2. Measures of Dispersion | 离散度测度
The range is the simplest measure of spread, found by subtracting the lowest score from the highest score.
Range = Highest Score – Lowest Score
范围是最简单的离散测度，用最高分减去最低分。
Standard deviation (s) shows how much scores deviate from the mean. For a sample, the formula uses n-1 to give an unbiased estimate.
s = √( Σ(x – x̄)² ÷ (n – 1) )
标准差 (s) 表示分数与平均数的偏离程度。对于样本，公式使用 n-1 以给出无偏估计。
A larger standard deviation indicates greater variability in the data set; a smaller one indicates scores are clustered closely around the mean.
标准差越大说明数据变异性越大；越小说明分数紧密聚集在平均数周围。
3. Chi-Square Test of Association | 卡方关联性检验
State the null hypothesis (H₀): there is no association between the two categorical variables. The alternative hypothesis (H₁) states there is an association.
陈述零假设 (H₀)：两个类别变量之间没有关联。备择假设 (H₁) 表示有关联。
Calculate expected frequency (E) for each cell: E = (Row Total × Column Total) ÷ Grand Total.
E = (Row Total × Column Total) ÷ Grand Total
计算每个单元格的期望频数 (E)：E = (行合计 × 列合计) ÷ 总计。
Apply the chi-square formula using observed (O) and expected (E) frequencies.
χ² = Σ((O – E)² ÷ E)
使用观察频数 (O) 和期望频数 (E) 代入卡方公式。
Degrees of freedom (df) = (number of rows – 1) × (number of columns – 1). Compare the calculated χ² value with the critical value from a table at the chosen significance level (usually p < 0.05).
自由度 (df) = (行数 – 1) × (列数 – 1)。将计算出的 χ² 值与选定显著性水平（通常 p < 0.05）的临界值表中的数值进行比较。
4. Mann-Whitney U Test | 曼-惠特尼U检验
The Mann-Whitney U test is used for independent groups designs and ordinal (or non-normal interval) data. It tests whether there is a significant difference between two conditions.
曼-惠特尼 U 检验用于独立组设计以及定序（或非正态区间）数据，检验两种条件之间是否存在显著差异。
Rank all the scores from both groups together (1 = lowest). Sum the ranks for each group: R₁ for group 1 and R₂ for group 2. n₁ and n₂ are the sample sizes.
将两组合并后对所有分数排序（1为最低）。分别计算各组的秩和：R₁（组1）和 R₂（组2）。n₁ 和 n₂ 为样本量。
Use the formulas to find U₁ and U₂. The smaller U value is the test statistic.
U₁ = R₁ – (n₁(n₁ + 1) ÷ 2)
U₂ = R₂ – (n₂(n₂ + 1) ÷ 2)
用公式计算 U₁ 和 U₂。较小的 U 值为检验统计量。
Compare the smaller U with the critical U value. If the calculated U is less than or equal to the critical value, the result is significant.
将较小的 U 值与临界 U 值比较。如果计算出的 U 值小于或等于临界值，结果显著。
5. Wilcoxon Signed-Rank Test | 威尔科克森符号秩检验
This test is used for repeated measures or matched pairs designs with ordinal data. It examines whether there is a significant difference between two related sets of scores.
该检验用于重复测量或配对设计且数据为定序数据，考察两组相关分数之间是否存在显著差异。
For each pair, calculate the difference score (D = Score₂ – Score₁). Ignore any zero differences. Rank the absolute differences, giving the smallest a rank of 1.
对每一对计算差值 (D = 分数₂ – 分数₁)。忽略差值为零的情况。对差值的绝对值进行排序，最小的赋予秩次 1。
Sum the ranks for positive differences (W⁺) and negative differences (W⁻). The test statistic W is the smaller of these two sums.
分别计算正差值秩和 (W⁺) 与负差值秩和 (W⁻)。检验统计量 W 是两者中较小的那个。
Compare W with the critical value for the given number of non-zero differences (N). If W ≤ critical value, the result is significant at that level.
将 W 与给定非零差值个数 (N) 的临界值比较。如果 W ≤ 临界值，则该水平上结果显著。
6. Spearman’s Rank Correlation | 斯皮尔曼等级相关
Spearman’s rho (rₛ) measures the strength and direction of a relationship between two sets of ordinal data. Values range from -1 (perfect negative) to +1 (perfect positive).
斯皮尔曼等级相关系数 (rₛ) 衡量两组定序数据之间关系的强度和方向。取值范围从 -1（完全负相关）到 +1（完全正相关）。
Rank each variable separately. For each pair, find the difference (d) between the two ranks. Square each d and sum them (Σd²). n is the number of pairs.
分别对每个变量排序。对每一对计算两个秩次之差 (d)。求每个 d 的平方并求和 (Σd²)。n 为对数。
rₛ = 1 – (6Σd² ÷ n(n² – 1))
Compare the obtained rₛ with the critical value from the Spearman table. If rₛ > critical value, the correlation is significant.
将得到的 rₛ 与斯皮尔曼表中的临界值进行比较。如果 rₛ > 临界值，相关显著。
7. Significance, Probability and Errors | 显著性、概率与错误
The significance level (α) is usually set at 0.05. If p ≤ 0.05, the null hypothesis is rejected, meaning the result is statistically significant.
显著性水平 (α) 通常设为 0.05。如果 p ≤ 0.05，则拒绝零假设，这意味着结果在统计上显著。
A Type I error occurs when the null hypothesis is rejected when it is true (a false positive).
第一类错误发生在零假设为真却被拒绝时（假阳性）。
A Type II error occurs when the null hypothesis is retained when the alternative hypothesis is true (a false negative).
第二类错误发生在备择假设为真却保留了零假设（假阴性）。
Probability is not the same as effect size or practical significance. Rejecting the null only suggests the result is unlikely due to chance alone.
概率不等于效应量或实际显著性。拒绝零假设仅仅表明该结果不太可能仅由偶然因素引起。
8. Operationalising Variables | 变量操作化
The independent variable (IV) is the factor the researcher manipulates. The dependent variable (DV) is the factor that is measured.
自变量 (IV) 是研究者操控的因素。因变量 (DV) 是测量的因素。
To operationalise a variable means to define it precisely in terms of how it will be manipulated or measured. For example, ‘aggression’ could be operationalised as number of shouts or time spent on a loud button.
对变量进行操作化意味着根据如何操控或测量来精确定义它。例如，”攻击性”可被操作化为喊叫次数或按压高声按钮的时间。
A testable hypothesis must include clearly operationalised IV and DV. A simple formula: ‘There will be a significant difference in [DV] between [IV condition 1] and [IV condition 2].’
一个可检验的假设必须包含清晰操作化的 IV 和 DV。一个简单的公式：”在 [DV] 上，[IV 条件1] 和 [IV 条件2] 之间存在显著差异。”
9. Classical Conditioning Formula | 经典条件反射公式
Before conditioning, the unconditioned stimulus (UCS) naturally elicits an unconditioned response (UCR). A neutral stimulus (NS) produces no specific response.
UCS → UCR
条件反射形成前，无条件刺激 (UCS) 自然引发无条件反应 (UCR)。中性刺激 (NS) 不引发特定反应。
During conditioning, the NS is repeatedly paired with the UCS just before the response.
NS + UCS → UCR
条件反射形成中，NS 在反应前反复与 UCS 配对。
After conditioning, the NS becomes a conditioned stimulus (CS) and now elicits the conditioned response (CR), which is similar to the UCR.
CS → CR
条件反射形成后，NS 成为条件刺激 (CS)，并引发条件反应 (CR)，该反应与 UCR 相似。
Extinction occurs when the CS is repeatedly presented without the UCS, causing the CR to weaken.
CS alone → gradual disappearance of CR
当 CS 反复单独出现而没有 UCS 时，就发生消退，导致 CR 减弱。
10. Operant Conditioning Schedules | 操作性条件反射程式
Positive reinforcement: a desirable stimulus is added after a behaviour, increasing the likelihood of that behaviour.
Behaviour → Addition of pleasant stimulus → Behaviour strengthened
正强化：行为后加入愉快刺激，增加该行为发生的可能性。
Negative reinforcement: an unpleasant stimulus is removed after a behaviour, also strengthening the behaviour.
Behaviour → Removal of aversive stimulus → Behaviour strengthened
负强化：行为后移除厌恶刺激，同样能强化该行为。
Punishment: an unpleasant consequence follows a behaviour, reducing the likelihood of that behaviour.
Behaviour → Addition of aversive stimulus (positive punishment) → Behaviour weakened
惩罚：行为后跟随不愉快后果，减少该行为发生的可能性。
Schedules of reinforcement affect how quickly a behaviour is learned and how resistant it is to extinction. Continuous reinforcement is when every correct response is reinforced.
强化程式影响行为学习的速度和对消退的抗性。连续强化是指每次正确反应都得到强化。
11. Multi-Store Model of Memory | 记忆的多存储模型
The Atkinson-Shiffrin model proposes three separate stores: sensory memory, short-term memory (STM), and long-term memory (LTM).
阿特金森-希夫林模型提出了三个独立的存储：感觉记忆、短时记忆 (STM) 和长时记忆 (LTM)。
Information flows in a linear sequence: environmental stimulus → sensory memory → (attention) → STM → (elaborative rehearsal) → LTM.
Stimulus → Sensory Memory → Attention → Short-Term Memory → Rehearsal → Long-Term Memory
信息按线性顺序流动：环境刺激 → 感觉记忆 → （注意）→ 短时记忆 → （精细复述）→ 长时记忆。
Without attention, sensory memory decays rapidly (iconic memory in about 0.5 sec, echoic in about 2 sec). Without rehearsal, STM traces fade within about 18-30 seconds and are lost through displacement.
没有注意，感觉记忆迅速衰退（图像记忆约0.5秒，声象记忆约2秒）。没有复述，STM痕迹约在18-30秒内衰退，并通过替代而丢失。
Rehearsal is the key process that maintains information in STM and transfers it to LTM, which has unlimited capacity and duration.
复述是将信息保持在STM并传输至LTM的关键过程，LTM具有无限容量和持续时间。
12. Agency Theory and Obedience | 代理状态理论与服从
Milgram’s agency theory proposes that people operate in either an autonomous state, where they direct their own actions, or an agentic state, where they act as an agent for an authority figure.
米尔格拉姆的代理状态理论提出，人们要么处于自主状态，自己指挥行动，要么处于代理状态，作为权威人物的代理人行动。
The agentic shift occurs when an individual moves from the autonomous state to the agentic state. This shift is accompanied by moral strain — the discomfort felt when obeying orders that conflict with one’s conscience.
当个体从自主状态转向代理状态时发生代理转移。伴随这种转移出现道德紧张——在服从与良心相悖的命令时感受到的不适。
According to the theory, obedience is a function of being in the agentic state. Individuals assign responsibility for their actions to the authority, thus diffusing their own personal responsibility.
Autonomous State → (Legitimate Authority + Binding Factors) → Agentic State → Obedience + Moral Strain
根据该理论，服从是处于代理状态的结果。个体将行动的责任归于权威，从而分散了自己的个人责任。
Binding factors such as politeness, fear of disrupting the experiment, or the gradual nature of the requests keep the person in the agentic state and increase obedience.
约束因素，如礼貌、害怕干扰实验或要求的渐进性，使人保持在代理状态并增加服从。
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