📚 Year 12 WJEC Psychology: Formula & Theorem Quick Reference Handbook | WJEC 心理学公式定理速查手册
This quick-reference handbook brings together essential formulas, statistical tests, and key theoretical models that you need for success in WJEC AS Psychology (Year 12). It covers the mathematical underpinnings of research methods, step-by-step calculations for non-parametric tests, and concise formulations of influential psychological laws. Each entry is presented in plain language with the formal statement, so you can use it for both revision and exam preparation.
本速查手册汇集了 WJEC AS 心理学（12 年级）取得好成绩所需的关键公式、统计检验和重要理论模型。手册涵盖研究方法的数学基础、非参数检验的分步计算以及有影响力的心理学定律的简明表述。每个条目均以通俗易懂的语言呈现，并搭配规范陈述，方便你用于复习和备考。
1. Yerkes-Dodson Law | 耶克斯-多德森定律
The Yerkes-Dodson Law states that performance increases with physiological or mental arousal, but only up to a point. When arousal becomes too high, performance deteriorates. The relationship forms an inverted U-shaped curve. The optimal level of arousal is lower for complex or cognitively demanding tasks and higher for simple or well-practised tasks.
耶克斯-多德森定律指出，表现会随着生理或心理唤醒水平的提高而提高，但只提高到一定程度。当唤醒水平过高时，表现反而会下降。这种关系呈倒 U 形曲线。对于复杂或认知要求高的任务，最佳唤醒水平较低；对于简单或熟练的任务，最佳唤醒水平较高。
Practical implication: Moderate stress can enhance exam performance, whereas excessive anxiety impairs recall. This model is often cited when evaluating the effects of arousal on eyewitness testimony accuracy.
实际意义：适度压力可以提升考试成绩，但过度焦虑会损害回忆能力。在评估唤醒水平对目击者证词准确性的影响时，常引用该模型。
2. Social Impact Theory Formula | 社会影响理论公式
Latané’s social impact theory proposes that the impact (i) of a source on a target is a multiplicative function of three factors: Strength (S), Immediacy (I), and Number (N). Symbolically, i = f(S × I × N). When any one factor approaches zero, the overall social impact diminishes sharply. The theory also describes the psychosocial law: as the number of sources increases, each additional source has a progressively smaller influence, producing a negatively accelerating power function.
拉塔内社会影响理论提出，影响源对目标产生的社会影响（i）是三个因素的乘积函数：强度 (S)、即时性 (I) 和数量 (N)。用符号表示为 i = f(S × I × N)。当任一因素趋近于零时，总社会影响力会急剧下降。该理论还描述了心理社会法则：随着影响源数量增加，每增加一个影响源，其额外影响力逐渐减弱，呈现出负加速的幂函数。
In applied research: Conformity increases when a group is physically closer (high immediacy), perceived as more credible (high strength), and larger in size, though the effect levels off after about three to five people. This links directly to Asch-type experiments in the WJEC specification.
应用研究中：当群体物理距离更近（高即时性）、被认为更可信（高强度）、规模更大时，从众行为增强，但人数达到大约三至五人后效应趋于平缓。这与 WJEC 考纲中阿希型实验直接相关。
3. Measures of Central Tendency | 集中趋势度量
The mean (x̄) is the arithmetic average calculated by summing all scores and dividing by the number of scores. The formula is: x̄ = Σx / n. The median is the middle score when data are arranged in order; it is more robust against extreme outliers. The mode is the most frequently occurring value, useful for nominal (categorical) data.
平均数 (x̄) 是算术平均值，等于所有分数之和除以分数个数，公式为：x̄ = Σx / n。中位数是将数据按顺序排列后处于中间位置的数值，对极端异常值更具抗干扰性。众数是出现频率最高的值，适用于名义（分类）数据。
For WJEC Research Methods, you must be able to justify your choice: use the mean for normally distributed interval/ratio data, the median for skewed distributions or ordinal data, and the mode for nominal categories.
在 WJEC 研究方法中，你必须能够论证你的选择：正态分布的等距/等比数据使用均值，偏态分布或顺序数据使用中位数，名义分类数据使用众数。
4. Measures of Dispersion | 离散程度度量
Dispersion describes how spread out scores are. The range is the difference between the maximum and minimum values: Range = max − min. Variance (s²) measures the average squared deviation from the mean. For a sample, variance is: s² = Σ(x − x̄)² / (n − 1). The standard deviation (s) is the square root of variance, bringing the measure back to the original units: s = √[ Σ(x − x̄)² / (n − 1) ].
离散程度描述的是分数的分散程度。全距是最大值与最小值之差：全距 = 最大值 − 最小值。方差 (s²) 衡量各数据与均值之差的平方的平均数。对于样本，方差公式为：s² = Σ(x − x̄)² / (n − 1)。标准差 (s) 是方差的平方根，将度量还原到原始单位：s = √[ Σ(x − x̄)² / (n − 1) ]。
A low standard deviation indicates that data points cluster closely around the mean; a high standard deviation signals greater variability. In WJEC exams, you may be required to calculate s from raw data and interpret what it tells us about consistency of behaviour.
标准差较小表明数据点紧密聚集在均值附近；标准差较大则意味着变异性更高。在 WJEC 考试中，你可能会被要求根据原始数据计算标准差，并解释它反映出行为的一致性如何。
5. Standard Scores (z-scores) | 标准分数（z 分数）
A z-score expresses how far a raw score lies from the mean in standard deviation units. It is calculated as: z = (x − x̄) / s. A positive z-score means the score is above the mean; a negative z-score means it is below the mean. A z of +2.0 indicates the score is two standard deviations above the mean.
z 分数表示一个原始分数距离均值有多少个标准差。计算公式为：z = (x − x̄) / s。z 分数为正表示分数高于均值；为负表示低于均值。z 值为 +2.0 意味着该分数比均值高出两个标准差。
Psychologists use z-scores to compare performance across different tests or conditions by putting all scores on a common scale. In WJEC, this underpins your understanding of the normal distribution and probability: approximately 95% of scores lie within z = ±1.96 if the data are normally distributed.
心理学家使用 z 分数将不同测验或条件下的表现放在同一尺度上进行比较。在 WJEC 中，这是你理解正态分布和概率的基础：如果数据呈正态分布，约 95% 的分数落在 z = ±1.96 之内。
6. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s rho (rs) tests the strength and direction of association between two sets of ranked (ordinal) data. The formula is: rs = 1 − (6 Σ d²) / [n (n² − 1)], where d is the difference between the ranks of each pair, and n is the number of paired observations. Values range from −1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no relationship.
斯皮尔曼等级相关系数 (rs) 检验两组等级（顺序）数据之间关联的强度和方向。公式为：rs = 1 − (6 Σ d²) / [n (n² − 1)]，其中 d 为每对数据的等级差，n 为配对观测值的个数。数值范围从 −1（完全负相关）到 +1（完全正相关），0 表示无相关。
After calculating rs, you compare it against the critical value in the Spearman table for a given n and chosen significance level (usually p < 0.05). If the obtained rs equals or exceeds the critical value, the correlation is statistically significant, and the null hypothesis can be rejected.
计算出 rs 后，你需要将其与斯皮尔曼临界值表进行比较，根据特定的 n 和选定的显著性水平（通常为 p < 0.05）。如果所得 rs 等于或大于临界值，相关性具有统计显著性，可以拒绝零假设。
7. Chi-Square Test for Independence | 独立性卡方检验
The chi-square test (χ²) assesses whether there is a significant association between two categorical (nominal) variables in a contingency table. The test statistic is: χ² = Σ [(O − E)² / E], where O stands for observed frequency and E for expected frequency under the null hypothesis. Expected frequencies are calculated by: E = (row total × column total) / grand total.
卡方检验 (χ²) 用于评估列联表中两个分类（名义）变量之间是否存在显著关联。检验统计量为：χ² = Σ [(O − E)² / E]，其中 O 代表观测频次，E 代表零假设下的期望频次。期望频次的计算方式为：E = （行合计 × 列合计）/ 总计。
Degrees of freedom (df) for the test of independence are df = (number of rows − 1) × (number of columns − 1). To be significant, the computed χ² must be larger than the critical value found in the chi-square table at the appropriate df and alpha level (commonly 0.05). WJEC candidates are expected to interpret the result in terms of the research hypothesis.
独立性检验的自由度 (df) 为 df = （行数 − 1）×（列数 − 1）。要达到显著水平，计算出的 χ² 值必须大于在相应 df 和 α 水平（通常 0.05）下的卡方临界值。WJEC 考生需要结合研究假设对结果进行解释。
8. Sign Test | 符号检验
The sign test is a simple non-parametric test used with paired (repeated measures or matched pairs) data when the direction of difference is known but the magnitude is not. It converts differences into ‘+’ and ‘−’ signs and takes the test statistic S = the smaller number of plus or minus signs. Pairs showing no difference (ties) are excluded from the analysis, reducing the effective N.
符号检验是一种简单的非参数检验，用于配对（重复测量或匹配对）数据，当已知差异的方向但不知其大小时适用。它将差异转换为“+”和“−”符号，并以 S = 出现次数
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