📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This revision handbook collects the key formulas, laws, and quantitative principles you will encounter in GCSE Eduqas Psychology. From descriptive statistics and sensory thresholds to memory constants and social influence percentages, all the ‘hard numbers’ are assembled here for quick recall.
本复习手册汇编了GCSE Eduqas心理学课程中会遇到的关键公式、定律与量化原则。从描述统计、感觉阈限，到记忆常量和社会影响百分比，所有”硬核数字”都汇集于此，方便你快速回顾。
1. Descriptive Statistics Formulas | 描述统计公式
These statistics summarise a data set. The mean is the arithmetic average, calculated by adding all scores and dividing by the number of scores.
这些统计量可以概括整个数据集。平均数（mean）是算术平均值，由所有分数相加后除以分数的个数得出。
Mean = (Σx) / n
The median is the middle value when scores are arranged in order. If there are two middle values, take their average.
中位数（median）是把分数按顺序排列后处于中间位置的值。如果有两个中间值，则取它们的平均数。
The mode is the most frequently occurring score in a data set. A set can have more than one mode, or none at all.
众数（mode）是数据集中出现次数最多的分数。一个数据集可以有多个众数，也可能一个都没有。
The range measures spread by subtracting the smallest score from the largest. A larger range indicates greater variability.
全距（range）是衡量离散程度的指标，用最大值减去最小值。全距越大，数据的变异性越高。
Range = Highest score – Lowest score
2. Calculating Percentages & Fractions | 百分比与分数计算
Percentages are essential for interpreting data in experiments and surveys. The basic formula converts a fraction into a percentage by multiplying by 100.
百分比对于解读实验和调查数据至关重要。基本公式是将分数乘以100转换成百分数。
Percentage (%) = (Part / Whole) × 100
To find a percentage change, use the difference between the new and original value, divide by the original, then multiply by 100.
要计算百分比变化，用新数值与原数值之差除以原数值，再乘以100。
Percentage Change = [(New – Original) / Original] × 100
Fractions can be simplified by dividing numerator and denominator by a common factor. Ratios, like 3:1, can be turned into fractions to report findings.
分数可以通过分子分母同除以公因子来化简。比例（如3:1）也可转化为分数，以便报告研究发现。
3. Normal Distribution & the Empirical Rule | 正态分布与经验法则
Many psychological characteristics, such as IQ scores, follow a normal distribution – a symmetrical, bell-shaped curve where most scores cluster around the mean.
许多心理特征（如智商分数）呈正态分布——一种对称的钟形曲线，大多数分数聚集在平均数周围。
The empirical rule (68–95–99.7 rule) describes the proportion of scores within 1, 2, and 3 standard deviations of the mean in a normal curve.
经验法则（68–95–99.7规则）描述了正态曲线下，平均数周围1、2、3个标准差范围内所包含的分数比例。
68% of scores lie within ±1 SD
95% within ±2 SD
99.7% within ±3 SD
Understanding this distribution helps you judge how unusual a particular score is, which is useful when interpreting experimental data or case studies.
理解这种分布有助于判断某个分数有多不寻常，这在解释实验数据或案例分析时很有用。
4. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
When studying the relationship between two co-variables (e.g. hours of revision and exam score), you can compute a correlation. Spearman’s rho (rs) uses ranks.
当研究两个共变量（例如复习时长与考试分数）之间的关系时，可以计算相关。斯皮尔曼rho（rs）使用等级数据。
rs = 1 – (6∑d2) / (n3 – n)
where d = difference in ranks for each pair, and n = number of participants. A coefficient of +1 means a perfect positive correlation; -1 means a perfect negative correlation; 0 means no correlation.
其中d = 每对数据的等级之差，n = 被试对数。系数为+1表示完全正相关；-1表示完全负相关；0表示没有相关。
The strength of correlation tells you how consistently the two variables go together, but it does not imply causation – another variable may be responsible.
相关强度表示两个变量一起变化的一致程度，但并不意味着因果关系——可能有第三个变量在起作用。
5. Weber’s Law: Just Noticeable Difference | 韦伯定律：最小可觉差
In the Perception topic, Weber’s Law explains the size of the ‘just noticeable difference’ (JND) – the minimum change needed in a stimulus for a person to detect it 50% of the time.
在知觉章节中，韦伯定律解释了”最小可觉差”（JND）的大小——即人们有50%几率察觉到的刺激最小变化量。
ΔI / I = k
where ΔI is the change in stimulus intensity, I is the original intensity, and k is a constant (the Weber fraction). For example, for brightness the constant is roughly 0.08, so you need an 8% change to notice a difference.
其中ΔI是刺激强度的变化量，I是原始强度，k是韦伯常数（韦伯分数）。例如，对亮度来说常数约0.08，所以需要大约8%的变化才能察觉不同。
This law highlights that our senses are tuned to relative rather than absolute changes, which has implications for illusions and perceptual sensitivity.
这一定律强调，我们的感觉是对相对变化而非绝对变化敏感，这对错觉和知觉敏感性有一定的解释意义。
6. Fechner’s Law: Logarithmic Sensation | 费希纳定律：感觉的对数关系
Building on Weber’s work, Fechner’s Law states that the perceived intensity of a stimulus grows logarithmically with its physical intensity.
在韦伯研究基础上，费希纳定律指出，感觉到的强度随着物理刺激强度的对数增长。
S = k log I
where S = perceived sensation, I = physical stimulus intensity, and k is a constant. This means you need much larger physical changes to produce the same ‘felt’ difference when the stimulus is already strong.
其中S = 感觉强度，I = 物理刺激强度，k为常数。这意味着，当刺激已经很强时，需要非常大的物理变化才能产生相同的”主观感觉”差异。
Although this law is not required in every GCSE specification, it underpins modern understanding of sensory scaling and can enrich discussion of perceptual processes.
虽然并非所有GCSE大纲都要求这一定律，但它支撑着现代感觉标度理论，可以丰富你对知觉过程的讨论。
7. Miller’s Magic Number: 7 ± 2 | 米勒的神奇数字：7±2
George Miller’s (1956) classic finding is a cornerstone of the Multi-Store Model: short-term memory (STM) can hold approximately 7 chunks of information (plus or minus 2).
米勒（1956）的经典发现是多存储模型的基石：短时记忆（STM）可以容纳大约7个组块的信息（±2）。
A chunk is a meaningful unit – a single digit, a letter, a word, or even a short phrase. By chunking information, we can expand effective STM capacity.
组块是一个有意义的信息单元——可以是一个数字、一个字母、一个单词，甚至一个短语。通过组块化信息，我们能够扩大有效的短时记忆容量。
STM Capacity ≈ 7 ± 2 chunks
This principle explains why phone numbers are often grouped into short segments, and it is a key argument in favour of separate short- and long-term memory stores.
这一原则解释了为什么电话号码常被分成短小的段，也是支持短时记忆与长时记忆分属不同储存区的关键论据。
8. Yerkes-Dodson Law of Arousal | 耶基斯-多德森唤醒定律
The Yerkes-Dodson Law describes an inverted U-shaped relationship between arousal and performance. Moderate arousal leads to optimal performance, while very low or very high arousal harms it.
耶基斯-多德森定律描述了唤醒水平与表现之间的倒U形关系。中等唤醒导致最佳表现，而唤醒过低或过高都会损害表现。
The curve shifts depending on task difficulty: for simple or well-learned tasks, higher arousal can improve performance; for complex or new tasks, lower arousal is better.
曲线的位置取决于任务难度：对于简单或熟练的任务，较高唤醒有助于表现；对于复杂或新任务，较低唤醒更有利。
Performance = f(task complexity, arousal level)
This law is frequently used to explain exam anxiety – a certain amount of stress is motivating, but too much can lead to cognitive overload and poorer recall.
这一定律常被用来解释考试焦虑——适度的压力具有激励作用，但压力过大可能导致认知超载和回忆变差。
9. Multi-Store Memory Model Constants | 多存储记忆模型常量
Atkinson and Shiffrin’s model describes three distinct memory stores with fixed characteristics. The table below sums up their published constants.
阿特金森和谢夫林的模型描述了三个具有固定特征的独立记忆存储。下表总结了其公开的常量数据。
| Store | Encoding | Capacity | Duration |
|---|---|---|---|
| Sensory Register | Modality-specific (iconic, echoic) | Very large | 0.25–0.5 seconds |
| Short-Term Memory | Acoustic (mainly) | 7±2 chunks | 18–30 seconds |
| Long-Term Memory | Semantic (mainly) | Potentially unlimited | Potentially a lifetime |
中文对应：感觉登记——编码形式依感觉通道（图像、声响），容量极大，持续时间约0.25–0.5秒；短时记忆——主要按声学编码，容量为7±2个组块，持续18–30秒；长时记忆——主要按语义编码，容量和持续时间理论上是无限的。
These ‘laws’ of the model are testable: if rehearsal is prevented, STM duration collapses; chunking can boost apparent capacity. They are central to both Memory and Research Methods questions.
这些模型”定律”是可检验的：若阻止复述，短时记忆时长会骤减；组块化能提升有效容量。它们是记忆和研究方法题目的核心内容。
10. Conformity & Obedience Rates | 从众与服从比率
Two landmark numbers from Social Influence studies act as psychological ‘laws’ in context: Asch’s conformity rate and Milgram’s obedience rate.
社会影响研究中有两个里程碑式的数字，在特定情境下如同心理学”定律”：阿希的从众比率和米尔格拉姆的服从比率。
In Asch’s line-judgement task, on critical trials where confederates gave wrong answers, the real participant conformed on approximately 37% of the responses. Although 75% of participants conformed at least once, the 37% figure is widely quoted as the probability of going along with an incorrect majority.
在阿希的线条判断任务中，当假被试给出错误答案的关键试次上，真被试大约在37%的反应中选择了从众。尽管75%的被试至少从众过一次，但37%这个数字被广泛引用为跟随错误多数人意见的概率。
Asch Conformity Rate ≈ 37% of critical responses
In Milgram’s obedience experiment, 65% of participants continued to administer shocks up to the maximum 450 V when prompted by an authority figure in a laboratory coat.
在米尔格拉姆的服从实验中，65%的被试在穿白大褂的权威人物催促下，一直施加电击到最高的450伏。
Milgram Obedience Rate = 65% to 450 V
These figures serve as powerful constants for evaluating situational factors, but remember they apply to the specific set-ups used; variations in proximity or uniform altered the rates.
这些数字可作为评估情境因素的强有力常量，但需记住它们适用于特定的实验设制；距离或制服等变体会改变比率。
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