📚 Year 8 CIE Psychology: Formula & Theorem Quick Reference Handbook | Year 8 CIE 心理学：公式定理速查手册
Welcome to your handy quick-reference guide for Year 8 CIE Psychology. This handbook compiles the essential formulas, statistical measures, and fundamental laws or theorems you will encounter in your studies. Understanding these building blocks will help you analyse research data, interpret behaviour, and explain psychological phenomena with precision. From descriptive statistics to classic laws of perception and memory, each entry is explained clearly with a paired formula and its application.
欢迎使用这本 Year 8 CIE 心理学的速查手册。手册汇集了你将在学习中遇到的核心公式、统计量度以及基本定律或定理。掌握这些构件将帮助你精确分析研究数据、解释行为并阐述心理现象。从描述统计到经典的感觉与记忆定律，每个条目都以成对公式和应用进行清晰说明。
1. Measures of Central Tendency | 集中趋势度量
ean = Σx / n, where Σx represents the sum of all scores and n is the total number of observations.
平均值计算一组分数的平均数。它通过将所有数据值相加再除以数值的个数得到。公式为 Mean = Σx / n，其中 Σx 代表所有分数之和，n 是观测总数。
Mean = Σx / n
The median is the middle value when the data are arranged in ascending order. For an even number of observations, the median is the mean of the two central numbers. It is less affected by extreme outliers than the mean.
中位数是将数据按升序排列后位于中间的值。若观测个数为偶数，中位数是中间两个数的平均值。它受极端离群值的影响比平均值小。
The mode is the most frequently occurring score in a dataset. A distribution can be unimodal (one mode), bimodal (two modes) or multimodal. The mode is especially useful for categorical data.
众数是数据集中出现频率最高的分数。分布可以是单峰的、双峰的或多峰的。众数对于分类数据尤其有用。
2. Range: A Measure of Dispersion | 值域：离散量数
tween the highest and the lowest values in a dataset. The formula is Range = Maximum value – Minimum value.
值域是最简单的变异量度，它是数据集中最大值与最小值之差。公式为 Range = 最大值 – 最小值。
Range = Xmax − Xmin
A small range indicates that the scores are tightly clustered, while a large range suggests greater spread. However, the range is easily distorted by outliers, so researchers often combine it with other measures of dispersion.
较小的值域表明分数紧密聚集，而较大的值域表明散布更广。但是，值域易受离群值扭曲，因此研究者常将其与其他离散量数结合使用。
3. Percentage Change Formula | 百分比变化公式
ange in anxiety scores following treatment. The formula is: Percentage change = (New value – Old value) / Old value × 100%.
心理学家经常计算百分比变化来比较前后测量值，例如治疗前后焦虑分数的变化。公式为：百分比变化 = (新值 – 旧值) / 旧值 × 100%。
Percentage change = [(Xnew − Xold) / Xold] × 100%
A positive result indicates an increase, while a negative result reflects a decrease. This tool is fundamental for evaluating intervention effectiveness and expressing results in a standardised format.
正数结果表示增加，负数结果反映减少。该工具对于评价干预效果和用标准化格式呈现结果至关重要。
4. Basic Probability Formula | 基本概率公式
onding in a particular way. The formula is P(A) = Number of favourable outcomes / Total number of possible outcomes.
概率量化了某事件发生的可能性。在行为研究中，它可用于预测参与者作出特定反应的机会。公式为 P(A) = 有利结局数目 / 可能结局总数。
P(A) = f / N
Probability values range from 0 (impossible event) to 1 (certain event). This foundational concept underpins inferential statistics and null hypothesis testing, which you will explore in later years.
概率值介于 0（不可能事件）到 1（必然事件）之间。这一基础概念支撑着推论统计和零假设检验，你将在更高年级学习这些内容。
5. Weber's Law | 韦伯定律
Weber' essed as ΔI / I = k, where ΔI is the minimal change needed to detect a difference, I is the initial intensity, and k is the Weber fraction.
韦伯定律指出，两个刺激之间的最小可觉差是原始刺激强度的一个恒定比例。公式为 ΔI / I = k，其中 ΔI 是察觉差异所需的最小变化量，I 是初始强度，k 是韦伯分数。
ΔI / I = k
For example, when lifting weights, a larger weight requires a greater addition before the change is noticed. The constant k varies across senses — it is approximately 0.02 for weight discrimination and 0.08 for brightness perception.
例如，在举重时，初始重量越大，则需要增加更多才能觉察到变化。常数 k 因感觉而异——对于重量辨别，它约为 0.02；对于亮度知觉，约为 0.08。
6. Fechner's Law | 费希纳定律
Building on Weber's work, Fechner' ived sensation, I is the physical intensity, and k is a constant dependent on the sensory modality.
在韦伯的基础上，费希纳定律提出感觉量随物理刺激强度呈对数增长。公式为 S = k log I，其中 S 是感知到的感觉，I 是物理强度，k 是依赖于感觉通道的常数。
S = k log I
This means that as a stimulus becomes more intense, increasingly larger changes are needed to produce the same perceived increase. Fechner's law helps explain why we are more sensitive to changes in dim light than in bright light.
这意味着当刺激变得更强烈时，需要增长更大的变化才能产生同等的感觉增加。费希纳定律有助于解释为什么我们对暗光下的变化比在亮光下更敏感。
7. Yerkes-Dodson Law | 耶克斯-多德森定律
The Yerkes-Dodson Law describes the empirical relationship between arousal and performance. It states that performance improves with increasing arousal up to an optimal point, after which further arousal leads to a decline. This can be depicted as an inverted-U shaped curve.
耶克斯-多德森定律描述了唤醒水平与表现之间的实证关系。它指出，表现随着唤醒水平的提高而改善，直至一个最佳点，此后进一步的唤醒反而导致表现下降。这可以用一个倒 U 形曲线表示。
Performance = f (Arousal) ; optimal at moderate arousal
Moreover, the law specifies that the optimal level of arousal depends on task complexity: simpler tasks benefit from higher arousal, whereas complex tasks require lower arousal for peak performance. This principle is widely applied in educational and sporting settings.
此外，该定律指出最佳唤醒水平取决于任务复杂度：简单任务在高唤醒下表现更好，而复杂任务则需要较低唤醒才能达到顶峰。这一原则被广泛应用于教育和运动领域。
8. Serial Position Effect | 系列位置效应
primacy effect, and items at the end show a recency effect, both remembered better than those in the middle. This can be summarised as: Recall probability = higher at extreme positions.
系列位置效应描述了项目在序列中的位置如何影响回忆概率。列表开头的项目表现出首因效应，末尾的项目表现出近因效应，两者都比中间项目记得更好。可概括为：回忆概率 = 在极端位置更高。
P(recall) ∝ Position: maximum at start and end
The primacy effect is attributed to greater rehearsal and transfer into long-term memory, while the recency effect reflects short-term memory storage. This dual-store explanation supports the multi-component model of memory.
首因效应归因于更多的复述并转入长时记忆，而近因效应反映了短时记忆存储。这种双存储解释支持了记忆的多成分模型。
9. Miller's Law (The Magical Number 7) | 米勒定律（神奇数字 7）
Miller' igit, a letter, or a word. The rule of thumb is: Short-term Memory Capacity = 7 ± 2 items.
米勒定律提出短时记忆的平均容量约为 7 ± 2 个组块的信息。一个组块是一个有意义的单位，如一个数字、字母或单词。经验法则为：短时记忆容量 = 7 ± 2 个项目。
STM Capacity = 7 ± 2 chunks
However, this capacity can be stretched by chunking — grouping individual pieces into larger meaningful wholes. For example, the letter sequence 'C, I, A, F, B, I' is difficult to recall as six separate items, but easily remembered as two chunks: 'CIA' and 'FBI'.
但是，通过组块化——将个体片段组合成更大的有意义整体——可以拉伸容量。例如，字母序列 C, I, A, F, B, I 作为六个单独项目难以回忆，但作为两个组块「CIA」和「FBI」就很容易记住。
10. Social Facilitation Theory | 社会助长理论
nses. For well-practised or simple tasks, performance improves; for novel or complex tasks, performance may worsen. The relationship can be expressed as: Performance change = f (Social arousal, task difficulty).
扎荣茨的社会助长理论认为，他人在场会增加唤醒并增强优势反应的表现。对于练习充分或简单的任务，表现会提升；对于新颖或复杂的任务，表现可能恶化。该关系可表述为：表现变化 = f (社会唤醒 , 任务难度)。
Performance change ≈ Arousal × Dominant response strength
This model explains why athletes often perform better in front of a crowd than in training, while a person learning a new skill might make more errors when observed. It illustrates the interplay between social context and individual ability.
这一模型解释了为什么运动员在观众前表现常优于训练时，而学习新技能的人在被观察时可能犯更多错误。它说明了社会情境与个体能力之间的相互作用。
11. Ebbinghaus Forgetting Curve | 艾宾浩斯遗忘曲线
attempt is made to retain it. The forgetting curve can be modelled mathematically as R = e−t/S, where R is retention, t is the elapsed time, and S is the relative memory strength.
艾宾浩斯证明，若不去保持记忆，新学信息的保持会随时间呈指数衰减。遗忘曲线可用数学模型表述为 R = e−t/S，其中 R 为保持量，t 为经过的时间，S 为相对记忆强度。
R = e−t/S
In practice, the steepest decline occurs within the first hour, and then the rate of forgetting gradually levels off. This has important implications for revision strategies — distributing practice over time (the spacing effect) significantly improves long-term recall.
实际中，最急剧的下降发生在一小时内，随后遗忘速度逐渐趋于平缓。这对复习策略有重要启示——将练习分散在时间中（间隔效应）能显著提升长时回忆。
12. Spearman's Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman's rank correlation coefficient (rs) is a non-parametric statistic that measures the strength and direction of association between two ranked variables. The formula is rs = 1 − (6
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