📚 Year 8 OCR Psychology: Formula & Theorem Quick Reference Guide | 八年级OCR心理学：公式定理速查手册
This quick reference guide brings together the key formulas, laws and mathematical rules that Year 8 OCR Psychology students need to know. From the classic psychophysical laws that explain how we detect changes in the world around us, to the formulas used in everyday research and intelligence testing, every entry is presented with a clear English explanation followed by its Chinese counterpart. Understanding these equations will strengthen your grasp of core topics including perception, memory, individual differences and research methods.
这份速查手册汇集了八年级OCR心理学学生需要掌握的关键公式、定律和数学规则。从解释我们如何察觉周围世界变化的经典心理物理学定律，到日常研究和智力测验中使用的公式，每一个条目都附有清晰的英文解释和相应的中文说明。理解这些等式将帮助你更好地掌握包括知觉、记忆、个体差异和研究方法在内的核心主题。
1. Weber’s Law | 韦伯定律
Weber’s Law describes the relationship between a physical stimulus and the smallest noticeable change in that stimulus. It states that the just noticeable difference (JND) between two stimuli is proportional to the magnitude of the original stimulus.
韦伯定律描述了物理刺激与该刺激能够被察觉的最小变化之间的关系。它指出两个刺激之间的最小可觉差与原始刺激的强度成正比。
ΔI / I = k
In this formula, ΔI represents the increase in stimulus intensity needed for a person to notice a change, I stands for the initial intensity of the stimulus, and k is a constant (the Weber fraction) that varies depending on the sensory modality, such as vision, hearing or touch.
在这个公式中，ΔI代表让人察觉到变化所需的刺激强度增量，I代表刺激的初始强度，k是一个常数（韦伯分数），它因感觉通道（如视觉、听觉或触觉）的不同而变化。
2. Fechner’s Law | 费希纳定律
Building directly on Weber’s work, Fechner’s Law describes the mathematical relationship between the physical intensity of a stimulus and the perceived sensation it produces. It suggests that as the physical intensity of a stimulus grows geometrically, the perceived sensation increases only arithmetically.
费希纳定律直接建立在韦伯的研究基础上，描述了刺激的物理强度与其产生的感觉体验之间的数学关系。它表明，当刺激的物理强度以几何级数增长时，感觉经验只以算术级数增加。
S = k log I
Here S represents the subjective sensation magnitude, I is the physical intensity of the stimulus, and k is a constant that depends on the type of stimulus being measured. Because the relationship involves a logarithm, very large increases in physical energy are required to produce a small increase in sensation.
在这里，S代表主观感觉量，I是刺激的物理强度，k是一个取决于所测量刺激类型的常数。由于这种关系涉及对数，要产生很小的感觉增量，也需要非常大幅度的物理能量增加。
3. Stevens’ Power Law | 史蒂文斯幂定律
Stevens argued that Fechner’s logarithmic law was not flexible enough to describe all sensory experiences, so he proposed a more general formula known as the power law. This law is used to predict the relationship between the magnitude of a physical stimulus and the perceived intensity across many different senses.
史蒂文斯认为费希纳的对数定律不够灵活，无法描述所有的感觉经验，因此他提出了一种更具通用性的公式，即幂定律。该定律用于预测多种不同感觉中物理刺激的大小与知觉强度之间的关系。
S = k I ⁿ
In this equation S is the perceived magnitude, I is the physical intensity, k is a constant and the exponent n determines the shape of the psychophysical function. When n is less than 1, sensation grows more slowly than the physical stimulus; when n is greater than 1, sensation grows faster.
在这个等式中，S代表知觉量，I代表物理强度，k是一个常数，指数n决定了心理物理函数的形状。当n小于1时，感觉增长比物理刺激缓慢；当n大于1时，感觉增长更快。
4. Yerkes-Dodson Law | 耶克斯-多德森定律
The Yerkes-Dodson Law explains the relationship between arousal and performance. Rather than a single formula, it describes an inverted-U shaped function: performance improves as arousal increases up to an optimal point, but if arousal becomes too high, performance declines.
耶克斯-多德森定律解释了唤醒水平与表现之间的关系。它不是一个单独的公式，而是描述了一种倒U形函数：随着唤醒水平上升，表现会提高直至一个最优点；但如果唤醒过高，表现就会下降。
Performance = inverted-U function of arousal
The optimal level of arousal also depends on the complexity of the task. For simple or well-learned tasks, a higher level of arousal is usually beneficial, whereas for difficult or new tasks, a lower level of arousal tends to produce the best results.
最佳唤醒水平还取决于任务的复杂程度。对于简单或熟练的任务，较高的唤醒水平通常是有益的；而对于困难或新的任务，较低的唤醒水平往往能产生最好的结果。
5. The Intelligence Quotient Formula | 智商计算公式
One of the most famous formulas in psychology comes from the early work on intelligence testing. The intelligence quotient (IQ) was originally calculated by comparing a person’s mental age to their chronological age and then multiplying by one hundred.
心理学中最著名的公式之一来自早期的智力测验研究。智商最初是通过将一个人的心理年龄除以实际年龄，再乘以一百来计算得出的。
IQ = (MA / CA) × 100
In this formula, MA stands for mental age, which is a measure of a person’s cognitive ability compared with the average performance of a particular age group, and CA represents chronological age, the individual’s actual age in years. A child with an MA of 10 and a CA of 8 would have an IQ of 125, indicating above-average ability.
在这个公式中，MA代表心理年龄，用于衡量个人认知能力相对于特定年龄组平均表现的比较值；CA代表实际年龄，即个体按年计算的实际年龄。一个心理年龄为10岁、实际年龄为8岁的孩子，其智商为125，表明能力高于平均水平。
6. Miller’s Law (The Magic Number 7 ± 2) | 米勒定律（神奇数字7±2）
George Miller’s famous paper proposed that the capacity of short-term memory is limited to about seven items, plus or minus two. This has become a widely cited rule of thumb in cognitive psychology for understanding how much information we can hold in mind at one time.
乔治·米勒的著名论文指出，短时记忆的容量限制在七个项目左右，上下浮动一到两个。这一规律已成为认知心理学中一个被广泛引用的经验法则，用于理解我们一次能在头脑中保持多少信息。
Short-term memory capacity = 7 ± 2 items
Miller emphasised that the ‘items’ could be individual digits, letters or words, but the capacity can be expanded by chunking – grouping information into meaningful units. For example, a sequence of twelve letters might be remembered more easily if they are grouped into four familiar three-letter chunks.
米勒强调，“项目”可以是单个数字、字母或单词，但通过组块化——将信息组合成有意义的单元——可以扩展容量。例如，连续十二个字母如果被组合成四个熟悉的三字母组块，就可能更容易记住。
7. Percentage Change in Psychological Research | 心理学研究中的百分比变化
Psychologists often measure how much a score or behaviour has changed before and after an intervention, and the simplest way to express this change is as a percentage. This allows researchers to compare the size of change across different conditions or participants.
心理学家经常测量在干预前后分数或行为变化了多少，而表达这种变化的最简单方式就是百分比。这使研究者能够在不同条件或参与者之间比较变化的大小。
% Change = ((New Value − Original Value) / Original Value) × 100
For example, if the number of stressful thoughts reported by a participant drops from 20 to 12 after relaxation training, the percentage reduction can be calculated by taking (12 − 20) / 20 × 100 = −40%, meaning a 40% decrease. Negative values indicate a reduction, while positive values show an increase.
例如，如果一位参与者报告的压力想法数量在放松训练后从20降至12，可以用(12 − 20) / 20 × 100 = −40%来计算百分比降幅，即减少了40%。负值表示下降，正值则表示增长。
8. Arithmetic Mean Formula | 算术平均数公式
The arithmetic mean is the most commonly used measure of central tendency in psychology. It provides a single representative value for a set of scores and is calculated by adding all the scores together and dividing by the total number of scores.
算术平均数是心理学中最常用的集中趋势量度。它为一组分数提供了一个具有代表性的单一数值，通过将所有分数相加再除以分数的总数来计算。
M = ΣX / N
In this formula, M stands for the mean, ΣX (sigma X) represents the sum of all individual scores, and N is the total number of scores in the data set. The mean is used extensively in studies of memory, social influence and developmental psychology to summarise data and compare groups.
在这个公式中，M代表平均数，ΣX（西格玛X）表示所有个别分数的总和，N是数据集中分数的总个数。平均数在记忆、社会影响和发展心理学研究中被广泛使用，用于总结数据和比较不同组别。
9. Range as a Measure of Dispersion | 作为离散量度的极差
While the mean tells us about the centre of a data set, the range tells us about its spread. It is the simplest measure of dispersion and is found by subtracting the smallest value from the largest value in the set.
平均数告诉我们数据集的中心在哪里，而极差则告诉我们数据的分散程度。它是最简单的离散量度，通过用数据集中的最大值减去最小值得到。
Range = Xmax − Xmin
Although the range is quick to calculate, it is easily affected by outliers – a single exceptionally high or low score can make the range appear much larger than the typical spread of the data. Psychologists therefore often use the range alongside other measures like the interquartile range.
虽然极差计算很快，但它容易受到异常值的影响——单一一个极高或极低的分数就可能让极差看起来比数据的典型散布大得多。因此，心理学家常常将极差与四分位距等其他量度一起使用。
10. Proportional Reasoning in Social Influence | 社会影响中的比例推理
Many social psychology studies report results in terms of proportions or ratios, especially when examining conformity, obedience or bystander behaviour. The basic proportion formula helps you compare a part of the sample to the whole sample.
许多社会心理学研究在报告结果时会用到比例或比率，特别是在研究从众、服从或旁观者行为时。基本的比例公式可以帮助你比较样本中的某一部分与整个样本的关系。
Proportion = f / N
Here f stands for the frequency of a particular behaviour (for example the number of participants who conformed in a trial) and N is the total number of participants in that condition. A proportion can also be expressed as a percentage by multiplying by 100, which is a useful skill for evaluating findings from studies like Asch’s conformity experiments.
这里，f代表某种特定行为的频次（例如在某次试验中从众的参与者人数），N是该条件下的参与者总数。比例也可以乘以100转换为百分比，这是评价阿希从众实验等研究结果时一项很有用的技能。
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