📚 Year 7 CCEA Psychology: Formula & Theorem Quick Reference Handbook | 七年级 CCEA 心理学：公式定理速查手册
This handbook gives you a rapid and reliable set of psychology formulas, laws and key numerical relationships that you need to know for your Year 7 CCEA Psychology course. Use it to revise how we measure behaviour, memory, motivation and social interaction in a clear, mathematical way.
本手册为你整理了七年级 CCEA 心理学课程中必须掌握的心理学公式、定律和关键数量关系。你可以利用它清晰、数学化地回顾我们如何测量行为、记忆、动机和社会互动。
1. Mean, Median, Mode and Range | 平均数、中位数、众数和范围
The mean is the arithmetic average. To find it, add up all the values in your data set and then divide the total by the number of values.
平均数是算术平均值。要计算它，需要先把数据集中所有的值加起来，然后用总和除以数值的个数。
Mean = (Sum of data values) ÷ (Number of data values) or (Σx)/n
The median is the middle value when you arrange the numbers in order from smallest to largest. If there are two middle numbers, take the mean of those two.
中位数是将所有数字从小到大排序后位于中间位置的那个值。如果有两个中间数，就取这两个数的平均数。
The mode is the data value that appears most often. A set of data can have more than one mode, or none at all if all values occur equally often.
众数是数据集中出现次数最多的值。一个数据集可以有多个众数，如果所有数值出现的次数相同，那么就没有众数。
The range shows how spread out the data are. It is simply the difference between the largest and smallest values.
范围显示了数据的分散程度，即最大值与最小值之间的差值。
Range = Largest value – Smallest value
These descriptive statistics are the foundation of psychological research. They help summarise behaviour, reaction times, questionnaire scores and much more.
这些描述性统计是心理学研究的基础，它们帮助总结行为、反应时、问卷得分等各种数据。
2. Weber’s Law | 韦伯定律
Weber’s Law states that the smallest change in a stimulus that can be detected is a constant proportion of the original stimulus intensity. This ‘just noticeable difference’ (JND) depends on the base level.
韦伯定律指出，能够被探测到的最小刺激变化量是原始刺激强度的一个恒定比例。这种“最小可觉差”依赖于基础水平。
ΔI / I = k
Here ΔI is the difference threshold (the change needed to notice a difference), I is the initial stimulus intensity, and k is the Weber fraction, which is constant for each type of sensation.
其中 ΔI 是差异阈限（即能注意到差异所需的变化量），I 是初始刺激强度，k 是韦伯分数，每一种感觉类型的 k 值都是常数。
For example, if you are holding a 100‑gram weight, you might need to add 2 grams to notice it feels heavier. If you are holding a 1‑kilogram weight, you would need to add 20 grams, not 2 grams, because the ratio stays the same.
举例来说，如果你拿着一个 100 克的砝码，可能需要增加 2 克才能察觉到变重了。而如果你拿着一个 1 千克的砝码，就需要增加 20 克而不是 2 克，因为比例保持不变。
3. Ebbinghaus Forgetting Curve and Savings Formula | 艾宾浩斯遗忘曲线与节省量公式
Hermann Ebbinghaus studied memory by learning nonsense syllables and measuring how much he forgot over time. The forgetting curve shows that forgetting is rapid at first and then levels off.
赫尔曼·艾宾浩斯通过记忆无意义音节并测量自己随时间的遗忘量，研究了记忆。遗忘曲线显示遗忘最初迅速发生，随后趋于平缓。
To measure memory, Ebbinghaus used a ‘savings’ method. He recorded how many trials (repetitions) it took to learn a list perfectly, and later how many trials it took to relearn the same list.
为了测量记忆，艾宾浩斯使用了“节省法”。他记录完整学习一个列表所需要的尝试次数，然后再记录重新学习同一个列表所需的尝试次数。
Savings % = [(Original trials – Relearning trials) ÷ Original trials] × 100
A high savings score means that some information was still stored in memory, even if it could not be actively recalled at first. This formula allows psychologists to measure the hidden strength of memories.
高分节省量意味着即使最初无法主动回忆，仍有一部分信息储存在记忆中。这个公式让心理学家能够测量记忆的隐藏强度。
If you originally needed 10 trials to learn a list and later only needed 3 trials, your savings score would be 70%. That tells you that 70% of the memory trace was retained.
如果你最初需要 10 次才能学会一个列表，后来仅需 3 次，那么节省分数就是 70%，说明保留了 70% 的记忆痕迹。
4. Miller’s Magic Number 7 ± 2 | 米勒的神奇数字 7 ± 2
George Miller proposed that human working memory has a limited capacity. Most adults can hold about 7 (plus or minus 2) items or ‘chunks’ of information at one time.
乔治·米勒提出，人类的工作记忆容量有限。大多数成年人在同一时间能够记住大约 7 个（加减 2 个）信息条目或“组块”。
Working memory span ≈ 7 ± 2 chunks
A chunk can be a single digit, a letter or a whole meaningful unit like a word. By grouping information into larger chunks, we can remember more. For example, the letters C,C,E,A can be chunked into the abbreviation ‘CCEA’.
一个组块可以是一个数字、一个字母或者一个有意义的单元，比如一个单词。通过将信息组合成更大的组块，我们可以记住更多。例如，字母 C、C、E、A 可以组块为缩写“CCEA”。
This ‘magic number’ helps explain why telephone numbers are often seven digits long and why it is easier to memorise a story than a random list of words. It is a key theorem when planning revision and designing experiments on memory.
这个“神奇数字”有助于解释为什么电话号码通常是 7 位数，以及为什么记住一个故事比记住一串随机的单词更容易。在规划复习和设计记忆实验时，这是一项关键定理。
5. Yerkes‑Dodson Law | 耶克斯‑多德森定律
The Yerkes‑Dodson Law describes the relationship between arousal (alertness or stress) and performance. The law states that performance increases with arousal up to an optimal point, after which more arousal causes performance to drop. The resulting graph is an inverted‑U shape.
耶克斯‑多德森定律描述了唤醒水平（警觉或压力）与表现之间的关系。该定律指出，表现随着唤醒水平的提高而提高，直到达到最佳点，之后更高的唤醒反而导致表现下降，图形为倒 U 形。
Performance = ƒ(Arousal) with an inverted‑U shaped curve
For easy or well‑practised tasks, the optimal level of arousal is higher. For difficult or new tasks, the optimal level is lower. This means a little bit of exam stress can boost your performance, but too much anxiety can make your mind go blank.
对于简单或熟练的任务，最佳唤醒水平较高；对于困难或新任务，最佳唤醒水平较低。这意味着适度的考试压力可以提升表现，但过度焦虑会使大脑一片空白。
Psychologists use this law to help athletes, students and performers find their ideal level of alertness. It shows that a formula‑like link between mind and body controls how well we do.
心理学家运用这一定律帮助运动员、学生和表演者找到理想的警觉水平。它展示了身心之间类似公式的联系如何控制我们的表现。
6. Expectancy Value Theory | 期望价值理论
Expectancy Value Theory is used to explain motivation. According to this idea, the strength of a person’s motivation to succeed at a task is the product of two factors: how much they expect to succeed (expectancy) and how much they value the goal (value).
期望价值理论被用来解释动机。根据这一观点，一个人完成任务的动机强度取决于两个因素的乘积：他们预期成功的程度（期望）以及他们对目标的重视程度（价值）。
Motivation = Expectancy × Value
If either expectancy or value is zero, the entire motivation becomes zero. For example, even if you value a top grade very highly, if you are absolutely certain you will fail, you might not even try.
如果期望或价值其中一个为零，整个动机就为零。例如，即使你非常看重高分，但如果你百分之百确信自己会失败，你可能根本不会去尝试。
This multiplicative formula is a powerful psychological theorem. It explains why teachers try to build both students’ confidence and their interest in the subject: both must be present to fuel learning.
这个乘法公式是一项强大的心理学定理。它解释了为什么教师既要培养学生的信心，又要激发他们对学科的兴趣：两者必须兼备才能推动学习。
7. Social Exchange Theory Formula | 社会交换理论公式
Social Exchange Theory views relationships like a balance sheet. The basic idea is that people try to maximise rewards and minimise costs. The net outcome of a relationship can be calculated simply.
社会交换理论把人际关系比作资产负债表。其基本思想是人们试图最大化收益并最小化成本。关系的净结果可以简单计算。
Outcome = Rewards – Costs
Rewards include things like companionship, support and fun. Costs include effort, time, arguments and stress. If the outcome is positive, the relationship is likely to continue. If it is negative, the person may end it.
收益包括陪伴、支持和乐趣等。成本包括精力、时间、争吵和压力。如果结果是正值，关系很可能继续；如果是负值，人们可能会终止关系。
Psychologists also consider a ‘comparison level’, which is what a person expects from a relationship. Satisfaction = Outcome – Comparison Level. This helps explain why two people with the same rewards and costs can feel differently about their friendship.
心理学家还会考虑“比较水平”，即一个人对关系的期待值。满意度 = 结果 – 比较水平。这有助于解释为什么两个拥有相同收益和成本的人会对友谊产生不同的感受。
8. Cognitive Dissonance Ratio | 认知失调比例
Leon Festinger’s theory of cognitive dissonance says that when people hold two contradictory thoughts (cognitions), they feel mental discomfort. The magnitude of dissonance can be thought of as a ratio of inconsistent to consistent cognitions, multiplied by the importance of the issue.
利昂·费斯廷格的认知失调理论认为，当人们持有两个矛盾的认知时，会感到心理不适。失调的程度可以看作是矛盾认知与一致认知的比率乘以问题的重要性。
Dissonance ∝ (Inconsistent cognitions ÷ Consistent cognitions) × Importance
For instance, if you believe that being healthy is very important, but you eat a lot of junk food, you have one major inconsistency against many consistent beliefs about the value of health. The high importance will create strong dissonance, which you might reduce by changing your beliefs (‘junk food isn’t that bad’) or your behaviour (eating more healthily).
例如，如果你认为健康非常重要，但你吃了很多垃圾食品，那么你就有一项重大矛盾，与之相对的是许多关于健康价值的一致信念。较高的重要性会造成强烈的失调感，你可能会通过改变信念（“垃圾食品没那么糟糕”）或行为（吃得更健康）来减轻这种不适。
This ratio‑style theorem helps psychologists predict when people are most likely to change their attitudes. It is a crucial formula for understanding persuasion, decision‑making and self‑justification.
这个比率式的定理帮助心理学家预测人们在何时最有可能改变态度。它是理解说服、决策和自我辩护的关键公式。
9. Bystander Intervention and Diffusion of Responsibility | 旁观者干预与责任扩散
Research on the bystander effect shows that people are less likely to help in an emergency when other people are present. A simple way to model this is through a diffusion of responsibility formula.
旁观者效应的研究表明，当有他人在场时，人们在紧急情况下提供帮助的可能性反而降低。一种简单的建模方法就是使用责任扩散公式。
Perceived personal responsibility ≈ 1 ÷ Number of bystanders
If you are the only witness, your sense of responsibility is high (1/1 = 1). If four other people are present, your perceived responsibility drops to 1/5. Because everyone assumes someone else will act, often no one does.
如果你是唯一的目击者，你的责任感就会很高（1/1 = 1）。如果有其他四个人在场，你的责任感就下降到 1/5。因为每个人都假设别人会行动，结果常常是无人出手。
Psychologists also note that the probability of a quick helping response depends on more than just numbers. It includes noticing the event, interpreting it as an emergency and feeling capable. Still, the 1/N rule gives a powerful mathematical summary of the social psychology at work.
心理学家还指出，快速助人反应的概率取决于多个因素，不仅仅是人数，还包括是否注意到事件、将其解释为紧急情况，以及是否感觉自己有能力帮助。尽管如此，1/N 法则为社会心理学的运作提供了一个强有力的数学总结。
10. Spearman’s Rank Correlation Coefficient (Simplified) | 斯皮尔曼等级相关系数（简化版）
In psychology, we often want to know if two variables are related. Spearman’s rank correlation coefficient (rs) measures the strength and direction of a relationship between two ranked sets of data. It works out a value between -1 and +1.
在心理学中，我们常常想知道两个变量是否相关。斯皮尔曼等级相关系数（rs）测量两组排序数据之间关系的强度和方向，得出的值介于 -1 到 +1 之间。
rs = 1 – [ (6 × Σd²) ÷ (n(n² – 1)) ]
In this formula, d is the difference between the ranks for each pair of scores, and n is the number of pairs. A result close to +1 means a strong positive correlation; close to -1 means a strong negative correlation; near 0 means no correlation.
在这个公式中，d 是每对数据的等级差，n 是对数。结果接近 +1 表示强正相关，接近 -1 表示强负相关，接近 0 表示不相关。
For Year 7, you might use a simplified version or just understand that a formula exists to turn messy data into a neat number that tells us how two things move together, such as hours of revision and test scores.
对于七年级同学，你可能使用简化过程或只需理解存在这样一个公式，能把杂乱的数据转化为一个规整的数字，告诉我们两个事物如何共同变化，比如复习时间和测验分数的关系。
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