📚 Year 9 CIE Psychology: Formula and Theorem Quick Reference Handbook | CIE 九年级心理学：公式定理速查手册
This quick reference handbook brings together the essential formulas, models, and foundational theories you need for Year 9 CIE Psychology. From statistical measures used in research methods to classic psychological theories that explain human behaviour, each section is presented in a clear, bilingual format to support your revision and understanding.
本速查手册汇集了 CIE 九年级心理学必备的公式、模型与基础理论。从研究方法中的统计量度到解释人类行为的经典心理学理论，每个小节均以清晰的双语对照呈现，助力你的复习与理解。
1. Measures of Central Tendency | 集中趋势的度量
The mean is the arithmetic average of a set of scores, sensitive to every value in the dataset.
平均数是一组分数的算术平均值，它对数据中的每一个数值都很敏感。
Mean (M) = (Σx) / N
Σx represents the sum of all scores, and N is the total number of observations.
其中 Σx 代表所有分数之和，N 为观察值的总数。
The median is the middle value when data are sorted in ascending order; for an even number of scores, it is the average of the two middle numbers.
中位数是将数据按升序排列后中间的那个值；当分数为偶数个时，它是中间两个数的平均值。
The mode is the most frequently occurring score in a distribution, and a data set can have one mode (unimodal), two modes (bimodal) or more.
众数是一组数据中出现次数最多的分数；一个数据集可以有一个众数（单峰）、两个众数（双峰）或更多。
When data are normally distributed, the mean, median and mode all have the same value.
当数据呈正态分布时，平均数、中位数和众数的值均相等。
2. Measures of Dispersion | 离散度的度量
The range is the simplest measure of spread, calculated by subtracting the smallest value from the largest value.
全距是最简单的离散度指标，由最大值减去最小值得到。
Range = Xmax - Xmin
A large range indicates greater variability in the data, while a small range suggests scores are clustered together.
全距越大表示数据的变异性越大，全距越小则说明分数较为集中。
The standard deviation (SD) tells us the average distance of each data point from the mean; a smaller SD means scores are tightly packed around the mean.
标准差（SD）告诉我们每个数据点与平均数的平均距离；标准差越小，分数围绕平均数越紧密。
SD = √[ Σ(x - M)² / (N - 1) ]
Here (x - M) is the deviation of each score from the mean, squared to remove negative signs, and N - 1 is used for sample standard deviation.
这里 (x - M) 是每个分数与平均数的离差，平方以消除负号，N - 1 用于计算样本标准差。
Both the range and standard deviation are crucial for interpreting the consistency of behaviour in psychological research.
全距和标准差对于解释心理学研究中行为数据的一致性都至关重要。
3. Normal Distribution and Skew | 正态分布与偏态
A normal distribution is a symmetrical, bell-shaped curve where most observations cluster around the central peak.
正态分布是一种对称的钟形曲线，绝大多数观察值聚集在中央峰周围。
In a perfect normal distribution, the mean, median, and mode coincide, and 68% of all scores lie within one standard deviation of the mean.
在完美的正态分布中，平均数、中位数和众数重合，且 68% 的分数落在平均数的一个标准差范围内。
A positively skewed distribution has a long tail on the right, with the mean pulled in the direction of the extreme high scores.
正偏态分布在右侧拖着长尾，平均数被拉向极高值的方向。
For positive skew: Mean > Median > Mode
When the skew is negative, the long tail is on the left and the relationship among the three measures reverses.
当数据呈负偏态时，长尾出现在左侧，三者的大小关系也随之逆转。
For negative skew: Mean < Median < Mode
Recognising skew is vital for choosing the most appropriate measure of central tendency; the median is often preferred for skewed distributions.
识别偏态对于选择最合适的集中趋势指标至关重要；对于偏态分布，通常首选中位数。
4. Correlation and Scatter Plots | 相关与散点图
A correlation describes the strength and direction of a relationship between two co-variables, illustrated by a scatter plot.
相关描述了两个共变量之间关系的强度和方向，并通过散点图加以展示。
, r = -1 means a perfect negative correlation, and r = 0 indicates no linear relationship.
相关系数 (r) 的取值范围在 -1 到 +1 之间：r = +1 表示完全正相关，r = -1 表示完全负相关，r = 0 则意味着不存在线性关系。
-1 ≤ r ≤ 1
In a positive correlation, as one variable increases, the other also tends to increase; the points on the scatter plot slope upwards.
在正相关中，当一个变量增加时另一个也倾向于增加，散点图中的点向上倾斜。
In a negative correlation, one variable increases while the other decreases, producing a downward slope on the graph.
在负相关中，一个变量增加而另一个减少，在图上呈现出向下的斜率。
Correlation does not imply causation; a third variable may be influencing both measured factors.
相关并不代表因果关系；可能第三个变量同时在影响所测量的两个因素。
5. Multi-Store Model of Memory | 记忆的多存储模型
Atkinson and Shiffrin (1968) proposed that memory consists of three separate stores linked by control processes.
Atkinson 和 Shiffrin（1968）提出记忆由三个独立的存储库组成，它们通过控制过程相互连接。
Sensory Memory → Attention → Short-Term Memory → Elaborative Rehearsal → Long-Term Memory
Sensory memory holds information from the senses for a fraction of a second; only attended information passes on to STM.
感觉记忆保存来自感官的信息仅几分之一秒，唯有受到注意的信息才能进入短时记忆。
mory (STM) has a limited capacity of about 7 ± 2 chunks and a duration of approximately 18–30 seconds without rehearsal.
短时记忆（STM）的容量有限，大约为 7 ± 2 个组块，若无复述，持续时间约 18–30 秒。
Information can be maintained in STM through maintenance rehearsal; elaborative rehearsal links new information to existing knowledge, transferring it into long-term memory (LTM).
通过维持性复述可将信息保持在短时记忆中；精细复述则将新信息与已有知识关联，从而将其转入长时记忆。
Long-term memory has potentially unlimited capacity and duration, storing memories for factual knowledge, skills, and life events.
长时记忆的容量和持续时间可能无限，它存储着事实知识、技能和生活事件的记忆。
6. Bartlett’s Reconstructive Memory and Schema Theory | 巴特利特的重构记忆与图式理论
Bartlett’s 'War of the Ghosts' study demonstrated that memory is not a perfect recording but an active reconstruction influenced by schemas.
巴特利特的“战争之鬼”实验表明记忆并非完美的记录，而是在图式影响下的主动重构。
A schema is a mental framework of knowledge and expectations about the world, shaped by culture and experience.
图式是关于世界的知识与预期的心理框架，由文化和经验塑造而成。
When we recall an event, we fill gaps with schema-consistent details, often omitting unfamiliar elements or transforming them to make the story more coherent.
当我们回忆事件时，会用与图式一致的细节填补空缺，常常删除不熟悉的元素，或对其进行改编以使故事更加连贯。
Memory = Original trace + Schema-based reconstruction
Bartlett found that participants shortened the story, rationalised puzzling parts, and altered the narrative to fit their Western cultural schemas.
巴特利特发现参与者缩短了故事，使令人困惑的部分合理化，并改编叙事以符合他们的西方文化图式。
This 'reconstructive memory' theorem is essential for understanding why eyewitness testimony can be unreliable.
这一“重构记忆”定理对于理解为何目击者证词可能不可靠至关重要。
7. Piaget’s Stages of Cognitive Development | 皮亚杰的认知发展阶段
Jean Piaget proposed that children pass through four invariant stages of cognitive development, driven by assimilation and accommodation.
让·皮亚杰提出，儿童在顺应与同化的驱动下，经历四个不变的认知发展阶段。
| Stage | 阶段 | Age | 年龄 | Key Achievement | 关键成就 |
|---|---|---|
| Sensorimotor | 0–2 years | Object permanence: understanding objects exist even when out of sight |
| Pre-operational | 2–7 years | Egocentrism: difficulty seeing others’ viewpoints; symbolic play |
| Concrete operational | 7–11 years | Conservation: understanding that quantity stays the same despite changes in appearance |
| Formal operational | 11+ years | Abstract reasoning: ability to think hypothetically and systematically |
The conservation task, such as the classic liquid conservation experiment, reveals whether a child has shifted from pre-operational to concrete operational thinking.
守恒任务，例如经典的液体守恒实验，能揭示儿童是否已从前运算阶段过渡到具体运算阶段的思维。
Piaget’s theory is a cornerstone of developmental psychology, although later research suggests some abilities may emerge earlier than he predicted.
皮亚杰的理论是发展心理学的基石，尽管后来的研究表明某些能力可能比他预计的出现得更早。
8. Asch’s Conformity: Factors Influencing Conformity | 阿希从众实验与从众因素
Solomon Asch (1951) demonstrated the power of majority influence through a simple line-judgement task, revealing that people often conform to an obviously incorrect group answer.
所罗门·阿希（1951）通过简单的线段判断任务展示了多数人影响力的力量，揭示出人们常常会屈从于明显错误的群体答案。
Overall conformity rate ≈ 37% of critical trials
About 75% of participants conformed at least once; the average conformity rate across all critical trials was approximately 37%.
约 75% 的参与者在至少一次判断中从众；所有关键试次的平均从众率大约为 37%。
Conformity increased when the unanimous majority had three or more members, but the rate plateaued beyond three; a single dissenter dramatically reduced conformity.
当一致性多数群体有三人或以上时从众行为增加，但超过三人后趋于平缓；只要有一名异议者，从众率便显著下降。
Additional factors: task difficulty (higher conformity when the task is ambiguous), group attractiveness, and cultural context (higher conformity in collectivist cultures).
其他因素包括：任务难度（任务越模糊从众越强）、群体吸引力以及文化背景（集体主义文化中从众率更高）。
The Asch paradigm provides a 'conformity formula' for understanding social pressure and normative influence.
阿希范式为理解社会压力与规范性影响提供了“从众公式”。
9. Classical Conditioning: UCS, UCR, NS, CS, CR | 经典条件作用：范式速查
Pavlov’s classical conditioning explains how a neutral stimulus can come to elicit a reflexive response through association.
巴甫洛夫的经典条件作用解释了中性刺激如何通过联结而引发反射性反应。
Before conditioning: UCS → UCR ; NS → no response
The unconditioned stimulus (UCS) naturally triggers an unconditioned response (UCR); the neutral stimulus (NS) initially produces no relevant response.
无条件刺激（UCS）自然地引发无条件反应（UCR）；中性刺激（NS）起初不产生相关反应。
During conditioning: NS + UCS → UCR
After repeated pairings, the NS becomes a conditioned stimulus (CS), and the response it now elicits is the conditioned response (CR).
经过多次配对后，中性刺激成为条件刺激（CS），此时它所引发的反应即为条件反应（CR）。
After conditioning: CS → CR
Extinction occurs when the CS is repeatedly presented without the UCS, and the CR gradually weakens; spontaneous recovery can happen after a rest period.
消退发生在条件刺激反复单独呈现而无无条件刺激相随时，条件反应逐渐减弱；休息一段时间后可能出现自发恢复。
Classical conditioning is the basis for many phobia treatments, such as systematic desensitisation.
经典条件作用是众多恐惧症治疗方法的基础，例如系统脱敏疗法。
10. Operant Conditioning: Reinforcement Schedules | 操作性条件作用：强化程式
Skinner’s operant conditioning states that behaviours are shaped and maintained by their consequences: reinforcement increases a behaviour, punishment decreases it.
斯金纳的操作性条件作用指出，行为是由其后效塑造和维持的：强化增加行为发生的频率，惩罚则降低行为发生的频率。
Positive reinforcement: Add pleasant stimulus → behaviour ↑
Negative reinforcement involves removing an unpleasant stimulus to strengthen a behaviour; note that all reinforcement increases the likelihood of the behaviour.
负强化是通过消除厌恶刺激来增强行为；请记住，所有强化形式都会提高行为发生的可能性。
Negative reinforcement: Remove unpleasant stimulus → behaviour ↑
The pattern of delivering reinforcement is called the schedule, and it dramatically affects the rate and persistence of responding.
呈现强化的模式称为程式，它对反应的速率和持久性有着显著影响。
- Fixed Ratio (FR): Reinforcement after a set number of responses. Produces a high response rate with a brief post-reinforcement pause.
固定比率 (FR)： 在特定次数的反应后给予强化。产生很高的反应速率，但在强化后有短暂的停顿。 - Variable Ratio (VR): Reinforcement after an unpredictable number of responses. Produces a very high and steady response rate; most resistant to extinction.
可变比率 (VR)： 在不可预测的反应次数后给予强化。产生极高且稳定的反应速率，最不容易消退。 - Fixed Interval (FI): Reinforcement for the first response after a fixed time period has elapsed. Produces a scalloped pattern of responding.
固定间隔 (FI)： 在经过一段固定时间后出现的第一个反应得到强化。产生扇贝形的反应模式。 - Variable Interval (VI): Reinforcement for the first response after varying time intervals. Produces a moderate, steady response rate.
可变间隔 (VI)： 在不同时间间隔后出现的第一个反应得到强化。产生中等而稳定的反应速率。
Understanding schedules helps explain real-world behaviour, such as why gambling (VR) is highly addictive or why monthly salaries (FI) can produce predictable work patterns.
理解强化程式有助于解释现实世界的行为，例如为什么赌博（VR）极易成瘾，或月薪制（FI）如何产生可预测的工作模式。
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