📚 Year 9 CCEA Psychology: Formula & Theorem Quick Reference Handbook | CCEA Year 9 心理学：公式定理速查手册
This quick reference handbook summarises the key formulas, theorems, and essential principles you need for Year 9 CCEA Psychology. From research methods and statistics to memory models and social influence, each section provides concise definitions, mathematical expressions, and classic study findings. Use it as a portable revision tool to reinforce your understanding of how psychologists design studies, analyse data, and explain behaviour.
这本速查手册总结了Year 9 CCEA心理学所需的关键公式、定理和基本原理。从研究方法和统计到记忆模型和社会影响，每个部分都提供简明定义、数学表达式和经典研究结论。把它当作便携复习工具，巩固你对心理学家如何设计研究、分析数据和解释行为的理解。
1. Research Variables | 研究变量
An independent variable (IV) is the factor the researcher deliberately changes or manipulates in an experiment. The dependent variable (DV) is the outcome that is measured to see if it has been affected by the IV. For cause and effect to be established, the IV must be the only systematic difference between conditions.
自变量（IV）是研究者在实验中故意改变或操纵的因素。因变量（DV）是被测量的结果，用来观察它是否受自变量的影响。要确立因果关系，自变量必须是不同实验条件之间唯一的系统性差异。
Extraneous variables (EVs) are any other variables that might influence the DV and must be controlled. Confounding variables are EVs that change systematically with the IV, making it impossible to tell which variable caused the effect.
额外变量（EVs）是任何可能影响因变量的其他变量，必须加以控制。混淆变量是那些随自变量一起系统性变化的额外变量，会使得无法判断究竟是哪个变量导致了效应。
Operationalisation means defining the IV and DV in precise, measurable terms so that the experiment can be replicated. For example, instead of testing "memory", you might measure "the number of words recalled from a list of 20".
操作化是指用精确、可测量的方式定义自变量和因变量，以便实验能够重复。例如，不是测试“记忆力”，而是测量“从20个单词列表中正确回忆的个数”。
2. Experimental Designs | 实验设计
Independent groups design allocates different participants to each condition of the IV. This avoids order effects but may introduce participant variables – individual differences between the groups that could affect the DV.
独立组设计将不同的参与者分配到自变量的每一个条件。这避免了顺序效应，但可能引入参与者变量——各组之间的个体差异可能影响因变量。
Repeated measures design uses the same participants in all conditions. This controls participant variables perfectly, but order effects such as practice or fatigue can distort results. Counterbalancing (changing the order of conditions for half the participants) can reduce this problem.
重复测量设计在所有条件下使用同一批参与者。这完美控制了参与者变量，但顺序效应（如练习效应或疲劳效应）可能歪曲结果。平衡法（让一半参与者按相反顺序接受条件）可以减轻这个问题。
Matched pairs design uses different but similar participants in each condition. Participants are matched on key characteristics (e.g. age, IQ) before being randomly assigned to conditions. This reduces participant variables without order effects, but matching is never perfect.
配对组设计在每个条件下使用不同但相似的参与者。参与者在关键特征（如年龄、智商）上进行匹配后，被随机分配到各个条件。这减少了参与者变量且没有顺序效应，但匹配永远无法做到完美。
3. Sampling Techniques | 取样技术
Random sampling gives every member of the target population an equal chance of being selected, often using a random number generator. This method is unbiased but can be impractical and may still produce an unrepresentative sample by chance.
随机抽样让目标人群中的每个成员都有同等被选中的机会，通常使用随机数生成器。这种方法无偏差，但可能不切实际，并且偶尔仍会因偶然得到不具代表性的样本。
Opportunity sampling selects participants who are readily available, such as students in the same school. It is quick and cheap, but the sample is likely to be biased because it only includes a narrow type of person.
机会抽样选择随手可得的参与者，如同一所学校的学生。它速度快、成本低，但样本很可能有偏差，因为它只包含了单一类型的人。
Volunteer (self-selected) sampling involves participants putting themselves forward to take part, often in response to an advertisement. Volunteers tend to be highly motivated, but the sample may not be representative of the wider population because of volunteer bias.
志愿者（自我选择）抽样让参与者主动报名参加，通常是通过广告招募。志愿者往往积极性很高，但由于志愿者偏差，样本可能无法代表更广泛的人群。
Stratified sampling divides the population into subgroups (strata) based on relevant characteristics and then randomly selects participants from each stratum in proportion to their occurrence in the population. This gives a very representative sample but is time-consuming and requires detailed knowledge of the population.
分层抽样根据相关特征将人群划分为子群体（层），然后按各层在总体中的比例从每层随机选择参与者。这能获得极具代表性的样本，但耗时且需要详细了解总体情况。
4. Ethical Principles | 伦理原则
The British Psychological Society (BPS) Code of Ethics and Conduct sets out four core principles: respect, competence, responsibility, and integrity. In school‑based research, we particularly focus on six practical guidelines designed to protect participants.
英国心理学会（BPS）的伦理准则规定了四项核心原则：尊重、能力、责任和诚信。在校园研究中，我们特别关注六条旨在保护参与者的实践指南。
Informed consent: Participants (or their guardians) must be told the true aim and procedures of the study and then give their permission to take part. Deception should be avoided unless scientifically essential and justified.
知情同意：必须告知参与者（或其监护人）研究的真实目的与程序，之后他们同意才能参与。除非有科学上的必要且理由充分，否则应避免欺骗。
Right to withdraw: Participants must be able to stop taking part at any time and have their data removed without penalty. Privacy must be respected, so data is often anonymised by using codes instead of names. Protection from harm: no physical or psychological harm should come to participants beyond what they would encounter in daily life.
退出权：参与者必须能够随时停止参与，并将其数据删除而不受任何惩罚。隐私必须得到尊重，因此数据常通过编码而非姓名来匿名化。免受伤害：参与者不应遭受超出日常生活中遇到的任何身体或心理伤害。
Debriefing: after the study, the researcher must explain the full purpose, reveal any deception, and check the wellbeing of participants. These ethical safeguards are not just rules; they are a theorem of good practice – without them, psychological knowledge cannot be gained responsibly.
事后解说：研究结束后，研究者必须解释完整目的、揭示任何欺骗并检查参与者的状态。这些伦理保障不仅是规则，更是良善实践的定理——没有它们，就无法负责任地获取心理学知识。
5. Measures of Central Tendency | 集中趋势测量
Measures of central tendency summarise a data set by identifying a typical or average score. The three main measures are the mean, the median, and the mode. Choosing the right one depends on the level of measurement and the presence of outliers.
集中趋势测量通过确定一个典型或平均数值来概括一组数据。三种主要指标是平均值、中位数和众数。选择合适的指标取决于测量尺度以及是否存在异常值。
Mean = Σx / n
The mean takes every score into account. Σx is the sum of all values, and n is the number of values. It is used for interval or ratio data and is sensitive to extreme scores.
平均值考虑了每一个分数。Σx 是所有值的总和，n 是值的个数。它用于等距或等比数据，对极端分数很敏感。
The median is the middle value when scores are ordered from smallest to largest. If there is an even number of scores, the median is the mean of the two middle values. It is unaffected by outliers, making it the best measure for skewed data sets or ordinal data.
中位数是将分数从小到大排序后位于中间的数值。如果分数个数为偶数，中位数是中间两个值的平均数。它不受异常值影响，是偏态数据或顺序数据最适合的测量指标。
The mode is the most frequently occurring score. It can be used with nominal data (categories) and is the only measure of central tendency suitable for non‑numerical labels. A data set may have one mode, more than one mode, or no mode at all.
众数是出现频率最高的分数。它可用于称名数据（类别），并且是唯一适用于非数值标签的集中趋势测量。一组数据可能有一个众数、多个众数或根本没有众数。
6. Measures of Dispersion | 离散趋势测量
Dispersion describes how spread out the scores are. The simplest measure is the range, but psychologists also use the interquartile range and standard deviation for more advanced analysis. For Year 9, the range is the key formula to know.
离散程度描述分数的分布有多广。最简单的指标是全距，但在更高级的分析中心理学家也会使用四分位距和标准差。对Year 9来说，全距是需要掌握的关键公式。
Range = Highest score − Lowest score
ge signals high variability. Always report the range as a single number (e.g. Range = 12).
全距只用到两个数值，因此它不能告诉我们中间分数的分布模式。全距小说明数据一致性高，全距大表明变异性高。一律将全距报告为一个单独的数字（例如全距=12）。
When two data sets have the same mean but very different ranges, the one with the larger range is more dispersed. Outliers can dramatically inflate the range, so sometimes the interquartile range is preferred for a truer picture of spread.
当两组数据具有相同的平均值但全距差异很大时，全距较大的那组数据更分散。异常值可能会显著夸大全距，因此有时人们更偏好用四分位距来更真实地反映离散情况。
7. Presenting Data | 数据呈现
Choosing the correct graph or chart is a theorem of good scientific communication. Bar charts display frequency data for separate categories (nominal data). The bars do not touch, emphasising that the categories are distinct.
选择正确的图形或图表是良好科学交流的一条定理。条形图展示离散类别（称名数据）的频数。条形之间不接触，以强调类别是互不相同的。
Histograms also show frequency but are used for continuous data that have been grouped into equal class intervals. The bars touch to indicate that the data sit on a continuous scale. Scattergrams plot two co‑variables to show correlations.
直方图同样展示频数，但用于已被分入等组距的连续数据。条形彼此接触，以表示数据位于连续尺度上。散点图绘出两个共变项，用于显示相关关系。
Positive correlation: as one variable increases, the other tends to increase. Negative correlation: as one variable increases, the other tends to decrease. Zero correlation means no linear relationship. A correlation coefficient (r) ranges from −1 to +1; values closer to the extremes indicate stronger associations.
正相关：一个变量增大，另一个也倾向于增大。负相关：一个变量增大，另一个倾向于减小。零相关表示没有线性关系。相关系数（r）的取值范围从−1 到 +1；数值越接近两端，关联越强。
Always label axes, give units, and provide a clear title. The visual presentation of data can reveal patterns that summary statistics alone might hide – a core theorem in any psychologist's toolbox.
务必标注坐标轴、提供单位并给出清晰标题。数据的可视化呈现能够揭示仅靠汇总统计可能隐藏的模式——这是每位心理学家工具箱中的一项核心定理。
8. Multi-Store Model of Memory | 记忆多存储模型
Atkinson and Shiffrin's (1968) multi‑store model describes memory as a flow of information through three separate stores. Information enters sensory memory, and if we pay attention to it, it passes into short‑term memory. Rehearsal then transfers it into long‑term memory.
阿特金森和谢夫林（1968）的多存储模型将记忆描述为信息流经三个独立存储器的过程。信息首先进入感觉记忆，如果我们加以注意，它便进入短时记忆。复述再将其转入长时记忆。
y for hearing (≈2 seconds). It has a very large capacity but decays rapidly if unattended.
感觉记忆（SM）将原始感觉印象保持几分之一秒：视觉的瞬时记忆约0.5秒，听觉的回声记忆约2秒。它的容量非常大，但若不加以注意便会迅速衰退。
Short‑term memory (STM) is a temporary store with a limited duration of about 18–30 seconds and a limited capacity. Miller' s. Rehearsal can maintain information in STM, but without it, information is lost through displacement or decay.
短时记忆（STM）是一个临时存储，持续时间有限，约18–30秒，容量也有限。米勒定律指出其容量为7±2个组块。复述可以把信息维持在短时记忆中，但若不复述，信息会因被替换或衰退而丧失。
Long‑term memory (LTM) is believed to have unlimited capacity and can hold information for a lifetime. Encoding in LTM is mainly semantic, based on meaning. Forgetting from LTM is likely due to interference or retrieval failure, not simple decay.
长时记忆（LTM）被认为具有无限容量，可终身保持信息。长时记忆中的编码主要是语义性的，基于意义。长时记忆中的遗忘很可能是由于干扰或提取失败，而非简单的衰退。
9. Miller's Law and Chunking | 米勒定律与组块
STM capacity ≈ 7 ± 2 items
6) proposed that most people can hold between five and nine pieces of information in short‑term memory at once. The magic number 7 ± 2 applies to chunks – meaningful units that can be individual items or grouped material.
乔治·米勒（1956）提出，大多数人的短时记忆一次大约能容纳五到九个信息单元。神奇数字7±2适用于组块——即有意义的信息单元，可以是单独的项目，也可以是组合材料。
Chunking is the process of combining smaller units into larger, meaningful wholes. For example, remembering the sequence "FBICIAUK" is easier if you chunk it into "FBI – CIA – UK". By increasing the size of each chunk, we expand the amount of information held in STM without increasing the number of chunks.
组块是将较小单元组合成较大有意义整体的过程。例如，记住序列“FBICIAUK”，如果将它组块为“FBI – CIA – UK”，就容易得多。通过增大每个组块的容量，我们在不增加组块数量的前提下扩展了短时记忆的信息量。
Teachers use chunking when they break complex topics into manageable sections. When revising, actively group related facts together to turn a long list into a few chunks – a revision theorem supported by decades of cognitive research.
教师将复杂课题拆解为易操作的部分时，就是在使用组块策略。复习时，主动将相关事实归类，把长串信息变成少量组块——这是一条得到数十年认知研究支持的复习定理。
10. Serial Position Effect | 序列位置效应
The serial position effect is a theorem of memory retrieval: when we are given a list of words to recall, we tend to remember the first few items (primacy effect) and the last few items (recency effect) better than the middle ones.
序列位置效应是记忆提取的定理：当我们被要求回忆一个单词列表时，我们往往对开头几个项目（首因效应）和末尾几个项目（近因效应）的记忆优于中间的项目。
The primacy effect occurs because the first items receive more rehearsal and are transferred into long‑term memory. The recency effect occurs because the last items are still held in short‑term memory at the moment of recall, so they can be quickly output.
首因效应出现的原因是最初的项目获得了更多复述，并转入了长时记忆。近因效应出现的原因是，在回忆的时刻，末尾的项目仍保留在短时记忆中，因此能被迅速输出。
If a distractor task (e.g. counting backwards for 30 seconds) is introduced after the list, the recency effect disappears because the distraction disrupts the fragile contents of STM. The primacy effect remains unaffected because it relies on LTM.
如果在呈现列表后引入干扰任务（例如倒计数30秒），近因效应就会消失，因为干扰破坏了短时记忆中的脆弱内容。首因效应则不受影响，因为它依赖的是长时记忆。
This dual‑store evidence supports the distinction between STM and LTM, making the serial position effect a straightforward empirical formula for demonstrating the multi‑store model in action.
这种双存储证据支持了短时记忆和长时记忆的区分，使序列位置效应成为证明多存储模型运作的一个直接的经验公式。
11. Attachment Types | 依恋类型
Mary Ainsworth's Strange Situation assessed the quality of attachment between an infant and caregiver. Three main patterns emerged, and their approximate distributions in the UK are often cited as a descriptive theorem of early social development.
玛丽·安斯沃斯的陌生情境评估了婴儿与照看者之间依恋的质量。出现了三种主要模式，它们在英国的大致分布常被引用为早期社会发展的一项描述性定理。
Secure attachment (Type B, ≈65% , but is easily comforted upon return. The caregiver is a safe base from which to explore.
安全型依恋（B类型，约65%）：照看者在场时，婴儿自由探索；照看者离开时表现出忧伤，但照看者回来时容易得到安抚。照看者是探索的安全基地。
Insecure‑avoidant attachment (Type A, ≈20% he caregiver returns. The infant behaves as if the caregiver is not important for comfort.
不安全-回避型依恋（A类型，约20%）：婴儿在很大程度上忽视照看者，被单独留下时忧伤甚少，照看者返回时回避接触。婴儿的表现仿佛照看者对安慰并不重要。
Insecure‑resistant (ambivalent) attachment (Type C, ≈15% n the caregiver leaves, but resists comfort and shows conflicting behaviours upon reunion.
不安全-反抗型（矛盾型）依恋（C类型，约15%）：婴儿十分粘人且不愿探索，照看者离开时极度忧伤，但在重聚时抗拒安慰并表现出矛盾行为。
The mother's sensitivity to the child's signals is one of the strongest predictors of secure attachment. These three categories, though simplified, remain a foundational classification theorem in developmental psychology.
母亲对婴儿信号的敏感性是预测安全型依恋的最强因子之一。尽管这三种分类有所简化，但它们依然是发展心理学中一项基础性的分类定理。
12. Conformity and Obedience | 从众与服从
Conformity is a change in a person's behaviour or opinions as a result of real or imagined pressure from a group. Asch (1951) found that on critical trials where the majority gave an obviously wrong answer, participants conformed about 37% of the time.
从众是指个人行为或观点因来自群体的真实或想象的压力而发生改变。阿西（1951）发现，在多数人给出明显错误答案的关键测试中，参与者大约有37%的试次表现出从众。
Key factors affecting conformity: group size (conformity increases up to about three or four confederates), unanimity (a single dissenter reduces conformity significantly), and task difficulty (harder tasks increase conformity). These variables function almost like adjustable parameters in a social influence formula.
影响从众的关键因素：群体大小（增加到三四个假被试时从众增加）、一致性（哪怕只有一个异议者也能显著降低从众）以及任务难度（任务越难从众越高）。这些变量几乎像社会影响公式中可调节的参数一样发挥作用。
Obedience involves following a direct order from an authority figure. Milgram (1963) found that 65% of participants administered the full 450 V shock when instructed by an experimenter in a lab coat, a result that shocked the scientific community.
服从涉及遵循权威人物发出的直接命令。米尔格拉姆（1963）发现，当一位身穿实验室白大褂的实验者发出指令时，65%的参与者给出了全部450伏电击，这一结果令科学界震惊。
Obedience rates dropped when the authority figure was remote (telephoned instructions), when the victim was in the same room, or when another confederate disobeyed
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