📚 Year 8 SQA Psychology: Formula & Theorem Quick Reference Guide | Year 8 SQA 心理学：公式定理速查手册
This guide brings together the essential statistical formulas, experimental principles, and key theories you will encounter in Year 8 SQA Psychology. Using these formulas and theorems correctly will help you describe data, understand behaviour, and design fair research.
本手册汇集了 Year 8 SQA 心理学中你将遇到的必备统计公式、实验原理和核心理论。正确运用这些公式与定理，能帮助你描述数据、理解行为，并设计公正的研究。
1. Mean, Median and Mode | 平均数、中位数与众数
The mean is calculated by adding all scores together and dividing by the number of scores. It is the most sensitive measure of central tendency but can be distorted by extreme values.
平均数是将所有分数相加，再除以分数的个数。它是最灵敏的集中趋势量数，但容易受到极端值的扭曲。
Mean = (X₁ + X₂ + ... + Xₙ) ÷ n
The median is the middle score when all scores are arranged in order. For an even number of scores, take the mean of the two middle values. The median is not affected by outliers.
中位数是将所有分数排序后处于正中间的分数。若分数的个数为偶数，则取中间两个分数的平均数。中位数不受异常值的影响。
The mode is the most frequently occurring score in a data set. A set of scores can have one mode, more than one mode (bimodal), or no mode at all.
众数是数据集中出现次数最多的分数。一组分数可以有一个众数、多个众数（双众数），或者完全没有众数。
2. Range and Percentage | 范围与百分比
The range is a simple measure of dispersion. It tells you how spread out the scores are. A larger range indicates greater variability.
范围是一种简单的离差量数，表明分数的分布广度。范围越大，说明数据变异性越大。
Range = Highest score – Lowest score
Percentage expresses a score as a fraction of the total, multiplied by 100. In psychology, you might calculate the percentage of participants who recalled at least five words in a memory test.
百分比将某个分数表示为占总数的比例，再乘以 100。在心理学中，你可能会计算在一个记忆测验中至少回忆起五个单词的被试所占的百分比。
Percentage = (Part ÷ Whole) × 100
3. Experimental Design: IV and DV | 实验设计：自变量与因变量
The independent variable (IV) is the factor the researcher manipulates or changes. The dependent variable (DV) is the factor the researcher measures. Everything else should be controlled to prevent confounding variables.
自变量（IV）是研究者操纵或改变的因素。因变量（DV）是研究者测量的因素。其他所有因素都应加以控制，以防止混淆变量。
For example, in an experiment testing whether background music affects concentration (measured by the number of puzzles solved), the IV is the presence or type of music, and the DV is the number of puzzles solved correctly.
例如，在一个测试背景音乐是否影响专注力（以解谜数量衡量）的实验中，自变量是音乐的有无或类型，因变量是正确解谜的数量。
Key principle: The IV comes before the DV in time, and the DV should depend on the IV. Always identify these two variables clearly in any experiment question.
关键原则：自变量在时间上先于因变量，且因变量应取决于自变量。在任何实验问题中，务必清晰地识别这两个变量。
4. Classical Conditioning: Pavlov's Law | 经典条件反射：巴甫洛夫定律
Classical conditioning involves learning through association. A neutral stimulus becomes associated with an unconditioned stimulus that naturally triggers a response. After repeated pairings, the neutral stimulus alone can evoke a conditioned response.
经典条件反射通过学习联结而实现。一个中性刺激与一个自然引发反应的非条件刺激建立关联。反复配对后，仅中性刺激本身就能唤起条件反应。
Pavlov' r conditioning, Conditioned Stimulus (CS - bell) → Conditioned Response (CR - salivation).
巴甫洛夫的经典公式：非条件刺激（UCS——食物）→ 非条件反应（UCR——分泌唾液）。中性刺激（NS——铃声）+ UCS → UCR。条件作用形成后，条件刺激（CS——铃声）→ 条件反应（CR——分泌唾液）。
The key theorem states that acquisition occurs when the CS reliably predicts the UCS. Extinction happens when the CS is presented alone repeatedly, and spontaneous recovery shows the response can briefly return after a rest period.
核心定理表明，当条件刺激可靠地预测非条件刺激时，习得就发生了。消退则发生在条件刺激被单独多次呈现时，而自然恢复表明，反应在休息一段时间后可以短暂重现。
5. Operant Conditioning: Skinner's Principles | 操作性条件反射：斯金纳原理
Operant conditioning is learning through consequences. Behaviour is shaped and maintained by reinforcement and punishment. Skinner’s law states that behaviours followed by favourable outcomes are strengthened, while those followed by unfavourable outcomes are weakened.
操作性条件反射是通过后果进行学习。行为由强化和惩罚所塑造和维持。斯金纳定律指出，带来有利结果的行为会得到加强，带来不利结果的行为则会减弱。
Positive reinforcement: adding something pleasant to increase behaviour (e.g., praise for completing homework). Negative reinforcement: removing something unpleasant to increase behaviour (e.g., taking a painkiller to remove a headache).
正强化：增加愉快刺激以提高行为频率（如完成作业后给予表扬）。负强化：移除厌恶刺激以增加行为频率（如服用止痛药消除头痛）。
Positive punishment: adding something unpleasant to decrease behaviour (e.g., a fine for littering). Negative punishment: removing something pleasant to decrease behaviour (e.g., losing screen time for breaking a rule). Do not confuse negative reinforcement with punishment.
正惩罚：增加厌恶刺激以减少行为（如乱扔垃圾处以罚款）。负惩罚：移除愉快刺激以减少行为（如违规后减少屏幕时间）。切勿将负强化与惩罚混为一谈。
6. Piaget's Stages of Cognitive Development | 皮亚杰认知发展阶段
Piaget’s theory proposes that children’s thinking develops in four invariant stages. Each stage is characterised by different cognitive abilities and ways of understanding the world.
皮亚杰的理论认为，儿童的思维发展经历四个恒定的阶段。每个阶段具有不同的认知能力和理解世界的方式。
| Stage | Age Range | Key Features |
|---|---|---|
| Sensorimotor | 0–2 years | Object permanence; learning through senses and actions |
| Preoperational | 2–7 years | Egocentrism; symbolic play; lack of conservation |
| Concrete Operational | 7–11 years | Conservation; logical thinking about concrete objects; reversibility |
| Formal Operational | 11+ years | Abstract reasoning; hypothetical thinking; systematic problem solving |
The theorem of conservation is a key milestone: understanding that quantity remains the same despite changes in appearance. Children in the preoperational stage lack this, while those in the concrete operational stage have mastered it.
守恒定理是一个关键里程碑：理解即使物体的外观发生变化，其数量依然不变。前运算阶段的儿童尚未具备该能力，而具体运算阶段的儿童已经掌握。
7. Maslow's Hierarchy of Needs | 马斯洛需求层次理论
Maslow’s theorem suggests that human motivation is organised in a hierarchy. Lower-level needs must be reasonably satisfied before higher-level needs can become motivators. The original five-stage pyramid progresses from basic to self-fulfilment needs.
马斯洛的定理认为，人类动机是按层次组织的。必须先大致满足较低层次的需求，较高层次的需求才能成为激励因素。最初的五层金字塔由基本需求逐步升至自我实现需求。
Physiological → Safety → Love/Belonging → Esteem → Self-actualisation
Physiological needs include food, water, and sleep. Safety needs involve security and freedom from danger. Love and belonging refers to friendships, family, and intimacy. Esteem includes self-respect and recognition from others. Self-actualisation is the desire to achieve one’s full potential.
生理需求包括食物、水和睡眠。安全需求涉及安全感和远离危险。归属与爱指的是友谊、家庭和亲密关系。尊重需求包含自尊和他人的认可。自我实现是发挥个人全部潜能的愿望。
In Year 8 psychology, this hierarchy helps explain why a child who is hungry or tired will struggle to focus on learning until those basic needs are met.
在 Year 8 心理学中，这个层次理论有助于解释为什么饥饿或疲倦的儿童，在基本需求得到满足之前，很难专注于学习。
8. Asch's Conformity Theorem | 阿希从众定理
Solomon Asch’s line judgement experiments demonstrated normative social influence. Even when the correct answer was obvious, participants often conformed to an incorrect group decision. Asch found that about 75% of participants conformed at least once.
所罗门·阿希的线条判断实验证明了规范性社会影响。即使正确答案显而易见，被试也常常顺从群体的错误决定。阿希发现，约 75% 的被试至少从众过一次。
Key variables that affect conformity according to Asch’s theorem: group size (conformity increases with up to three confederates, then levels off), unanimity (if one other person breaks the consensus, conformity drops sharply), and task difficulty (more conformity when the task is harder).
根据阿希定理，影响从众的关键变量有：群体规模（三名同谋之内从众率上升，随后趋于平缓）、一致性（只要有一人打破共识，从众率便急剧下降）和任务难度（任务越难，从众程度越高）。
The theoretical explanation is that people either conform because they want to fit in (normative influence) or because they believe the group is better informed (informational influence).
理论解释是，人们从众的原因要么是为了合群（规范性影响），要么是因为他们认为群体掌握了更准确的信息（信息性影响）。
9. Bartlett's Schema Theory | 巴特利特图式理论
Bartlett argued that memory is not a passive retrieval of information but an active reconstruction based on schemas – mental frameworks of knowledge and experience. His famous 'War of the Ghosts' study showed that people tend to alter memories to fit their existing schemas.
巴特利特主张，记忆不是被动的信息提取，而是基于图式——即知识与经验的心理框架——的主动重构。他著名的“幽灵之战”研究表明，人们往往将记忆改变，以契合自己已有的图式。
According to the theorem, schemas influence every stage of memory: they affect how we encode information, how we store it, and how we retrieve it. Omissions, rationalisations, and transformations are common when we retell a story.
根据该定理，图式影响记忆的每一个阶段：它们影响我们编码信息的方式、存储的方式和提取的方式。当我们复述故事时，遗漏、合理化和转化现象很常见。
This theory is essential for understanding why eyewitness testimony can be unreliable. Our pre-existing schemas about gender, race, or crime can distort what we think we saw.
这个理论对于理解目击者证词为何可能不可靠至关重要。我们关于性别、种族或犯罪的已有图式，可能会扭曲我们以为自己看到的东西。
10. The Multi-Store Model of Memory (Atkinson & Shiffrin) | 多储存记忆模型（阿特金森与谢夫林）
This model describes memory as consisting of three separate stores: sensory memory, short-term memory (STM), and long-term memory (LTM). Information flows through these stores in a linear fashion, provided attention and rehearsal take place.
这个模型将记忆描述为由三个独立的储存库组成：感觉记忆、短时记忆（STM）和长时记忆（LTM）。只要发生注意和复述，信息便以线性方式流经这些储存库。
Sensory memory → (Attention) → STM → (Rehearsal) → LTM
heorem: STM has a limited capacity of about 7 ± 2 items and a duration of approximately 18– fetime. Information in STM is encoded mainly acoustically, while LTM encodes semantically.
关键定理：短时记忆的容量有限，约为 7 ± 2 个项目，且若无复述，持续时间约为 18–30 秒。长时记忆被认为拥有无限的容量，可以储存信息达一生之久。短时记忆中的信息主要为声学编码，而长时记忆为语义编码。
Rehearsal acts as a maintenance loop. If you repeat a phone number to yourself, you keep it in STM. If you process it meaningfully, you transfer it to LTM. This explains why elaborative rehearsal is more effective for learning than rote repetition.
复述充当了一种维持回路。如果你对自己重复一个电话号码，就能将它保持在短时记忆中。如果你对它进行意义加工，就会将其转入长时记忆。这就解释了为什么精细复述比机械重复更有利于学习。
11. Ethical Guidelines (BPS) | 伦理准则（BPS）
All psychological research in the UK must follow ethical principles set by the British Psychological Society (BPS). These principles protect the welfare of participants. The core ethical formula is that the benefits of research should always outweigh the potential risks.
英国所有的心理学研究必须遵循英国心理学会（BPS）制定的伦理原则。这些原则保护被试的福祉。核心伦理公式是，研究的益处必须始终大于潜在风险。
Six key principles: informed consent (participants should know what they are agreeing to), deception should be avoided unless justified, right to withdraw at any time, protection from physical and psychological harm, confidentiality of data, and full debriefing after the study.
六项关键原则：知情同意（被试应知晓自己同意什么）、除非有正当理由否则避免欺骗、随时退出的权利、免受身体和心理伤害、数据保密，以及研究结束后的完整解释性报告。
In Year 8 research tasks, always state how you will gain consent, keep identities anonymous, and allow participants to stop at any time. References to these ethical standards will strengthen your evaluation marks.
在 Year 8 的研究任务中，始终要说明你将如何获取同意、如何匿名处理身份信息，以及允许被试随时中止参与。提及这些伦理规范能为你的评估得分添彩。
12. Research Methods: Hypothesis and Variables | 研究方法：假设与变量
A hypothesis is a precise, testable statement predicting the relationship between an IV and a DV. For an experiment, you need an experimental hypothesis (predicts a difference or effect) and a null hypothesis (states there will be no difference or effect).
假设是一份精确、可检验的陈述，预测自变量与因变量之间的关系。对于实验而言，你需要提出实验假设（预测差异或效应）和虚无假设（陈述将没有差异或效应）。
Operationalisation means defining the variables clearly so they can be measured. For instance, 'memory' might be operationalised as 'the number of words correctly recalled from a list of 15'. Without operationalisation, a study cannot be replicated.
操作化意味着明确界定变量，使其可以被测量。例如，“记忆力”可操作化为“从 15 个单词的列表中正确回忆出的单词数”。缺乏操作化，研究便无法重复。
Control of extraneous variables is a central theorem of experimental psychology. Standardised instructions, same environment, and random allocation of participants to conditions all help ensure the IV is the only systematic difference between groups.
控制额外变量是实验心理学的一项核心定理。标准化指示语、相同的环境以及将被试随机分配到各实验条件中，均有助于确保自变量是各组之间唯一的系统性差异。
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