SQA Psychology Formula & Theorem Quick Reference | SQA 心理学公式定理速查手册

📚 SQA Psychology Formula & Theorem Quick Reference | SQA 心理学公式定理速查手册

This quick-reference handbook presents key formulas, models, and principles for Year 11 SQA Psychology. Designed for National 5 revision, it covers essential descriptive statistics, research design concepts, and core theoretical frameworks that often appear in exam questions. Use these cards to master the numerical side of psychology and to recall the 'theorems' that explain human behaviour and mental processes.

这本速查手册汇集了 Year 11 SQA 心理学中的关键公式、模型和原理。专为 National 5 复习设计，涵盖了常出现在考题中的重要描述统计、研究设计概念以及核心理论框架。通过这些卡片，你既能掌握心理学中的数字计算，也能牢记那些解释人类行为与心理过程的“定理”。

1. Independent and Dependent Variables | 自变量与因变量

DV) is the outcome that is measured; it should change as a result of alterations to the IV. The core 'theorem' experimental design can be stated as: DV = f(IV), meaning the DV is a function of the IV.

在任何实验中，自变量（IV）是研究者有意操纵或改变的因素。因变量（DV）是被测量的结果；它应当随着自变量的变化而变化。实验设计的核心“定理”可以表述为：DV = f(IV)，意即因变量是自变量的函数。

2. Mean – The Average | 平均数 – 平均值公式

The mean is the most commonly used measure of central tendency. It is calculated by summing all the scores in a dataset and dividing by the number of scores. The formula helps psychologists summarise large datasets into a single representative number.

平均数是最常用的集中量数。计算方法是把数据集中所有分数相加，再除以分数的个数。该公式帮助心理学家将大量数据概括为一个代表性数值。

Mean (M) = (∑x) / n

tal number of scores. For example, for scores 5, 8, 12, 15: M = (5+8+12+15)/4 = 40/4 = 10.

其中 ∑x 表示所有单个分数的总和，n 表示分数的总个数。例如，对于分数 5, 8, 12, 15：M = (5+8+12+15)/4 = 40/4 = 10。

3. Median – The Middle Value | 中位数 – 中间值

The median is the central score when all data points are arranged in ascending order. If the dataset contains an even number of scores, the median is the average of the two middle numbers. This measure is less affected by extreme outliers than the mean.

中位数是将所有数据点按升序排列后位于中间的数值。如果数据集的分数个数为偶数，中位数则是中间两个分数的平均值。相比平均数，中位数受极端异常值的影响较小。

For odd n: Median = the (n+1)/2 th score
For even n: Median = average of the n/2 th and (n/2 + 1) th scores

Example: Scores 3, 5, 7, 9, 11 → Median = 7. For 3, 5, 7, 9 → Median = (5+7)/2 = 6.

示例：分数 3, 5, 7, 9, 11 → 中位数 = 7。对于 3, 5, 7, 9 → 中位数 = (5+7)/2 = 6。

4. Mode – The Most Frequent | 众数 – 出现最频繁的值

The mode is the score that occurs most frequently in a dataset. A set of scores may have one mode (unimodal), two modes (bimodal), or more. The mode is particularly useful for categorical data where numerical averaging is not meaningful.

众数是数据集中出现频率最高的分数。一组分数可能有一个众数（单峰）、两个众数（双峰）或更多。对于无法进行数值平均的类别数据，众数尤其有用。

ecause it appears three times. A psychology example: most frequently reported emotion in a diary study.

对于数据集：2, 3, 3, 5, 5, 5, 7 → 众数 = 5，因为它出现了三次。心理学例子：日记研究中被报告得最频繁的情绪。

5. Range – A Measure of Spread | 范围 – 离散度的量度

The range is the simplest measure of dispersion. It calculates the difference between the highest and lowest scores in a dataset, showing how spread out the data are. A larger range indicates greater variability.

范围是最简单的离散量数。它计算数据集中最高分与最低分之间的差值，显示数据的分布广度。范围越大，说明变异性越大。

Range = Highest score – Lowest score

If the highest reaction time is 450 ms and the lowest is 210 ms, the range is 240 ms. Psychologists must be aware that the range ignores the distribution of scores between the extremes.

如果最高反应时为 450 毫秒，最低为 210 毫秒，则范围为 240 毫秒。心理学家须注意，范围忽略了极端值之间的分数分布情况。

6. Percentage and Ratio | 百分比与比率

Psychologists frequently convert raw frequencies into percentages for easier comparison, especially when groups are of unequal sizes. The ratio is used to compare the relative size of two categories without converting to 100.

心理学家经常将原始频数转换为百分比以便比较，特别是在各组大小不相等时。比率用于比较两个类别的相对大小，无需转化为百分数。

Percentage (%) = (Part / Whole) × 100
Ratio = Part A : Part B

rmity study, 18 out of 40 participants conformed. Percentage conforming = (18/40)×100 = 45%. The ratio of conformists to non-conformists is 18 : 22, which simplifies to 9 : 11.

示例：在一项从众研究中，40 名参与者中有 18 人从众。从众百分比 = (18/40)×100 = 45%。从众者与非从众者的比率为 18 : 22，可简化为 9 : 11。

7. Hypotheses: Null and Experimental | 假设：虚无假设与实验假设

A hypothesis is a precise, testable prediction. The experimental (alternative) hypothesis states that the IV will have an effect on the DV. The null hypothesis states that any observed difference or relationship is due to chance. These form the logic of inferential testing.

假设是一种精确的、可检验的预测。实验假设（备择假设）陈述自变量会对因变量产生影响。虚无假设则陈述任何观察到的差异或关系都是由偶然因素造成的。它们构成了推论检验的逻辑基础。

• Experimental (H₁): 'Participants who drink caffeine will recall more words than participants who do not.'
• 实验假设（H₁）：“摄入咖啡因的参与者比未摄入者能回忆更多单词。”
• Null (H₀): 'There will be no significant difference in word recall between the caffeine and no-caffeine groups; any difference is due to chance.'
• 虚无假设（H₀）：“咖啡因组与无咖啡因组在单词回忆量上没有显著差异；任何差异均由偶然因素造成。”

8. Multi-Store Model of Memory | 记忆多存储模型

Atkinson and Shiffrin (1968) proposed a foundational 'theorem' of memory architecture. Information enters sensory memory, and if attended to, passes into short-term memory (STM). Through rehearsal, it can be transferred to long-term memory (LTM). Each store differs in capacity, duration, and encoding.

Atkinson 和 Shiffrin（1968）提出了一个关于记忆结构的基础“定理”。信息先进入感觉记忆，若受到注意，便进入短时记忆。通过复述，信息可被转入长时记忆。每个存储库在容量、持续时间和编码方式上均不相同。

Sensory Memory → Attention → Short-Term Memory → Rehearsal → Long-Term Memory

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Store	Capacity	Duration	Encoding
Sensory Memory	Very large	¼ to 2 seconds	Sense-specific
Short-Term Memory	7±2 chunks	18–30 seconds	Acoustic
Long-Term Memory	Unlimited	Potentially lifetime	Semantic

Evidence includes the serial position effect: primacy (LTM) and recency (STM) effects observed in free recall tasks.

支持性证据包括系列位置效应：在自由回忆任务中观察到首因效应（长时记忆）和近因效应（短时记忆）。

9. Working Memory Model | 工作记忆模型

Baddeley and Hitch (1974) replaced the idea of a unitary STM with a multi-component working memory system. This model acts as a 'mental workspace' and consists of the central executive, phonological loop, visuo-spatial sketchpad, and episodic buffer (added later).

Baddeley 和 Hitch（1974）用一个多成分的工作记忆系统取代了单一短时记忆的概念。该模型充当“心理工作台”，由中央执行器、语音回路、视空间画板以及后来添加的情节缓冲器组成。

• Central Executive: Controls attention, coordinates slave systems, and switches between tasks.
• 中央执行器：控制注意力，协调附属系统，并在任务间切换。
• Phonological Loop: Processes spoken and written verbal material; comprises the phonological store and articulatory control process.
• 语音回路：处理口头和书面的言语材料；包括语音存储库和发音控制过程。
• Visuo-Spatial Sketchpad: Manipulates visual and spatial information; helps with navigation and mental imagery.
• 视空间画板：处理视觉与空间信息；有助于导航和心理意象。
• Episodic Buffer: Integrates information across modalities into a single, multi-dimensional representation.
• 情节缓冲器：将多种模态的信息整合成单一、多维的表征。

10. Stages of Sleep and the Sleep Cycle | 睡眠阶段与睡眠周期

The sleep-wake cycle follows a predictable architecture often termed the 'theorem of sleep architecture.' A complete cycle lasts around 90 minutes and comprises NREM stages 1–4 and REM sleep. Over the night, deep sleep (stage 3 & 4) decreases while REM duration increases.

睡眠-觉醒周期遵循一种可预测的结构，常被称为“睡眠结构定理”。一个完整周期约持续 90 分钟，包含非快速眼动睡眠 1–4 阶段和 REM 睡眠。在整个夜晚，深度睡眠（第 3、4 阶段）逐渐减少，而 REM 睡眠时长增加。

• Stage 1 (N1): Light sleep, theta waves, easily woken.
• 第一阶段（N1）：浅睡，θ波，易被唤醒。
• Stage 2 (N2): Sleep spindles and K-complexes; body temperature drops.
• 第二阶段（N2）：出现睡眠纺锤波和 K 复合波；体温下降。
• Stage 3 & 4 (N3): Slow-wave sleep, delta waves; physically restorative.
• 第 3、4 阶段（N3）：慢波睡眠，δ波；具有体力恢复功能。
• REM Sleep: Rapid eye movements, brain activity resembles wakefulness, vivid dreams occur, muscle atonia.
• REM 睡眠：快速眼动，脑活动类似清醒状态， vivid 梦境出现，肌肉张力丧失。

11. Conformity: Asch's Paradigm | 从众：Asch 范式

Solomon Asch (1951) demonstrated a powerful 'social influence theorem': individuals often conform to an incorrect majority even when the correct answer is unambiguous. This normative social influence arises from the desire to fit in and be accepted. The paradigm involved judging line lengths.

Solomon Asch（1951）演示了一个强有力的“社会影响定理”：即使在正确答案明确无误的情况下，个体也常会服从错误的大多数。这种规范性的社会影响源于渴望融入和被接纳。其研究范式涉及判断线段长度。

Asch's Key Findings	Asch 的关键发现
75% of participants conformed at least once.	75% 的参与者至少从众了一次。
Average conformity rate across trials was 32%.	所有试次的平均从众率为 32%。
Conformity decreased with one dissenter or when writing answers privately.	当有一个持异议者或私下书写答案时，从众降低。

12. Ethical Principles in Research | 研究中的伦理原则

Psychological research is governed by ethical 'theorems' that protect participants. The British Psychological Society (BPS) sets out key principles: informed consent, right to withdraw, confidentiality, protection from harm, and debriefing. Researchers must balance scientific goals with participant welfare.

心理学研究受保护参与者的伦理“定理”所制约。英国心理学会（BPS）制定的关键原则包括：知情同意、退出权、保密、免受伤害以及事后解释。研究者必须在科学目标与参与者福祉之间取得平衡。

• Informed Consent: Participants must know the aims and procedures and voluntarily agree.
• 知情同意：参与者必须了解研究目的与程序并自愿同意。
• Right to Withdraw: Participants can stop at any time without penalty.
• 退出权：参与者可随时退出，不受任何处罚。
• Confidentiality: Data is anonymised; identities are not revealed.
• 保密：数据匿名化处理；不透露身份信息。
• Protection from Harm: Physical and psychological risks must be minimised.
• 免受伤害：必须将生理和心理风险降至最低。
• Debriefing: After the study, the true nature is explained, and any deception is justified.
• 事后解释：研究结束后，须解释真实情况，并为任何欺骗行为提供正当理由。

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