📚 Year 9 SQA Psychology: Quick Reference Handbook of Formulas and Theorems | SQA 心理学：公式定理速查手册
This quick reference handbook compiles the essential formulas, numerical laws, and psychological theorems you need to master for Year 9 SQA Psychology. From psychophysics to memory span, from IQ calculation to descriptive statistics, each entry is presented with a clear explanation and the exact formulation used in assessments. Use this guide to revise efficiently and boost your confidence before the exam.
这本速查手册汇集了 Year 9 SQA 心理学必须掌握的核心公式、数值法则与心理学定理。从心理物理学到记忆广度，从智商计算到描述统计，每一个条目都配有清晰的解释和考试中使用的精确表述。请用本手册高效复习，在考试前提升你的信心。
1. Weber's Law & Psychophysics | 韦伯定律与心理物理学
Weber's Law states that the just noticeable difference (JND) between two stimuli is proportional to the magnitude of the original stimulus. The formula helps quantify sensory thresholds.
韦伯定律指出，两个刺激之间的最小可觉差（JND）与原始刺激的强度成正比。该公式有助于量化感觉阈限。
ΔI / I = k
Where ΔI is the increment needed for detection, I is the initial stimulus intensity, and k is the Weber fraction (a constant for each sensory modality).
其中 ΔI 是检测所需的增量，I 是初始刺激强度，k 是韦伯分数（每种感觉形态的常数）。
For lifted weights, k ≈ 0.02 (a 2% increase is noticeable).
对于提举重量，k ≈ 0.02（增加 2% 就能察觉）。
For loudness, k ≈ 0.05 to 0.10 depending on frequency.
对于响度，k ≈ 0.05 至 0.10，取决于频率。
2. Fechner's Law | 费希纳定律
Fechner built upon Weber's work and proposed that perceived sensation intensity is proportional to the logarithm of the physical stimulus intensity. This law describes the relationship between mind and body quantitatively.
费希纳在韦伯的研究基础上提出，感知到的感觉强度与物理刺激强度的对数成正比。该定律定量地描述了心身关系。
S = k log I
Here S is the subjective sensation magnitude, I is the physical intensity, and k is a constant that depends on the Weber fraction. Fechner's logarithmic scale explains why a doubling of physical light seems like a much smaller brightness increase.
这里 S 是主观感觉量，I 是物理强度，k 是依赖于韦伯分数的常数。费希纳的对数量表解释了为什么物理光强加倍给人的亮度感觉增幅却小得多。
3. Ebbinghaus Forgetting Curve | 艾宾浩斯遗忘曲线
Hermann Ebbinghaus discovered that memory decay follows an exponential pattern. While there is no single closed-form equation required at Year 9, the saving score formula quantifies retention.
赫尔曼·艾宾浩斯发现记忆消退遵循指数模式。虽然 Year 9 不要求单一的闭合方程，但节省分数公式可以量化保持量。
Saving Score (%) = [(Original Learning Time − Relearning Time) / Original Learning Time] × 100
A high saving score means less time was needed to relearn the material, indicating strong retention. The classic curve shows a rapid drop within the first hour and then a more gradual decline.
节省分数高意味着再学习所需时间较短，表明保持牢固。经典曲线显示在学习后一小时内遗忘迅速，随后下降变得平缓。
4. Memory Span (7 ± 2 Items) | 记忆广度（7 ± 2 个项目）
George Miller's famous 'magical number' describes the capacity of short-term memory. The formula captures the average number of discrete items a person can hold.
乔治·米勒著名的“神奇数字”描述了短时记忆的容量。该公式概括了一个人能记住的非连续项目的平均数。
Short-term Memory Capacity = 7 ± 2 chunks
Chunking allows us to group information into meaningful units, effectively expanding capacity. For example, the sequence '1-9-4-5' can be chunked as the year '1945'.
组块化使我们能够将信息组合成有意义的单元，从而有效扩展容量。例如，序列“1-9-4-5”可被组块为年份“1945”。
5. IQ Formula (Stern's Ratio IQ) | 智商公式（斯特恩比率智商）
The classic intelligence quotient is calculated by comparing mental age to chronological age. Modern tests use deviation IQs, but the foundational formula remains essential learning.
经典的智力商数通过比较心理年龄与实际年龄来计算。现代测验使用离差智商，但这一基础公式仍然是必学内容。
IQ = (Mental Age / Chronological Age) × 100
10, giving IQ = (12/10) × 100 = 120. An IQ of 100 represents exactly average performance.
如果一个 10 岁儿童的表现达到典型 12 岁儿童水平，MA = 12，CA = 10，则 IQ = (12/10) × 100 = 120。IQ 为 100 代表完全的平均表现。
6. Yerkes-Dodson Law | 耶基斯–多德森定律
This law describes the empirical relationship between arousal and performance. It is often summarised by an inverted-U curve, but the underlying concept can be expressed as an optimal arousal theorem.
该定律描述了唤醒水平与表现之间的实证关系。它通常被总结为倒 U 形曲线，但核心概念可表达为最佳唤醒定理。
Performance improves with arousal up to an optimal point, then declines.
For well-learned or simple tasks, optimal arousal is higher; for complex tasks, it is lower. The law is fundamental in sports psychology, exam preparation, and stress management.
对于熟练或简单任务，最佳唤醒水平较高；对于复杂任务则较低。该定律在运动心理学、考试准备和压力管理中具有基础地位。
7. Classical Conditioning: Acquisition & Extinction | 经典条件反射：习得与消退
Pavlov's experiments revealed that the strength of a conditioned response follows a learning curve during acquisition and a decay curve during extinction. The processes can be summarised with the standard paradigm.
巴甫洛夫的实验揭示，条件反应的强度在习得阶段遵循学习曲线，在消退阶段遵循衰减曲线。这些过程可以用标准范式加以总结。
Acquisition: NS + UCS → UCR; after conditioning, CS → CR
Extinction: CS presented without UCS → CR weakens
d stimulus, CR = conditioned response. Spontaneous recovery can occur after a rest period.
其中 NS = 中性刺激，UCS = 非条件刺激，UCR = 非条件反应，CS = 条件刺激，CR = 条件反应。消退后经过一段休息，可能出现自发恢复。
8. Operant Conditioning: Schedules of Reinforcement | 操作性条件反射：强化程式
Skinner identified that the pattern and rate of responding depend directly on the schedule of reinforcement. The partial reinforcement effect is a key theorem: behaviours reinforced intermittently are more resistant to extinction.
斯金纳发现，反应的模式和速率直接依赖于强化程式。部分强化效应是一条关键定理：间歇强化的行为更难以消退。
Partial Reinforcement Effect: VR > FR, VI > FI for resistance to extinction.
Fixed Ratio (FR): reward after a set number of responses.
固定比率（FR）：在固定次数的反应后给予奖励。
Variable Ratio (VR): reward after an unpredictable number of responses (most resistant).
变动比率（VR）：在不可预测的反应次数后给予奖励（最能抵抗消退）。
Fixed Interval (FI): reward for the first response after a fixed time.
固定时距（FI）：在固定时间后的首次反应给予奖励。
Variable Interval (VI): reward after varying time intervals (generates steady responding).
变动时距（VI）：在不同时间间隔后给予奖励（产生稳定的反应速率）。
9. Descriptive Statistics: Mean, Median, Mode, Range | 描述统计：平均数、中位数、众数、极差
In psychological research, measures of central tendency and dispersion are used to summarise data sets. The formulas below are essential for any data analysis question.
在心理学研究中，集中趋势和离散量的测量被用来概括数据集。以下公式对于任何数据分析问题都是必不可少的。
Mean (M) = ΣX / N
ΣX is the sum of all scores, N is the number of scores. The mean is sensitive to extreme values (outliers).
ΣX 是所有分数的总和，N 是分数的个数。平均数对极端值（离群值）敏感。
Range = Highest score − Lowest score
The median is the middle score when data are ordered; the mode is the most frequent score. Use the median when outliers distort the mean.
中位数是数据排序后的中间值；众数是出现频率最高的分数。当离群值扭曲平均数时，应使用中位数。
10. Percentage Change & the Normal Distribution | 百分比变化与正态分布
Many SQA exam questions ask you to calculate percentage increase or decrease between two conditions. The normal distribution theorem provides a probability framework for interpreting standardised scores.
许多 SQA 考题会要求你计算两种条件之间的百分比增加或减少。正态分布定理为解释标准分数提供了一个概率框架。
Percentage Change (%) = [(New Value − Old Value) / Old Value] × 100
increase; a negative result, a decrease. Example: if recall improves from 15 to 20 words, % change = [(20-15)/15] × 100 ≈ 33.3%.
正值表示增加，负值表示减少。例如：回忆单词从 15 个提升到 20 个，百分比变化 = [(20-15)/15] × 100 ≈ 33.3%。
The empirical rule for normal distribution can be expressed as:
正态分布的经验法则可表达为：
68% of scores lie within ±1σ of the mean; 95% within ±2σ; 99.7% within ±3σ.
on. This rule helps interpret IQ scores (mean = 100, σ = 15) and other standardised tests.
其中 μ 为总体平均数，σ 为标准差。这个规则有助于解释 IQ 分数（平均数 = 100，σ = 15）以及其他标准化测验。
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