Year 9 SQA Psychology: Formula & Theorem Quick Reference Handbook | SQA 心理学公式定理速查手册

📚 Year 9 SQA Psychology: Formula & Theorem Quick Reference Handbook | SQA 心理学公式定理速查手册

Welcome to your go-to quick reference for the essential formulas, laws and theorems you will meet in Year 9 SQA Psychology. This handbook covers key descriptive statistics formulas, classical psychological laws and principles of learning that form the foundation of the course. Keep it handy when completing research tasks or revising for assessments.

欢迎使用这份为你准备的 Year 9 SQA 心理学核心公式与定理速查手册。本手册涵盖关键描述性统计公式、经典心理学定律以及学习理论的原理，这些都是课程的基础。完成研究任务或考前复习时，将它放在手边，随时查阅。

1. Calculating the Mean | 计算平均数

The mean is the arithmetic average of a set of scores. It is found by adding all the values together and dividing by the total number of values. In psychology, the mean is used to summarise central tendency in data from experiments or surveys. Formula: M = ΣX ÷ N, where ΣX is the sum of all scores and N is the number of scores.

平均数是一组分数的算术平均值。把所有数值相加，再除以数值的总个数即可求得。在心理学中，平均数用于概括实验或调查数据的集中趋势。公式：平均数 = ΣX ÷ N，其中 ΣX 是所有分数的总和，N 是分数的个数。

2. Finding the Median and Mode | 求中位数与众数

The median is the middle score when all scores are arranged in ascending order. If there is an even number of scores, the median is the mean of the two middle numbers. The mode is simply the most frequently occurring score in the dataset. These measures help psychologists understand the distribution of behaviours or responses.

将所有分数按从小到大的顺序排列，位于中间的就是中位数。如果分数个数是偶数，中位数是中间两个数的平均值。众数则是数据集中出现次数最多的分数。这些度量有助于心理学家理解行为或反应数据的分布形态。

3. Range and Standard Deviation (Simplified) | 全距与标准差（简化版）

The range measures the spread of scores: Range = Highest score − Lowest score. Standard deviation quantifies how much, on average, each score deviates from the mean. For a sample, the formula is: s = √[Σ(xᵢ − x̄)² ÷ (n − 1)]. A small standard deviation means scores cluster closely around the mean.

全距衡量分数的分散程度：全距 = 最高分 − 最低分。标准差则量化每个分数与平均数的平均偏差。样本标准差公式为：s = √[Σ(xᵢ − x̄)² ÷ (n − 1)]。标准差越小，分数越集中在平均数附近。

4. Percentage Change and Ratio | 百分比变化与比率

Percentage change is often needed when comparing before-and-after measurements in psychological studies. The formula is: Percentage change = [(New value − Old value) ÷ Old value] × 100. A simple ratio, such as the number of correct responses out of total trials, can be expressed as Ratio = a : b.

在心理学研究中比较前后测数据时，常需计算百分比变化。公式为：百分比变化 = [（新值 − 旧值）÷ 旧值] × 100。简单的比率，例如正确反应次数与总试验次数之比，可表示为 比率 = a : b。

5. Normal Distribution and the 68-95-99.7 Rule | 正态分布与 68-95-99.7 法则

Many psychological traits, such as IQ scores, are normally distributed. The empirical rule states: about 68% of data falls within 1 standard deviation (σ) of the mean (μ), 95% within 2σ, and 99.7% within 3σ. This helps psychologists decide whether a score is statistically typical or extreme.

许多心理特质（如智商分数）呈正态分布。经验法则表明：约 68% 的数据落在平均数 (μ) 加减 1 个标准差 (σ) 内，95% 落在 2σ 内，99.7% 落在 3σ 内。这有助于心理学家判断一个分数是典型还是极端。

6. Miller’s Law: The Magic Number 7 ± 2 | 米勒定律：神奇数字 7±2

Miller (1956) proposed that the capacity of short-term memory is approximately 7 (plus or minus 2) chunks of information. This means most people can hold between 5 and 9 items, such as digits or words, in immediate memory. Formula: STM capacity ≈ 7 ± 2 chunks.

米勒（1956）提出，短时记忆的容量约为 7±2 个信息组块。也就是说，大多数人在即时记忆中可保持 5 至 9 个项目，如数字或单词。公式：短时记忆容量 ≈ 7 ± 2 组块。

7. Ebbinghaus Forgetting Curve Theorem | 艾宾浩斯遗忘曲线定理

Ebbinghaus demonstrated that memory loss follows an exponential decay pattern. The mathematical form can be expressed as R = e⁻ᵗ⁄ˢ, where R is retention, t is time elapsed, and s is a time constant related to strength of memory. In simple terms, the fastest forgetting happens soon after learning, and the rate slows over time.

艾宾浩斯证明，记忆流失遵循指数衰减模式。其数学形式可表示为 R = e⁻ᵗ⁄ˢ，其中 R 为记忆保留量，t 为经过的时间，s 为与记忆强度有关的时间常数。简单来说，学习后遗忘最快发生在最初阶段，之后遗忘速率逐渐减缓。

8. Weber’s Law of Just Noticeable Difference | 韦伯最小可觉差定律

Weber’s Law states that the smallest detectable change in a stimulus (ΔI) is proportional to the original stimulus intensity (I). The law is written as ΔI ÷ I = k, where k is the Weber fraction constant. For example, if k = 0.02 for weight perception, you would notice a 2 g difference in a 100 g weight but need a 20 g difference for a 1000 g weight.

韦伯定律指出，能觉察到的最小刺激变化量 (ΔI) 与原始刺激强度 (I) 成正比。公式写作 ΔI ÷ I = k，其中 k 为韦伯分数常数。例如，若重量感知的 k = 0.02，那么在 100 克基础上增加 2 克即可觉察，而在 1000 克基础上需增加 20 克才能觉察。

9. Classical Conditioning: The Formula of Association | 经典条件反射：联结公式

Pavlov’s classical conditioning can be summarised as a sequence of associations. Before conditioning: US → UR (food → salivation). During acquisition: NS + US → UR (bell + food → salivation). After conditioning: CS → CR (bell alone → salivation). This ‘formula’ explains how a neutral stimulus gains the power to trigger a learned response.

巴甫洛夫的经典条件反射可概括为一个联结序列。条件作用前：US → UR（食物 → 分泌唾液）。习得阶段：NS + US → UR（铃声 + 食物 → 分泌唾液）。条件作用后：CS → CR（仅铃声 → 分泌唾液）。这个“公式”解释了一个中性刺激如何获得引发习得反应的能力。

10. Operant Conditioning Reinforcement Principles | 操作条件作用强化原理

Skinner’s operant conditioning relies on consequences to shape behaviour. The key principles are: positive reinforcement (add pleasant stimulus to increase behaviour), negative reinforcement (remove unpleasant stimulus to increase behaviour), and punishment (add or remove stimulus to decrease behaviour).

斯金纳的操作条件作用依靠行为结果来塑造行为。核心原则包括：正强化（加入愉悦刺激，增加行为）、负强化（移除厌恶刺激，增加行为）和惩罚（加入或移除刺激，减少行为）。

Published by TutorHao | Psychology Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）