Year 10 CAIE Psychology: Formula & Theorem Rapid Reference Handbook | 心理学公式定理速查手册

📚 Year 10 CAIE Psychology: Formula & Theorem Rapid Reference Handbook | 心理学公式定理速查手册

This rapid reference handbook brings together all the essential formulas, statistical methods, and key theoretical notations you will encounter in Year 10 CAIE Psychology. Designed for quick revision, it covers descriptive statistics, classical and operant conditioning outlines, ethical principles, and the core quantitative tools needed to analyse psychological data. Each formula is explained with a clear definition and a step-by-step example where relevant, so you can apply it confidently in exam-style questions on research methods and behaviour studies.

本速查手册汇总了 Year 10 CAIE 心理学课程中所有必备公式、统计学方法以及核心理论符号。手册旨在快速复习，涵盖描述性统计、经典条件作用与操作条件作用的公式化表达、伦理原则以及分析心理学数据所需的基本量化工具。每个公式都配有清晰的定义和逐步示例，帮助你自信地应对研究方法和行为研究相关的考试题目。

1. Calculating the Mean | 平均值计算

The mean is the arithmetic average of a set of scores. It is calculated by summing all the individual values and then dividing the total by the number of scores. In psychological research, the mean is used to represent the central tendency of interval or ratio data, such as reaction times or test scores. While it is sensitive to every value in the data set, extreme outliers can distort the result, so it must be interpreted alongside other measures of dispersion.

平均值是一组分数的算术平均数。计算方法是将所有个体数值相加，再用总和除以分数的个数。在心理学研究中，平均值用于描述等距或等比数据的集中趋势，例如反应时或测验得分。由于它对数据集中的每个值都很敏感，极端异常值可能扭曲结果，因此必须结合其他离散量数一起解读。

Mean = Σx / N

where Σx = sum of all scores, N = number of scores.

其中 Σx = 所有分数的总和，N = 分数的个数。

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2. Finding the Median | 中位数查找

The median is the middle score in an ordered list. If the number of scores (N) is odd, the median is the central value. If N is even, the median is the mean of the two middle scores. The median is less affected by outliers than the mean, making it a preferred measure of central tendency for skewed distributions or ordinal data, such as rating scales in a questionnaire.

中位数是按顺序排列后位于中间位置的分数。如果分数个数（N）为奇数，中位数就是中间那个值；若 N 为偶数，则取中间两个分数的平均值。与均值相比，中位数受异常值影响较小，因此常用于偏态分布或顺序数据，例如问卷中的等级评分。

Step-by-step: (1) Order scores from smallest to largest; (2) Identify the position using (N + 1) / 2.

步骤： (1) 将分数从小到大排列； (2) 用 (N + 1) / 2 确定位置。

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3. Identifying the Mode | 众数识别

The mode is the most frequently occurring score in a data set. A set can have one mode (unimodal), two modes (bimodal) or more. In psychology, the mode is particularly useful for nominal data, such as the most common response in a multiple-choice question or the most frequently diagnosed condition in a sample. It is not affected by extreme scores but may not represent the centre if data are highly varied.

众数是数据集中出现频率最高的分数。一组数据可以有一个众数（单峰）、两个众数（双峰）或更多。在心理学中，众数尤其适用于称名数据，例如多项选择题中最常见的回答，或样本中最常被诊断的状况。众数不受极端分数影响，但在数据高度分散时可能无法代表中心趋势。

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4. Range: Spread of Data | 极差：数据离散度

The range is the simplest measure of dispersion. It is found by subtracting the smallest score from the largest score in the data set. A small range indicates that scores are clustered closely together, while a large range suggests greater variability. Psychologists use the range as a quick check of spread, but because it only considers two values, it can be misleading if there are outliers.

极差是最简单的离散量数，即数据集中最大分数减去最小分数。极差小表示分数紧密聚集，极差大则说明变异性较大。心理学家将极差作为离散程度的快速检查方式，但由于它只考虑两个数值，如果存在异常值可能会产生误导。

Range = X_max − X_min

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5. Standard Deviation Formula | 标准差公式

Standard deviation (SD) measures how far, on average, each score is from the mean. A low SD indicates that scores are close to the mean; a high SD shows they are widely spread. In the CAIE specification, you may use the formula for a sample standard deviation, dividing by (n – 1) to give an unbiased estimate of the population standard deviation. Understanding standard deviation helps you interpret the consistency of data in experimental and correlational studies.

标准差（SD）衡量每个分数与平均值之间的平均距离。标准差低表明分数紧靠均值，标准差高则说明分数分布很广。在 CAIE 大纲中，你可能需要用到样本标准差公式，除以 (n – 1) 以给出总体标准差的无偏估计。理解标准差有助于解读实验和相关研究中数据的一致性。

SD = √(Σ(x − x̄)² / (n − 1))

x = each score, x̄ = sample mean, n = number of scores.

x = 每个分数，x̄ = 样本均值，n = 分数个数。

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6. Percentage & Proportion | 百分比与比例

Percentages and proportions are essential for summarising categorical data and comparing groups. A percentage expresses a number as a fraction of 100. In psychological reports, you may calculate the percentage of participants showing a particular behaviour or the proportion of correct responses. These simple conversions allow objective comparisons between conditions and are a key skill for the research methods paper.

百分比和比例对于总结分类数据以及比较组别至关重要。百分比将一个数值表示为100的分数。在心理学报告中，你可能需要计算表现出某种行为的参与者的百分比，或正确回答的比例。这些简单转换使条件间客观比较成为可能，也是研究方法考试的重要技能。

Percentage (%) = (Part / Whole) × 100

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7. Normal Distribution Curve | 正态分布曲线

(e.g., IQ scores) are assumed to follow a normal distribution. Key properties include: 68% of data fall within ±1 standard deviation from the mean, 95% within ±2 SD, and 99.7% ognising this pattern helps you judge whether data are typical or if outliers are present.

正态分布是一种钟形对称曲线，其均值、中位数和众数都落在中心。在心理学中，许多特质（例如智商分数）被假定服从正态分布。主要特征为：约 68% 的数据落在均值 ±1 个标准差以内，95% 落在 ±2 个标准差以内，99.7% 落在 ±3 个标准差以内。识别该模式有助于判断数据是否典型或是否存在异常值。

68 – 95 – 99.7 Rule

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8. Classical Conditioning Notation | 经典条件作用表示法

In classical conditioning, the acquisition of a conditioned response is often summarised using a standard notation. An unconditioned stimulus (UCS) naturally elicits an unconditioned response (UCR). When a neutral stimulus (NS) is repeatedly paired with the UCS, the NS becomes a conditioned stimulus (CS) that triggers a conditioned response (CR). This notation helps you describe experiments such as Pavlov's dogs and apply the principles to phobia acquisition or therapy.

在经典条件作用中，常常用一套标准符号来概括条件反应的习得过程。无条件刺激（UCS）天然引发无条件反应（UCR）。当一个中性刺激（NS）反复与 UCS 配对后，NS 便成为条件刺激（CS），引发条件反应（CR）。这套符号有助于描述巴甫洛夫的狗等实验，并将原理应用于恐惧症习得或治疗。

Before conditioning: UCS → UCR
During conditioning: NS + UCS → UCR
After conditioning: CS → CR

ned response, NS = neutral stimulus, CS = conditioned stimulus, CR = conditioned response.

UCS = 无条件刺激，UCR = 无条件反应，NS = 中性刺激，CS = 条件刺激，CR = 条件反应。

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9. Operant Conditioning Reinforcement Schedules | 操作性条件作用强化程式

Operant conditioning uses consequences to shape behaviour. The schedule of reinforcement determines how often a desired behaviour is rewarded, which affects the rate and persistence of responding. Psychologists categorise schedules as continuous or partial, with the partial types including fixed interval, variable interval, fixed ratio and variable ratio. Each schedule produces distinctive patterns of behaviour, observable in both animal studies and everyday human routines.

操作条件作用利用后果来塑造行为。强化程式决定了期望行为得到奖励的频率，从而影响反应的速度和持久性。心理学家将程式分为连续强化和部分强化，部分强化又包括固定时距、变动时距、固定比率和变动比率。每种程式都会产生独特的行为模式，既可见于动物研究，也可见于人类的日常活动中。

Schedule (English)	中文程式	Example	示例
Fixed Interval (FI)	固定时距	Weekly pocket money	每周零花钱
Variable Interval (VI)	变动时距	Pop quizzes	突击小测验
Fixed Ratio (FR)	固定比率	Piecework pay	按件计酬
Variable Ratio (VR)	变动比率	Slot machines	老虎机

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10. Ethical Principles | 伦理原则（速查表）

All psychological research must adhere to ethical guidelines to protect participants' wellbeing and dignity. The British Psychological Society (BPS) and CAIE specify key principles that you must be able to identify and apply when evaluating studies. These include informed consent, the right to withdraw, avoidance of deception wherever possible, protection from harm, confidentiality, and thorough debriefing. Ethical considerations often form the basis of evaluation questions in the exam.

所有心理学研究都必须遵守伦理准则，以保护参与者的福祉和尊严。英国心理学会（BPS）与 CAIE 规定了若干关键原则，你在评价研究时必须能够识别并运用。这些原则包括知情同意、退出权利、尽可能避免欺骗、免受伤害、保密以及充分的事后解释。伦理考量常常构成考试中评价性问题的基础。

Principle (English)	中文原则	Key Requirement	关键要求
Informed Consent	知情同意	Participants give permission knowing the true aims where possible.	参与者在可能情况下了解真实目的后给予许可。
Right to Withdraw	退出权利	Participants can leave at any time without penalty.	参与者可随时退出且不受惩罚。
Deception	欺骗	Avoid unless necessary; must be justified and followed by debrief.	除非必要应避免；若必须欺骗，须有充分理由并在事后进行解释。
Protection from Harm	免受伤害	Participants should not experience physical or psychological distress beyond everyday life.	参与者不应承受超出日常生活的身体或心理痛苦。
Confidentiality	保密	Personal data kept anonymous and stored securely.	个人数据匿名处理并安全保存。
Debriefing	事后解释	After the study, explain the true purpose and offer support if needed.	研究结束后说明真实目的，并在需要时提供支持。

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