📚 GCSE CCEA Psychology: Formulae and Theorems Quick Reference | GCSE CCEA 心理学：公式定理速查手册
This quick-reference handbook brings together every essential formula and key research principle you need for the GCSE CCEA Psychology specification. From calculating central tendency to understanding experimental designs, the following sections provide clear, paired English and Chinese explanations to reinforce your revision.
本速查手册汇集了 GCSE CCEA 心理学所需的所有基本公式和关键研究原则。从集中趋势的计算到实验设计的理解，以下各节提供了清晰的中英文双语解释，巩固你的复习。
1. Mean | 平均数
The mean is the arithmetic average of a data set. It is calculated by summing all the scores and dividing by the number of scores. The mean is sensitive to extreme values (outliers) and is suitable for interval or ratio data.
平均数是一组数据的算术平均值。计算方法是将所有分数相加，再除以分数的个数。平均数对极端值（异常值）敏感，适用于间隔或比率数据。
Mean = Σx ÷ n
Where Σx is the sum of all scores and n is the number of scores. Always order the data carefully and double‑check your total before dividing.
其中 Σx 是所有分数的总和，n 是分数的数量。务必先仔细整理数据，再核对总和，然后进行除法。
2. Median | 中位数
The median is the middle value when data are arranged in ascending order. For an odd number of scores, it is the exact centre value. For an even number, it is the mean of the two central scores. The median is not distorted by outliers, making it ideal for skewed distributions.
中位数是将数据按升序排列后位于中间的值。如果分数个数为奇数，它就是正中间的值；若为偶数，则是中间两个分数的平均数。中位数不受异常值影响，非常适合偏态分布。
Median position = (n + 1) ÷ 2 (ordered list)
Count along the ordered list to locate the median. For even n, average the values at positions n/2 and (n/2)+1.
按位置在排序列表中数出中位数。当 n 为偶数时，取第 n/2 位和第 (n/2)+1 位的值计算平均数。
3. Mode | 众数
The mode is the most frequently occurring score in a data set. A set may have one mode (unimodal), two modes (bimodal) or more. The mode is the only measure of central tendency that can be used with nominal (category) data. It is straightforward but may not represent the centre of a data set well if multiple peaks exist.
众数是一组数据中出现次数最多的分数。一组数据可能有一个众数（单峰）、两个众数（双峰）或更多。众数是唯一可用于名义（类别）数据的集中趋势度量。它简单直接，但若存在多个峰值，可能无法很好地代表数据的中心。
There is no mathematical formula; simply count frequencies. In a frequency table, the category with the highest tally is the mode.
众数没有数学公式，只需计算频数。在频数表中，计数最高的类别就是众数。
4. Range | 范围
The range is the simplest measure of dispersion. It is the difference between the highest and lowest scores. A large range indicates widespread data, while a small range suggests scores are clustered closely together. However, the range is heavily influenced by a single outlier.
范围是最简单的离散度量。它是最高分与最低分之间的差值。范围大表示数据分布广，范围小则说明分数聚集紧密。但是，范围极易受单个异常值的影响。
Range = Highest score − Lowest score
Always identify the maximum and minimum values before subtracting. Express the range in the same units as the original data.
计算前一定要先确定最大值和最小值。范围的单位与原始数据相同。
5. Percentage Change | 百分比变化
Percentage change calculates the relative increase or decrease from an original value to a new value. In psychology, it is often used to compare before‑and‑after scores, such as memory recall following an intervention, or to normalise data from different‑sized groups.
百分比变化计算从原始值到新值的相对增减。在心理学中，它常用来比较干预前后的分数，如干预后的记忆回忆率，或对不同规模小组的数据进行标准化。
Percentage Change = [(New value − Original value) ÷ Original value] × 100
A positive result indicates a percentage increase; a negative result shows a percentage decrease. Always state the direction of change clearly.
正数结果表示百分比增加；负数结果表示百分比减少。务必清楚地说明变化的方向。
6. Independent and Dependent Variables | 自变量与因变量
In an experiment, the independent variable (IV) is the factor that the researcher manipulates or changes to observe its effect. The dependent variable (DV) is the factor that is measured; it is expected to change as a result of the manipulation. All other variables must be controlled to establish a cause‑and‑effect relationship.
在实验中，自变量是研究者操纵或改变以观察其效应的因素。因变量是被测量的因素，预计会因自变量的操纵而改变。所有其他变量必须加以控制，才能确立因果关系。
For example, if testing whether noise affects concentration, the IV is the level of noise (present/absent) and the DV could be the score on a concentration test. Operational definitions are essential.
例如，测试噪音是否影响注意力时，自变量是噪音水平（有/无），因变量可以是注意力测试的分数。操作性定义至关重要。
7. Types of Hypotheses | 假设类型
An experimental hypothesis predicts the effect of the IV on the DV. A directional (one‑tailed) hypothesis states the specific direction of the expected difference, e.g. ‘Participants will recall more words in silence than in noise.’ A non‑directional (two‑tailed) hypothesis simply predicts a difference without specifying direction, e.g. ‘There will be a difference in recall between silent and noisy conditions.’
实验假设预测自变量对因变量的影响。方向性（单尾）假设指出预期差异的具体方向，例如“参与者在安静环境下比在嘈杂环境下能回忆起更多单词”。非方向性（双尾）假设仅预测存在差异而不指定方向，例如“安静与嘈杂条件之间的回忆量存在差异”。
The null hypothesis always states that there will be no significant difference or relationship; any observed effect is due to chance. Psychologists aim to reject the null hypothesis.
零假设总是声明不存在显著差异或关系；任何观察到的效应都是偶然造成的。心理学家的目标是拒绝零假设。
8. Ethical Guidelines | 伦理准则
The British Psychological Society (BPS) sets ethical principles for research with human participants. These include informed consent, right to withdraw, protection from harm, deception avoidance (unless justified), debriefing, confidentiality, and privacy. Researchers must obtain consent or, if deception is necessary, provide a full debrief afterwards and offer the chance to withhold data.
英国心理学会为人际参与者的研究制定了伦理原则，包括知情同意、退出权、免受伤害、避免欺骗（除非有正当理由）、事后说明、保密和隐私。研究人员必须获得同意，如果欺骗难以避免，则必须在事后进行完整说明，并提供扣留数据的机会。
When working with children (under 16) or vulnerable groups, parental consent and additional safeguarding are required. Ethical issues are weighed against the scientific benefits of the study.
针对儿童（16 岁以下）或弱势群体的研究，需要父母同意和额外的保护措施。伦理问题要与研究的科学效益进行权衡。
9. Experimental Designs | 实验设计
The three main experimental designs are independent groups, repeated measures, and matched pairs. In independent groups, different participants are used in each condition, avoiding order effects but requiring more participants and risking participant variables. Repeated measures uses the same participants in all conditions, which controls for individual differences but may cause order effects (practice or fatigue). Matched pairs matches participants on key characteristics and then splits them, reducing participant variables but being time‑consuming.
三种主要的实验设计是独立组设计、重复测量设计和匹配对设计。独立组设计在各条件下使用不同的参与者，可避免顺序效应，但需要更多的参与者，并存在参与者变量的风险。重复测量设计在所有条件下使用相同的参与者，控制了个体差异，但可能引起顺序效应（练习或疲劳）。匹配对设计根据关键特征匹配参与者，然后将他们分入不同条件，可减少参与者变量，但耗费时间。
Counterbalancing can be used in repeated measures to minimise order effects, and random allocation is crucial for independent groups to distribute participant variables evenly.
重复测量设计中可使用平衡对抗法以减少顺序效应；独立组设计中，随机分配对于均匀分布参与者变量至关重要。
10. Sampling Techniques | 抽样技术
A sample is a subset of the target population. Random sampling gives every member an equal chance of selection, reducing bias but requiring a full list. Opportunity sampling selects whoever is readily available, which is quick but often unrepresentative. Volunteer (self‑selected) sampling relies on individuals responding to an advertisement, which may attract a certain personality type. Stratified sampling divides the population into subgroups and randomly samples from each in proportion, providing high representativeness but demanding detailed population knowledge.
样本是目标总体的一个子集。随机抽样使每个成员都有均等的被选机会，减少偏差，但需要完整的名单。机会抽样选取任何方便找到的人，快捷但往往不具代表性。志愿者（自选）抽样依赖个人回应广告，可能吸引特定性格类型。分层抽样将总体分为亚群，并按比例从每个亚群中随机抽样，代表性很高，但需要详细的总体信息。
Evaluating a sampling method involves considering representativeness, generalisability, and practical constraints. A larger sample size generally increases reliability, but the sampling frame is equally important.
评估抽样方法需要考虑代表性、概括性及实际限制。较大的样本量通常能提高信度，但抽样框同样重要。
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