📚 GCSE Edexcel Psychology: Formula & Theorem Quick Reference Handbook | GCSE Edexcel 心理学：公式定理速查手册
This concise handbook is designed for GCSE Edexcel Psychology students to quickly access the essential formulas, statistical calculations, and core theoretical theorems that frequently appear in Research Methods and key topic areas. Mastering these numerical tools and principles will boost your confidence in data handling questions and strengthen your understanding of psychological studies.
这本简明手册专为 GCSE Edexcel 心理学学生设计，旨在快速查阅研究方法及关键主题领域中常见的基本公式、统计计算和核心理论定理。掌握这些数字工具和原理将提升你处理数据题的信心，并加深对心理学研究的理解。
1. Mean | 平均数
The mean is the arithmetic average of a set of scores. It is calculated by summing all the values and dividing by the number of observations. The mean is the most sensitive measure of central tendency because it takes every data point into account.
平均数是数据集的算术平均值，通过将所有数值相加再除以观察数量计算得出。平均数是最灵敏的集中趋势量数，因为它考虑了每一个数据点。
Mean = Sum of all scores ÷ Number of scores
平均数 = 所有分数之和 ÷ 分数个数
For example, if five participants scored 7, 9, 6, 8 and 10 on a memory test, the mean is (7+9+6+8+10) ÷ 5 = 40 ÷ 5 = 8.
例如，若五名参与者在记忆测试中得分为 7、9、6、8 和 10，则平均数为 (7+9+6+8+10) ÷ 5 = 40 ÷ 5 = 8。
2. Median | 中位数
The median is the middle value when all scores are arranged in order from smallest to largest. If there is an even number of scores, the median is the mean of the two middle numbers. The median is not distorted by extreme values and is therefore useful when data contains outliers.
中位数是将所有分数从小到大排序后处于最中间的数值。如果数据个数为偶数，中位数则是中间两个数的平均值。中位数不受极端值的扭曲，因此当数据含有异常值时非常有用。
Steps to find the median: order the data set, then locate the central position using (n + 1) ÷ 2, where n is the number of scores. If that gives a whole number, that is the median; if it gives a decimal, take the average of the two adjacent scores.
求中位数的步骤：先将数据排序，再用 (n + 1) ÷ 2 找出中心位置，其中 n 为分数个数。若结果为整数，则该位置的值即为中位数；若为小数，则取相邻两个分数的平均值。
3. Mode | 众数
The mode is the most frequently occurring value in a data set. A set can have one mode (unimodal), two modes (bimodal), or more. The mode is the only measure of central tendency that can be used with nominal (categorical) data, such as eye colour or favourite subject.
众数是数据集中出现次数最多的值。一组数据可以有一个众数（单峰）、两个众数（双峰）或更多。众数是唯一可用于称名（分类）数据的集中趋势量数，例如眼睛颜色或最喜欢的科目。
When analysing questionnaires in psychological studies, the mode is often used to identify the most common response. It is easy to spot in a frequency table or bar chart but may not represent the centre of the distribution accurately if data are skewed.
在心理学研究中分析问卷时，众数常用于确定最常见的回答。在频数表或条形图中很容易识别，但如果数据分布偏斜，众数可能无法准确代表分布的中心。
4. Range | 范围
The range is a simple measure of dispersion that shows the spread of data. It is calculated by subtracting the smallest value from the largest value. A larger range indicates greater variability in the data set.
范围是一个简单的离散量数，显示数据的散布程度。它的计算方法是最大值减去最小值。范围越大，说明数据集的变异性越大。
Range = Highest value − Lowest value
范围 = 最高值 − 最低值
For instance, if reaction times in a study range from 220 ms to 580 ms, the range is 580 − 220 = 360 ms. However, the range is easily affected by outliers. Therefore, researchers often also consider the interquartile range or standard deviation for a more robust picture of spread.
例如，若一项研究中的反应时间从 220 毫秒到 580 毫秒不等，则范围为 580 − 220 = 360 毫秒。然而，范围容易受到异常值的影响。因此，研究人员通常还会参考四分位距或标准差，以获得更稳健的离散程度图像。
5. Percentage Change | 百分比变化
Percentage change is used to compare the difference between an old and a new value in relative terms. In psychological experiments, it can show the improvement in recall after an intervention or the drop in anxiety scores following treatment.
百分比变化用于以相对的方式比较新旧值之间的差异。在心理学实验中，它可以显示干预后回忆成绩的提升，或治疗后焦虑分数的下降程度。
Percentage Change = (New Value − Original Value) ÷ Original Value × 100%
百分比变化 = (新值 − 原值) ÷ 原值 × 100%
A positive result indicates an increase, while a negative result indicates a decrease. For example, if a participant’s stress score decreases from 40 to 30 after relaxation training, the percentage change is (30 − 40) ÷ 40 × 100% = −25%, representing a 25% reduction in stress.
正值表示增加，负值表示减少。例如，若参与者在放松训练后压力分数从 40 降至 30，百分比变化为 (30 − 40) ÷ 40 × 100% = −25%，表示压力下降了 25%。
6. Calculating Percentages and Proportions | 计算百分比与比例
Percentages express a part of a whole as a fraction of 100. Proportions express the same relationship as a decimal between 0 and 1. These calculations are vital for interpreting behavioural categories in observations or response frequencies in surveys.
百分比将整体的一部分表示为 100 的分数。比例则将同一关系表示为 0 到 1 之间的小数。这些计算对于解读观察中的行为类别或调查中的回答频数至关重要。
Percentage = (Part ÷ Whole) × 100
百分比 = (部分 ÷ 整体) × 100
Proportion = Part ÷ Whole
比例 = 部分 ÷ 整体
In a conformity study, if 18 out of 30 participants conformed at least once, the percentage who conformed is (18 ÷ 30) × 100 = 60%, and the proportion is 18 ÷ 30 = 0.6. Always check whether the question asks for a percentage or a proportion.
在一项从众研究中，若 30 名参与者中有 18 人至少从众一次，则从众的百分比为 (18 ÷ 30) × 100 = 60%，比例为 18 ÷ 30 = 0.6。务必看清题目要求的是百分比还是比例。
7. Normal Distribution and Standard Deviation | 正态分布与标准差
The normal distribution is a bell-shaped, symmetrical curve that represents how traits like IQ or height are distributed in a population. Most scores cluster around the mean, and the frequency of extreme scores tails off in both directions. The standard deviation (SD) measures the average distance of each score from the mean; a small SD indicates data points are closely bunched around the mean, while a large SD indicates wide spread.
正态分布是一种钟形对称曲线，表示智商或身高等特质在人群中的分布方式。大多数分数聚集在平均值附近，极端分数的频率向两侧递减。标准差 (SD) 衡量每个分数与平均值的平均距离；标准差小表示数据点紧密分布在均值周围，标准差大则表示分散程度大。
Although GCSE students are not required to calculate SD, they should understand the 68–95–99.7 rule: in a normal distribution, approximately 68% of scores lie within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs. This helps in interpreting standardised scores and recognising outliers.
虽然 GCSE 学生不要求计算标准差，但应理解 68–95–99.7 法则：在正态分布中，约 68% 的分数落在平均值 ±1 个标准差的范围内，95% 落在 ±2 个标准差内，99.7% 落在 ±3 个标准差内。这有助于理解标准分数并识别异常值。
The theorem is often used in clinical psychology when diagnosing intellectual disabilities: an IQ score more than 2 SDs below the mean (IQ < 70) may indicate significant cognitive impairment.
该定理常用于临床心理学中诊断智力障碍：智商分数比平均值低超过 2 个标准差（IQ < 70）可能表明存在显著的认知障碍。
8. Correlation Coefficients | 相关系数定理
A correlation describes the strength and direction of a relationship between two co-variables, such as stress and illness, or screen time and sleep quality. Correlation is visualised on a scatter graph, where each point represents a pair of scores. The relationship can be positive (as one variable increases, the other tends to increase), negative (as one increases, the other decreases), or zero (no pattern).
相关系数描述两个共变量之间关系的强度和方向，例如压力与疾病，或屏幕时间与睡眠质量。相关关系用散点图表现，每个点代表一对分数。关系可以是正相关（一个变量增大，另一个也趋于增大）、负相关（一个增大，另一个减小）或零相关（无规律）。
Although the GCSE specification does not require calculation of the correlation coefficient r, students must know that coefficients range from −1 to +1. A coefficient close to +1 indicates a strong positive correlation; close to −1 indicates a strong negative correlation; and 0 indicates no correlation. However, correlation does not imply causation – a third variable may be responsible for the observed link.
虽然 GCSE 大纲不要求计算相关系数 r，但学生必须知道系数的取值范围为 −1 到 +1。接近 +1 表示强正相关；接近 −1 表示强负相关；0 表示无相关。然而，相关关系并不意味着因果关系——可能有一个第三变量导致了观察到的关联。
For example, a study by Bickham et al. found a positive correlation between violent media consumption and aggressive behaviour, but this does not prove that violent media causes aggression; other factors such as home environment could play a role.
例如，Bickham 等人的研究发现暴力媒体消费与攻击行为之间存在正相关，但这并不证明暴力媒体导致攻击行为；家庭环境等其他因素也可能起作用。
9. Ebbinghaus Forgetting Curve | 艾宾浩斯遗忘曲线
The Ebbinghaus forgetting curve is a fundamental theorem in memory research. Hermann Ebbinghaus discovered that memory retention declines exponentially over time after learning new information. He found that most forgetting occurs rapidly within the first hour, after which the rate of forgetting slows down. This curve provides the theoretical basis for spaced repetition and revision strategies.
艾宾浩斯遗忘曲线是记忆研究中的一项基础定理。赫尔曼·艾宾浩斯发现，学习新信息后，记忆保留随时间呈指数式衰减。他发现大部分遗忘发生在第一个小时之内，之后遗忘速度逐渐减慢。这条曲线为间隔重复和复习策略提供了理论依据。
The table below shows typical retention rates from Ebbinghaus’s experiments, which can be applied to understand why cramming before exams is less effective than distributing practice over time.
下表显示了艾宾浩斯实验中的典型保留率，可用于理解为何考前突击不如分散练习有效。
| Time since learning | Approximate retention % |
| Immediately | 100% |
| 20 minutes | 58% |
| 1 hour | 44% |
| 1 day | 33% |
| 6 days | 25% |
The theorem reminds us that without active revision, memory fades quickly; however, reviewing material at increasing intervals strengthens long-term retention.
这一定理提醒我们，如果不主动复习，记忆会迅速消退；然而，按照逐渐拉长的间隔复习材料可以增强长期保留。
10. Misinformation Effect and Recall Accuracy | 误导信息效应与回忆准确率
The misinformation effect, demonstrated by Loftus and Palmer (1974), is a theorem in cognitive psychology showing that post-event information can distort an eyewitness’s memory of an original event. In such experiments, researchers often calculate the percentage of participants who give an accurate recall or report a false detail, depending on the condition.
误导信息效应由 Loftus 和 Palmer (1974) 证实，是以知心理学中的一个定理，显示事件后信息可以扭曲目击者对原始事件的记忆。在这类实验中，研究人员通常会计算在不同条件下给出准确回忆或报告虚假细节的参与者百分比。
Recall Accuracy (%) = (Number of correct responses ÷ Total number of responses) × 100
回忆准确率 (%) = (正确回答个数 ÷ 回答总个数) × 100
In Loftus and Palmer’s study, participants who heard the word ‘smashed’ estimated higher speeds for the car crash and were more likely to falsely recall seeing broken glass than those who heard ‘hit’. Using the formula, one can compare the recall accuracy between groups to determine the effect of the leading verb.
在 Loftus 和 Palmer 的研究中，听到“撞毁”一词的参与者对车祸速度的估计值更高，且比听到“碰撞”的参与者更可能错误回忆起看到了碎玻璃。借助该公式，可以比较各组间的回忆准确率，从而判断诱导动词的效应。
This exercise illustrates how a simple percentage calculation can turn raw data into meaningful evidence for or against a psychological theory, a skill frequently assessed in GCSE Edexcel Psychology research methods questions.
这一实例显示了简单的百分比计算如何将原始数据转化为支持或反对某个心理学理论的有力证据，这正是 GCSE Edexcel 心理学研究方法题中经常考察的技能。
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