📚 Year 10 OCR Psychology: Formula & Theorem Quick Reference Guide | Year 10 OCR 心理学：公式定理速查手册
This quick reference handbook summarises the most important formulas, theorems and key principles you need for Year 10 OCR GCSE Psychology. From descriptive statistics to memory laws and experimental design frameworks, each entry is clearly defined with its relevant formula or principle, along with practical applications. Use this guide alongside your class notes to reinforce your understanding and boost your exam performance.
本速查手册总结了 Year 10 OCR GCSE 心理学所需掌握的最重要公式、定理和关键原理。从描述统计到记忆定律和实验设计框架，每个条目都清晰定义了其公式或原理及实际应用。请结合课堂笔记使用本手册，以巩固理解并提高考试成绩。
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 total number of values. The mean is the most commonly used measure of central tendency and works best with normally distributed data without extreme outliers.
平均数是一组分数的算术平均值。计算方法是将所有数值相加，再除以数值的总个数。平均数是最常用的集中趋势量数，最适合用于没有极端异常值的正态分布数据。
Mean = (∑x) ÷ N
example, if three participants recall 5, 7 and 9 words, the mean is (5+7+9) ÷ 3 = 7 words.
∑x 表示所有单个分数的总和，N 表示分数的总个数。例如，若三名参与者分别回忆出 5、7 和 9 个单词，则平均数为 (5+7+9) ÷ 3 = 7 个单词。
2. Median | 中位数
The median is the middle value when all scores are arranged in numerical order. If there is an odd number of scores, the median is the exact middle item. If there is an even number, the median is the mean of the two middle values. The median is less affected by extreme scores than the mean.
中位数是将所有分数按数值大小排列后处于中间位置的值。如果分数个数为奇数，中位数就是正中间的那一个；如果为偶数，中位数则是中间两个数的平均值。相对于平均数，中位数受极端值的影响更小。
Median position (odd N) = (N + 1) ÷ 2
ge them. For instance, with the ordered scores 5, 8, 10, 12, the median is (8+10) ÷ 2 = 9.
当分数个数为偶数时，先定位中间两项再求其平均。例如，有序数列 5, 8, 10, 12 的中位数是 (8+10) ÷ 2 = 9。
3. Mode | 众数
The mode is the most frequently occurring score in a data set. A distribution can have one mode (unimodal), two modes (bimodal) or multiple modes. The mode is the only measure of central tendency that works with nominal (category) data and is useful for identifying the most common response.
众数是数据集中出现次数最多的分数。一个分布可以有一个众数（单峰）、两个众数（双峰）或多个众数。众数是唯一适用于名义（类别）数据的集中趋势量数，常用于识别最常见的反应。
To find the mode, simply count the frequencies of each score and pick the one with the highest frequency. For example, in the set 3, 4, 4, 5, 5, 5, 7, the mode is 5.
寻找众数只需统计每个分数的频次，然后选出频次最高的分数。例如，在 3, 4, 4, 5, 5, 5, 7 这组数据中，众数为 5。
4. Range | 全距
The range is a simple measure of dispersion that shows the spread of scores by taking the difference between the highest and lowest values. While easy to calculate, the range can be distorted by a single outlier. It is best used alongside other measures of dispersion.
全距是一种简单的离散程度度量，通过取最高值和最低值的差来显示分数的分布范围。全距虽容易计算，但可能因单一异常值而失真，最好与其他离散度量一起使用。
Range = Highest score – Lowest score
If the highest anxiety score is 18 and the lowest is 3, the range is 18 – 3 = 15. This tells us the maximum distance between participants' scores but not how scores are distributed in between.
若最高焦虑分数为 18，最低为 3，则全距为 18 – 3 = 15。这告诉我们参与者分数之间的最大差距，但无法呈现分数在中间如何分布。
5. Percentage | 百分比
A percentage expresses a number as a fraction of 100, making it easier to compare different proportions. In psychology, percentages are frequently used to describe the proportion of participants showing a particular behaviour or choosing a certain option in a survey.
百分比将一个数表示为百的分数，便于比较不同比例。在心理学中，百分比常被用来描述表现出特定行为或在调查中选择了某一选项的参与者比例。
Percentage = (Part ÷ Whole) × 100
of 80 participants show a positive attitude change, the percentage is (32 ÷ 80) × 100 = 40%. Always check that the denominator represents the total sample.
如果 80 名参与者中有 32 人表现出积极的态度改变，则百分比为 (32 ÷ 80) × 100 = 40%。请务必确认分母代表总样本量。
6. Ratio | 比率
A ratio compares the sizes of two or more quantities. It can be written with a colon (A:B) or as a fraction (A/B). Ratios help describe the relationship between groups, such as the ratio of males to females in a study.
比率用于比较两个或多个数量的大小。它可以写成 A:B 或分数形式（A/B）。比率有助于描述组间关系，例如研究中男性与女性的比例。
Ratio = Part A : Part B
If there are 15 boys and 10 girls in a sample, the ratio of boys to girls is 15:10, which simplifies to 3:2. This means for every 3 boys there are 2 girls.
若样本中有 15 名男生和 10 名女生，则男女生比率为 15:10，简化为 3:2，表示每 3 名男生对应 2 名女生。
7. Percentage Change | 百分比变化
Percentage change measures the relative increase or decrease between an original value and a new value. This is particularly useful when evaluating the effectiveness of an intervention or comparing pre-test and post-test scores.
百分比变化测量原值与新值之间的相对增减幅度。在评估干预效果或比较前测与后测分数时，该指标尤为有用。
Percentage Change = [(New value – Original value) ÷ Original value] × 100
ercentage increase; a negative result indicates a decrease. For instance, if a participant's reaction time improves from 500 ms to 400 ms, the change is [(400 – 500) ÷ 500] × 100 = –20%, representing a 20% reduction.
正数表示百分比增加，负数表示减少。例如，若参与者的反应时间从 500 毫秒改善为 400 毫秒，变化为 [(400 – 500) ÷ 500] × 100 = –20%，即减少了 20%。
8. Variables in Experiments | 实验中的变量
In any controlled experiment, the independent variable (IV) is the factor deliberately manipulated by the researcher. The dependent variable (DV) is the factor that is measured to assess the effect of the IV. All other variables (extraneous variables) should be controlled or held constant to prevent confounding effects.
在任何控制实验中，自变量（IV）是研究者有意操纵的因素。因变量（DV）是被测量的因素，用以评估自变量的效果。所有其他变量（额外变量）必须加以控制或保持恒定，以防止混淆效应。
A confounding variable is an uncontrolled factor that varies systematically with the IV and could distort the findings. For example, if one group is tested in the morning and another in the afternoon, time of day could become a confounding variable. Researchers must identify potential confounding variables and use standardised procedures.
混淆变量是未受控制的因素，它随自变量系统性地变化，并可能扭曲结果。例如，如果一组在上午测试而另一组在下午测试，一天中的时间就可能成为混淆变量。研究者必须识别潜在混淆变量并使用标准化程序。
9. Hypotheses | 假设
An experimental hypothesis (alternative hypothesis) predicts that the independent variable will have an effect on the dependent variable. The null hypothesis asserts that there will be no significant difference or relationship. A directional (one‑tailed) hypothesis states the expected direction of the effect, whereas a non‑directional (two‑tailed) hypothesis simply predicts a difference without specifying direction.
实验假设（备择假设）预测自变量会对因变量产生影响。虚无假设声称不存在显著差异或关联。方向性（单尾）假设陈述了预期的效应方向，而非方向性（双尾）假设只预测存在差异，不指定方向。
Example of a directional hypothesis: 'Participants who drink 200 ml of water will recall more words than those who drink no water.' The corresponding null hypothesis is: 'There will be no difference in the number of words recalled between the water and no‑water groups.' A non‑directional version would simply state: 'There will be a difference in word recall between the two groups.'
例如，方向性假设：“饮用 200 毫升水的参与者比未饮水的参与者能回忆出更多单词。”相应的虚无假设是：“饮水组与未饮水组的单词回忆数量没有差异。”非方向性假设则简单表述为：“两组在单词回忆上存在差异。”
10. Experimental Designs | 实验设计
Psychologists use three main experimental designs to allocate participants to conditions: independent measures (different participants in each condition), repeated measures (the same participants take part in all conditions), and matched pairs (different but matched participants in each condition). Each design has its own strengths and limitations regarding participant variables, order effects and demand characteristics.
心理学家使用三种主要实验设计来分配参与者到不同条件：独立组设计（每个条件使用不同参与者）、重复测量设计（相同参与者参与所有条件）和匹配对设计（不同但经过匹配的参与者被分配至各条件）。每种设计在参与者变量、顺序效应和需求特征方面各有优缺点。
| Independent Measures Design | 独立组设计 | |
|---|---|
| No order effects, as participants experience only one condition. | 无顺序效应，因参与者只经历一种条件。 |
| Individual differences may confound the results; requires more participants. | 个体差异可能混淆结果；需要更多参与者。 |
| Repeated Measures Design | 重复测量设计 | |
|---|---|
| Controls for individual differences; fewer participants needed. | 控制个体差异；所需参与者较少。 |
| Order effects (e.g., fatigue, practice) can occur; counterbalancing is required. | 可能出现顺序效应（如疲劳、练习）；需要平衡顺序。 |
| Matched Pairs Design | 匹配对设计 | |
|---|---|
| Reduces participant variables and avoids order effects. | 减少参与者变量并避免顺序效应。 |
| Matching is time‑consuming; perfect matching is impossible. | 匹配过程耗时；无法做到完美匹配。 |
11. Miller's Law (7±2) | 米勒定律 (7±2)
George Miller’s classic paper 'The Magical Number Seven, Plus or Minus Two' established that the capacity of short‑ unk is a meaningful grouping of units that helps extend the functional capacity of memory.
乔治·米勒的经典论文“神奇数字7±2”确立了短时记忆的容量大约为7±2个组块。组块是对信息单元的有意义组合，有助于扩展记忆的实际容量。
For example, the sequence 'F B I T W A U K' is difficult to recall as eight individual letters. If chunked into 'FBI', 'TWA' and 'UK', it becomes three meaningful chunks, well within STM capacity. This principle applies to phone numbers, acronyms and rhythmic patterns.
例如，字母序列“F B I T W A U K”若作为八个单独字母很难记住。若组块化为“FBI”、“TWA”和“UK”三个有意义的组块，则完全在短时记忆容量之内。该原理适用于电话号码、首字母缩写和节奏模式。
12. Serial Position Effect | 序列位置效应
The serial position effect refers to the U‑shaped pattern of recall when participants learn a list of items. Words presented at the beginning benefit from the primacy effect, as they have been rehearsed longer and entered long‑term memory. Words at
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