📚 GCSE AQA Psychology: Formula & Theorem Quick Reference Handbook | GCSE AQA 心理学：公式定理速查手册
In GCSE AQA Psychology, success relies not just on understanding theories and studies, but also on confidently applying mathematical formulae and statistical tests within research methods. This quick reference handbook gathers all the essential equations, statistical concepts, and procedural rules you need for your exam, from measures of central tendency to interpreting correlation coefficients.
在 GCSE AQA 心理学中，成功不仅依赖于理解理论和研究，还依赖于在研究法中自信地应用数学公式和统计检验。这本速查手册汇集了所有你考试所需的基本方程、统计概念和程序规则，包括集中趋势测量和相关系数的解读。
1. Measures of Central Tendency: Mean | 集中趋势测量：平均值
The mean is the arithmetic average of a set of scores. Add all the values together and divide by the number of values. This is used when data are interval or ratio level and are normally distributed without extreme outliers.
平均值是一组分数的算术平均数。将所有数值相加，然后除以数值的个数。当数据为等距或比率水平且呈正态分布、没有极端异常值时使用。
Mean = Σx ÷ n
平均值 = Σx ÷ n
- Σx = sum of all scores (所有分数的总和)
- n = number of scores (分数的个数)
2. Measures of Central Tendency: Median | 集中趋势测量：中位数
The median is the middle value when scores are arranged in order. If there is an even number of scores, it is the midpoint between the two middle numbers. The median is preferred when data are ordinal or when the mean is distorted by outliers.
中位数是将分数按顺序排列后的中间值。如果有偶数个分数，则取中间两个数的中点。当数据为顺序水平或平均值受异常值影响扭曲时，优先使用中位数。
Procedure: order all scores, count to the (n+1)/2 position. For even n, average the two central scores.
步骤：将所有分数排序，定位到第 (n+1)/2 位。若 n 为偶数，取中间两个分数的平均值。
3. Measures of Central Tendency: Mode | 集中趋势测量：众数
The mode is the most frequently occurring value in a dataset. It is the only measure of central tendency suitable for nominal data (categories). A dataset can have one mode, more than one mode (bimodal), or no mode at all.
众数是数据集中出现最频繁的值。它是唯一适合名义数据（类别）的集中趋势测量。一个数据集可以有一个众数、多个众数（双峰）或没有众数。
4. Measures of Dispersion: Range | 离散程度测量：全距
The range is the simplest measure of spread. It is calculated by subtracting the lowest score from the highest score. A larger range indicates greater variability. However, the range is easily affected by outliers.
全距是最简单的离散度测量。用最高分减去最低分计算。全距越大表明变异性越大。但全距容易受异常值影响。
Range = Highest score − Lowest score
全距 = 最高分 − 最低分
5. Measures of Dispersion: Standard Deviation (Conceptual) | 离散程度测量：标准差（概念）
Standard deviation measures how spread out scores are around the mean. A low standard deviation means scores are clustered closely around the mean; a high standard deviation means greater spread. You are not required to calculate standard deviation from raw data in GCSE AQA Psychology, but you must understand its meaning and interpret given values.
标准差衡量分数在平均值附近的离散程度。标准差低表示分数紧密围绕平均值；标准差高表示离散程度大。在 GCSE AQA 心理学中不要求从原始数据计算标准差，但必须理解其含义并能解释给出的数值。
The formula for population standard deviation (σ) is often shown as:
总体标准差 (σ) 的公式通常表示为：
σ = √[ Σ(x − μ)² ÷ N ]
ion mean, N = number of scores. You simply need to recognise this formula, not compute it.
其中 μ = 总体均值，N = 分数个数。你只需认识该公式，无需计算。
6. Percentages and Ratios in Research | 研究中的百分比和比例
Many exam questions ask you to calculate a percentage from raw data, for example the percentage of participants who recalled words correctly in a condition. The formula is simple:
许多考题要求从原始数据计算百分比，例如在某一条件下正确回忆单词的参与者的百分比。公式很简单：
Percentage = (Part ÷ Total) × 100
百分比 = (部分 ÷ 总计) × 100
Also, you may need to express a finding as a ratio, e.g., the ratio of recall in condition A to condition B.
此外，你可能需要用比例表达结果，例如条件 A 与条件 B 的回忆比率。
7. Chi-Square Test of Association (Concept & Decision Rule) | 卡方关联性检验（概念与判定规则）
The chi-square test is used to determine whether there is a significant association between two categorical (nominal) variables. You are not expected to compute chi-square in GCSE, but you must understand the observed and expected frequency table and the decision rule. Compare the calculated chi-square value (given) against a critical value from a table.
卡方检验用于确定两个类别（名义）变量之间是否存在显著关联。在 GCSE 不要求计算卡方，但必须理解观察频数和期望频数表以及判定规则。将给出的计算卡方值与表中的临界值进行比较。
Conditions: use when data are nominal (categories), independent groups design, and expected frequencies are at least 5 in each cell.
条件：当数据为名义数据（类别）、独立组设计，且每个格的期望频数至少为 5 时使用。
If χ² calculated ≥ χ² critical → significant result (reject null hypothesis)
如果计算卡方值 ≥ 临界卡方值 → 显著结果（拒绝零假设）
8. Spearman’s Rank Correlation Coefficient (Concept) | 斯皮尔曼等级相关系数（概念）
Spearman’s rho (ρ or rₛ) measures the strength and direction of association between two ranked (ordinal) variables. The coefficient ranges from −1 (perfect negative correlation) to +1 (perfect positive correlation). 0 indicates no correlation. You are not required to calculate Spearman’s rho in the exam, but you should know how to interpret a given value and compare it to a critical value.
斯皮尔曼等级相关系数 (ρ 或 rₛ) 衡量两个排序（顺序）变量之间的关联强度和方向。系数范围从 −1（完全负相关）到 +1（完全正相关）。0 表示无关。考试不要求计算斯皮尔曼相关系数，但应会解释给定值并与临界值比较。
If |rₛ| ≥ critical value → significant correlation
如果 |rₛ| ≥ 临界值 → 相关性显著
number of pairs. Remember, this formula is provided as background; you apply the concept.
你可能会看到公式：rₛ = 1 − [6Σd² ÷ n(n²−1)]，其中 d = 等级差，n = 配对数目。记住，该公式作为背景提供；你运用的是概念。
9. Probability and Levels of Significance | 概率与显著性水平
ually p ≤ 0.05. This means the probability of the observed result occurring by chance is 5% critical value at p ≤ 0.05, the result is significant and the null hypothesis is rejected.
心理学中通常接受的显著性水平为 p ≤ 0.05。这意味着观察到的结果由于偶然发生的概率为 5% 或更小。当计算统计量超过 p ≤ 0.05 的临界值时，结果显著，拒绝零假设。
Key terms:
关键术语：
- Null hypothesis (H₀) – states there is no effect/difference/correlation. (零假设 H₀ – 表明没有效应/差异/相关。)
- Alternative hypothesis (H₁) – states there is an effect. (备择假设 H₁ – 表明存在效应。)
- Type I error – rejecting a true null hypothesis (false positive). (第一类错误 – 拒绝了真实的零假设，假阳性。)
- Type II error – failing to reject a false null hypothesis (false negative). (第二类错误 – 未能拒绝错误的零假设，假阴性。)
10. Normal Distribution and Skew | 正态分布与偏态
coincide. Many psychological traits are normally distributed. In a normal distribution, 68% of scores fall within ±1 standard deviation from the mean, 95% within ±2 standard deviations.
正态分布是一种钟形对称曲线，均值、中位数和众数重合。许多心理特征呈正态分布。在正态分布中，68% 的分数落在平均值 ±1 个标准差内，95% 落在 ±2 个标准差内。
Skew refers to asymmetry:
偏态指不对称：
- Positive skew: tail on the right (mean > median > mode). (正偏态：右侧尾巴，均值 > 中位数 > 众数。)
- Negative skew: tail on the left (mean < median < mode). (负偏态：左侧尾巴，均值 < 中位数 < 众数。)
11. Estimation and Decimal Place Rules | 估算和小数位规则
In calculations, always show your working and round final answers appropriately. For percentages, typically round to one or two decimal places unless instructed otherwise. For measures like standard deviation, the given value is often presented to two decimal places.
在计算中，始终展示步骤并恰当舍入最终答案。百分比通常舍入到一或两位小数，除非另有说明。标准差等测量通常以两位小数给出。
When calculating the mean, use all raw data in calculations and round the final mean to a sensible number of decimal places (usually two).
计算平均值时，使用所有原始数据计算，并将最终均值舍入到合理的小数位数（通常两位）。
12. Quick-Check Decision Flow for Statistical Tests | 统计检验速判流程
Exam questions may ask you to justify which inferential test to use. Follow these rules:
考题可能要求你说明使用哪种推论检验的理由。遵循以下规则：
| Data Type 数据类型 | Design 实验设计 | Test 检验方法 |
|---|---|---|
| Nominal (categories) 名义数据 | Independent groups 独立组 | Chi-square 卡方 |
| Ordinal (ranked) 顺序数据 | Correlation (paired scores) 相关（配对分数） | Spearman's rank 斯皮尔曼等级 |
| Ordinal 顺序数据 | Independent groups 独立组 | Mann-Whitney U* 曼-惠特尼 U 检验* |
| Ordinal 顺序数据 | Repeated measures/matched pairs 重复测量/配对组 | Wilcoxon signed-rank* 威尔科克森符号秩检验* |
*Note: Mann-Whitney and Wilcoxon are not calculated in GCSE AQA Psychology; the syllabus focuses on chi-square and Spearman's rho as the key inferential tests. However, understanding the logic of test selection is good extension knowledge.
*注：曼-惠特尼和威尔科克森检验在 GCSE AQA 心理学中不要求计算；教学大纲主要关注卡方和斯皮尔曼等级相关作为关键推论检验。不过，理解检验选择的逻辑是很好的拓展知识。
Always remember: use chi-square for nominal data (association), and Spearman's rho for ordinal data (correlation).
永远记住：名义数据用卡方（关联），顺序数据用斯皮尔曼等级相关（相关）。
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