Year 12 WJEC Psychology: Formula & Theorem Quick Reference | WJEC 12年级心理学：公式定理速查手册

📚 Year 12 WJEC Psychology: Formula & Theorem Quick Reference | WJEC 12年级心理学：公式定理速查手册

In WJEC Year 12 Psychology, success depends not only on grasping classic theories and studies but also on handling quantitative data confidently. This quick‑reference handbook collects the essential formulas, statistical tests and psychological ‘laws’ you need to revise for AS exams. Each entry is paired with a brief explanation to help you recall when to use it and what it means.

在 WJEC 12 年级心理学中，成功不仅依赖于掌握经典理论与研究，还需要能够自信地处理量化数据。这本速查手册整理了 AS 考试必备的核心公式、统计检验以及重要的心理学“定律”。每个条目都配有简要说明，帮助你回忆何时使用以及其含义。

1. Measures of Central Tendency | 集中趋势量数

The mean is the arithmetic average. Add all the scores (Σx) and divide by the number of scores (n). It is highly sensitive to extreme values.

均值是算术平均数。将所有分数相加 (Σx) 再除以分数个数 (n)。它对极端值非常敏感。

The median is the middle value when scores are arranged in order. For an even number of scores, take the average of the two middle values. It is unaffected by outliers.

中位数是将分数按顺序排列后处于中间位置的值。若分数个数为偶数，则取中间两个值的平均数。中位数不受异常值影响。

The mode is the most frequently occurring score. A data set may have no mode, one mode (unimodal) or more than one mode (bimodal/multimodal).

众数是出现频率最高的分数。一组数据可能没有众数、有一个众数（单峰）或多个众数（双峰/多峰）。

2. Measures of Dispersion | 离散趋势量数

The range is the difference between the highest and lowest scores. It is quick to calculate but only considers the extremes and ignores the spread of the middle scores.

极差是最高分与最低分之间的差值。计算简便，但只考虑极端值，忽略了中间分数的离散情况。

Variance measures how far each score deviates from the mean. Compute the squared deviation for each score, sum them (Σ(x – x̄)²) and divide by n (or n−1 for a sample).

方差衡量每个分数偏离均值的程度。计算每个分数离均差平方，求和 (Σ(x – x̄)²) 再除以 n（样本方差除以 n−1）。

Standard deviation is the square root of the variance: SD = √(Σ(x – x̄)² / n). A larger SD indicates greater spread of scores.

标准差是方差的平方根：SD = √(Σ(x – x̄)² / n)。标准差越大，说明分数分布越分散。

3. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数

Spearman’s rho (rₛ) tests the strength and direction of a relationship between two ordinal variables (or data you rank). The formula is rₛ = 1 – (6 Σd²) / (n(n² – 1)), where d is the difference between the ranks of each pair and n is the number of pairs.

斯皮尔曼相关系数 (rₛ) 检验两个顺序变量（或可排序数据）之间关系的强度与方向。公式为 rₛ = 1 – (6 Σd²) / (n(n² – 1))，其中 d 是每对数据的秩次差，n 是数据对的数量。

An rₛ value close to +1 shows a strong positive correlation, close to −1 shows a strong negative correlation, and around 0 indicates no correlation. The critical value table then determines significance.

rₛ 接近 +1 表示强正相关，接近 −1 表示强负相关，接近 0 则表示无线性相关。随后需查临界值表判断显著性。

4. Chi-Square Test for Independence | 独立性卡方检验

The chi‑square (χ²) test checks whether there is a significant association between two categorical variables. The formula is χ² = Σ ((O – E)² / E), where O is the observed frequency and E is the expected frequency.

卡方检验 (χ²) 用于判断两个分类变量之间是否存在显著关联。公式为 χ² = Σ ((O – E)² / E)，其中 O 为观察频数，E 为期望频数。

Expected frequencies are calculated assuming no association: E = (row total × column total) / grand total. Degrees of freedom (df) = (number of rows – 1) × (number of columns – 1).

期望频数假设变量独立时计算得出：E = (行合计 × 列合计) / 总合计。自由度 (df) = (行数 – 1) × (列数 – 1)。

A larger χ² value makes it more likely to reject the null hypothesis of no association, provided it exceeds the critical value at the chosen significance level (usually 0.05).

χ² 值越大，越有可能拒绝无关联的零假设，前提是它超过选定显著性水平（通常为 0.05）的临界值。

5. Sign Test | 符号检验

The sign test is a simple non‑parametric test used with repeated measures or matched pairs designs when the data are at least ordinal. It counts the number of positive and negative differences between paired scores.

符号检验是简单的非参数检验，适用于重复测量或配对设计，且数据至少为顺序水平。它统计成对分数之差的正负号个数。

The test statistic (S) is the smaller number of either the positive or negative signs. Compare S to a critical value from a binominal sign test table; if S is equal to or smaller than the critical value, the result is significant.

检验统计量 (S) 取正号数与负号数中较小的那个。将 S 与二项符号检验表的临界值比较；若 S 小于或等于临界值，则结果显著。

Pairs where the difference is zero are typically excluded, reducing the total number of pairs (N) used for the test.

差值为零的配对通常会被剔除，从而减少用于检验的总对数 (N)。

6. Wilcoxon Signed-Rank Test | 威尔科克森符号秩检验

The Wilcoxon signed‑rank test is used for related data (repeated measures or matched pairs) when the level of measurement is at least ordinal and you can rank the difference scores. It is more powerful than the sign test because it takes the magnitude of differences into account.

威尔科克森符号秩检验用于相关数据（重复测量或配对设计），当测量水平至少是顺序水平且可以对差值进行排序时使用。它比符号检验更具统计效力，因为它考虑了差值的大小。

Steps: calculate the difference between each pair, rank the absolute differences, assign the sign of the difference to the ranks, then sum the positive ranks (W+) and the negative ranks (W−). The test statistic (T) is the smaller sum.

步骤：计算每对数据的差值，按绝对差值排序，将差值的符号赋予秩次，然后分别计算正秩次之和 (W+) 和负秩次之和 (W−)。检验统计量 (T) 取较小的那个和。

Compare the obtained T with the critical value table; if T is equal to or less than the critical value, reject the null hypothesis.

将计算得到的 T 值与临界值表比较；若 T 等于或小于临界值，则拒绝零假设。

7. Mann-Whitney U Test | 曼-惠特尼 U 检验

The Mann‑Whitney U test is a non‑parametric alternative to the independent t‑test. It compares two independent groups when the dependent variable is at least ordinal.

曼-惠特尼 U 检验是独立样本 t 检验的非参数替代方案。当因变量至少为顺序水平且涉及两个独立组时使用。

First, rank all the scores from both groups together, giving each score a rank from 1 (lowest) to N (highest). Then calculate U for each group: U₁ = R₁ – (n₁(n₁+1))/2 and U₂ = R₂ – (n₂(n₂+1))/2, where R is the sum of ranks in that group and n is the group size. The test statistic is the smaller U value.

首先将两组所有分数合并排序，从 1（最低）排到 N（最高）。然后分别计算每组的 U 值：U₁ = R₁ – (n₁(n₁+1))/2，U₂ = R₂ – (n₂(n₂+1))/2，其中 R 是该组的秩次总和，n 是组的大小。检验统计量取较小的 U 值。

A small U indicates that the ranks in the two groups differ noticeably. Compare U with critical values; if U is equal to or less than the critical value, the difference is significant.

U 值越小，说明两组的秩次差异越明显。将 U 与临界值比较；若 U 等于或小于临界值，则差异显著。

8. Yerkes-Dodson Law | 耶克斯-多德森定律

The Yerkes‑Dodson law describes the relationship between arousal and performance. Performance improves with increased arousal up to an optimal point; beyond that, further arousal leads to a decline in performance, producing an inverted‑U curve.

耶克斯-多德森定律描述了唤醒水平与表现之间的关系。表现会随着唤醒水平增加而提升，直至达到一个最佳点；之后如果再增加唤醒，表现就会下降，形成一条倒 U 型曲线。

The optimal level of arousal depends on task complexity: for simple or well‑learned tasks, higher arousal is beneficial; for complex or novel tasks, lower arousal is preferable.

最佳唤醒水平取决于任务复杂性：对于简单或熟练的任务，较高唤醒水平有利；对于复杂或新异任务，较低的唤醒水平更好。

This law helps explain why moderate anxiety before an exam can enhance focus, while excessive anxiety impairs recall.

该定律有助于解释为什么考试前适度焦虑能提高注意力，而过度的焦虑则会损害提取记忆的能力。

9. Miller’s Law (The Magical Number 7 ± 2) | 米勒定律（神奇数字 7 ± 2）

George Miller (1956) proposed that the capacity of short‑term memory (STM) is approximately seven items (plus or minus two). This means most people can hold between five and nine chunks of information in immediate memory.

乔治·米勒 (1956) 提出短时记忆的容量大约为 7 个项目（加减 2）。这意味着大多数人可以在即时记忆中容纳 5 到 9 个信息组块。

A ‘chunk’ is a meaningful unit of information, such as a digit, a letter, a word, or even a familiar phrase. Chunking allows us to expand the amount of information stored by grouping smaller units into larger, meaningful wholes.

“组块”是有意义的信息单元，例如一个数字、一个字母、一个单词，甚至一个熟悉的短语。组块化通过将较小单元组合成更大的有意义的整体，扩展了可以存储的信息量。

Miller’s law underpins the multi‑store model of memory and justifies techniques like acronyms and rhyming in revision.

米勒定律为记忆的多存储模型提供了基础，也说明了复习中使用首字母缩略词和押韵等技巧的合理性。

10. Weber’s Law | 韦伯定律

Weber’s law states that the just noticeable difference (JND) between two stimuli is a constant proportion of the original stimulus intensity. The formula is ΔI / I = k, where ΔI is the JND, I is the initial intensity, and k is the Weber fraction (a constant specific to each sensory modality).

韦伯定律指出，两个刺激之间的最小可觉差 (JND) 与原始刺激强度的比例是一个常数。公式为 ΔI / I = k，其中 ΔI 是最小可觉差，I 是初始强度，k 是韦伯分数（每种感觉通道特有的常数）。

For example, if the Weber fraction for weight discrimination is 0.02, holding a 100‑gram weight you would need an increase of at least 2 grams to notice the change; for a 200‑gram weight, the JND would be 4 grams.

例如，如果重量辨别力的韦伯分数是 0.02，当你手持 100 克的重物时，至少需要增加 2 克才能察觉变化；如果重物为 200 克，最小可觉差就变成 4 克。

Weber’s law highlights that perception is relative rather than absolute, a key concept in psychophysics and biological psychology.

韦伯定律强调了知觉是相对的而非绝对的，这是心理物理学和生物心理学中的一个关键概念。

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Year 12 WJEC Psychology: Formula & Theorem Quick Reference | WJEC 12年级心理学：公式定理速查手册