AS WJEC Psychology: Quick Reference Handbook of Formulas and Theorems | AS WJEC 心理学：公式定理速查手册

📚 AS WJEC Psychology: Quick Reference Handbook of Formulas and Theorems | AS WJEC 心理学：公式定理速查手册

This article serves as a rapid revision companion for AS WJEC Psychology students, collecting the most important statistical formulas, psychophysical laws, and key theoretical principles into one accessible guide. Whether you are preparing for your examination or checking your understanding of research methods, this handbook makes it easy to recall the calculations and concepts you need.

本文是 AS WJEC 心理学学生的快速复习伴侣，将最重要的统计公式、心理物理学定律和关键理论原理汇聚到一本易用的指南中。无论是备考还是检测对研究方法的理解，这本手册都能帮你轻松回忆起所需的计算与概念。

1. Descriptive Statistics: Central Tendency & Dispersion | 描述统计：集中趋势与离散量数

The three measures of central tendency summarise a set of scores with a single typical value. The mean (M) is calculated by summing all scores and dividing by the number of scores (n). The median is the middle value when scores are ordered, and the mode is the most frequently occurring score. The range is the simplest measure of dispersion: highest score minus lowest score.

三种集中趋势量数用一个典型值概括一组分数。均值 (M) 是所有分数之和除以分数个数 (n)。中位数是排序后居中的值，众数是出现频率最高的分数。极差是最简单的离散量数：最高分减去最低分。

Mean (M) = ∑X ÷ n

M = (∑X)/n

Range = X_max − X_min

For grouped data, the midpoint of each interval is used to estimate the mean. When outliers are present, the median is often a more robust measure of central tendency than the mean.

对于分组数据，用每个区间的中点估计均值。存在异常值时，中位数通常比均值更稳健。

2. Variance and Standard Deviation | 方差与标准差

Variance (s²) and standard deviation (s) quantify how spread out the scores are around the mean. A larger standard deviation indicates greater variability.

方差 (s²) 和标准差 (s) 是量化分数围绕均值分散程度的指标。标准差越大，变异性越大。

The formula for sample variance uses n−1 (Bessel’s correction) to provide an unbiased estimate of the population variance:

样本方差公式使用 n−1 (贝塞尔校正) 以获得总体方差的无偏估计：

s² = ∑(X − M)² ÷ (n − 1)

s = √[ ∑(X − M)² ÷ (n − 1) ]

Step-by-step calculation: (1) find the mean, (2) subtract the mean from each score and square the result, (3) sum these squared deviations, (4) divide by n−1 to obtain variance, (5) take the square root to get the standard deviation.

计算步骤：(1) 求均值，(2) 每个分数减去均值并将结果平方，(3) 将这些平方差求和，(4) 除以 n−1 得到方差，(5) 开平方得出标准差。

3. Normal Distribution and Probability | 正态分布与概率

The normal distribution is a bell-shaped, symmetrical curve where the mean, median, and mode coincide. In a normal distribution, known proportions of scores lie within a certain number of standard deviations from the mean.

正态分布是一种钟形对称曲线，均值、中位数和众数重合。在正态分布中，已知比例的分数落在均值周围特定标准差范围内。

• About 68% of scores fall within ±1 SD of the mean.

  约 68% 的分数落在均值 ±1 个标准差内。

• About 95% of scores fall within ±2 SD of the mean.

  约 95% 的分数落在均值 ±2 个标准差内。

• About 99.7% of scores fall within ±3 SD of the mean.

  约 99.7% 的分数落在均值 ±3 个标准差内。

This knowledge is used in inferential testing to decide whether a result is statistically significant, as values far from the mean (e.g., beyond ±1.96 SD) occur rarely under the null hypothesis.

这一知识用于推断检验，判断结果是否具有统计显著性，因为远离均值的值（如超出±1.96 SD）在虚无假设下很少出现。

4. Inferential Statistics: Probability and Significance | 推断统计：概率与显著性

Inferential statistics allow psychologists to draw conclusions about populations based on sample data. The null hypothesis (H₀) states that there is no effect or no difference. The alternative hypothesis (H₁) suggests an effect or difference exists

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