Year 13 CIE Psychology: Formula & Statistical Test Quick Reference | CIE 心理学公式定理速查手册

📚 Year 13 CIE Psychology: Formula & Statistical Test Quick Reference | CIE 心理学公式定理速查手册

This quick-reference handbook covers the essential formulas, statistical tests, and decision rules required for Year 13 CIE Psychology. Use it to revise calculation steps, refresh the conditions for each test, and strengthen your understanding of inferential statistics ahead of the exam.

本速查手册涵盖了CIE Year 13 心理学所需的基本公式、统计检验和决策准则。您可以借此回顾计算步骤、重温每种检验的适用条件，并在考前巩固对推论统计的理解。

1. Mean, Median, Mode | 平均数、中位数、众数

The mean (x̄) is the arithmetic average, calculated by summing all scores and dividing by the number of scores. It is used for interval/ratio data but is sensitive to outliers. The median is the middle value when data are ordered; the mode is the most frequent score.

平均数是所有分数之和除以数据个数所得的算术平均值，适用于等距/等比数据，但易受极端值影响。中位数是将数据排序后位于中间的值；众数是出现频率最高的分数。

x̄ = Σx / n

Always check the level of measurement before choosing the appropriate average. The mean is suitable for symmetrical distributions, while the median is better for skewed data.

选择平均数类型前务必确认测量层次。均值适用于对称分布，而偏态分布更适合用中位数。

2. Range, Variance, Standard Deviation | 范围、方差、标准差

These measures describe the spread of scores. Range = maximum − minimum. Variance (s²) is the average of squared deviations from the mean, using n−1 for a sample. Standard deviation (s) is the square root of the variance and is expressed in the original units.

这些指标描述分数的离散程度。范围 = 最大值 − 最小值。方差 (s²) 是各数据与均值之差的平方和的平均值，样本方差分母为 n−1。标准差 (s) 是方差的平方根，单位为原单位。

s² = Σ(x − x̄)² / (n − 1)

s = √[ Σ(x − x̄)² / (n − 1) ]

A larger standard deviation indicates greater variability around the mean. In a normal distribution, approximately 68% of scores lie within ±1 s from the mean.

标准差越大，数据在均值附近的变异性越大。在正态分布中，约68%的数据落在均值±1个标准差之内。

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

Spearman’s rₛ is a non-parametric test for correlation between two sets of ordinal (or converted interval) data. It measures the strength and direction of a monotonic relationship. Steps: rank both variables, find the difference (d) between ranks for each pair, square the differences, and apply the formula.

斯皮尔曼等级相关系数 rₛ 是一种非参数检验，用于测量两组顺序数据（或转换后的等距数据）之间的相关强度和方向。步骤：将两个变量分别排序，计算每对数据的秩差 d，求 d² 之和，带入公式。

rₛ = 1 − (6 Σ d²) / (n(n² − 1))

rₛ ranges from –1 to +1. Use the Spearman critical value table to decide significance: if calculated rₛ ≥ critical value, reject H₀.

rₛ 取值介于 –1 至 +1。需查阅斯皮尔曼临界值表判断显著性

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