📚 A-Level Eduqas Psychology: Quick Reference to Formulas and Theorems | A-Level Eduqas 心理学：公式定理速查手册
This quick reference handbook distils the essential formulas, statistical tests, and timeless psychological laws that every Eduqas A-Level Psychology student needs at their fingertips. From descriptive statistics and inferential tests to classical psychophysical theorems, this guide provides the precise equations and conceptual summaries required for success in research methods and beyond.
这本速查手册浓缩了Eduqas A-Level心理学学生必须随手掌握的核心公式、统计检验以及经典心理学定律。从描述统计和推论检验到经典心理物理学定理，本指南提供了研究方法和相关领域中成功必备的准确方程和概念总结。
1. Measures of Central Tendency and Dispersion | 集中趋势与离散量数
The mean (x̄) is calculated by summing all scores (Σx) and dividing by the total number of scores (n): x̄ = Σx / n. It is the arithmetic average and is sensitive to outliers.
均值（x̄）通过将所有分数求和（Σx）再除以分数总数（n）得到：x̄ = Σx / n。它是算术平均值，对异常值敏感。
The median is the middle value when data are arranged in ascending order. For an even number of scores, it is the average of the two central values. It is less affected by extreme scores.
中位数是将数据按升序排列后的中间值。当分数个数为偶数时，它是中间两个数值的平均数。受极端分数的影响较小。
The mode is the most frequently occurring score in a dataset. A distribution can be unimodal, bimodal or multimodal. The range is the difference between the highest and lowest scores: Range = Xₘₐₓ − Xₘᵢₙ.
众数是数据集中出现频次最高的分数。分布可以是单峰、双峰或多峰的。全距是最高分与最低分之间的差值：全距 = Xₘₐₓ − Xₘᵢₙ。
2. Standard Deviation (Sample) | 标准差（样本）
Standard deviation measures the spread of scores around the mean. For a sample, it uses n − 1 as the denominator (Bessel’s correction):
标准差衡量分数围绕均值的分散程度。对于样本，使用 n − 1 作为分母（贝塞尔校正）：
SD = √[ Σ(x − x̄)² / (n − 1) ]
A larger SD indicates greater variability. It is used in parametric tests and forms the basis of effect size calculations.
标准差越大，变异性越强。它用于参数检验，并构成效应量计算的基础。
3. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s rho (ρ or rₛ) is a non-parametric test for association between two sets of ranked data. The test statistic is:
斯皮尔曼等级相关系数（ρ 或 rₛ）是用于两列等级数据之间关联的非参数检验。检验统计量为：
ρ = 1 − (6 Σ d²) / (n (n² − 1))
where d is the difference between ranks for each pair, and n is the number of paired observations. The obtained value is compared against critical values for ρ at a given significance level and n.
其中 d 为每对数据的等级差值，n 为成对观测值的数量。所得值与给定显著性水平和 n 下的 ρ 临界值进行比较。
4. Chi-Square Test for Independence | 卡方独立性检验
The chi-square (χ²) test examines whether there is a significant association between two categorical variables. The formula compares observed (O) and expected (E) frequencies:
卡方（χ²）检验考察两个类别变量之间是否存在显著关联。公式比较观测频次（O）与期望频次（E）：
χ² = Σ [ (O − E)² / E ]
Expected frequencies are calculated as (row total × column total) / grand total. Degrees of freedom (df) = (number of rows − 1) × (number of columns − 1). The calculated χ² is compared with a critical value from the χ² distribution table.
期望频次计算为（行总和 × 列总和）/ 总计总数。自由度（df）=（行数 − 1）× 列数 − 1）。将计算得到的 χ² 值与卡方分布表中的临界值比较。
5. Mann-Whitney U Test | 曼-惠特尼U检验
The Mann-Whitney U test is the non-parametric equivalent of an independent t-test, comparing two independent groups on an ordinal dependent variable. Compute:
曼-惠特尼U检验是独立样本t检验的非参数等价方法，用于在顺序因变量上比较两个独立组。需计算：
U₁ = n₁n₂ + (n₁(n₁ + 1))/2 − R₁
U₂ = n₁n₂ − U₁
where n₁ and n₂ are the sample sizes, and R₁ is the sum of ranks for group 1. The smaller of U₁ and U₂ is taken as the test statistic U. Compare U with critical values for the appropriate sample sizes.
其中 n₁ 和 n₂ 为样本量，R₁ 为第一组的秩和。取 U₁ 与 U₂ 中的较小值作为检验统计量 U。将 U 与相应样本量的临界值比较。
6. Wilcoxon Signed-Ranks Test | 威尔科克森符号秩检验
This test is the non-parametric counterpart of the paired-samples t-test, used for repeated measures or matched pairs. Compute the difference score for each pair, rank the absolute differences, and assign the sign of the difference. The test statistic W (or T) is the sum of the signed ranks for the less frequent sign.
该检验是配对样本t检验的非参数替代方法，用于重复测量或匹配配对设计。计算每对的差值分数，对差值的绝对值进行排秩，并赋予差值的符号。检验统计量 W（或 T）为频次较少符号的符号秩和。
Compare W against the critical Wilcoxon value for the given number of pairs (N). A significant result indicates a reliable difference between conditions.
将 W 与给定配对数量（N）下的威尔科克森临界值进行比较。结果显著则表示条件之间存在可靠差异。
7. Sign Test | 符号检验
The sign test is the simplest non-parametric test for repeated measures. Only the direction of change (+ or −) is recorded, ignoring magnitude. The test statistic S is the count of the less frequent sign.
符号检验是最简单的重复测量非参数检验，仅记录变化方向（+ 或 −），忽略变化幅度。检验统计量 S 是出现频次较少的符号的计数。
For a two-tailed hypothesis, compare S with binomial critical values (or a sign test table) using the total number of non-zero differences (n). Reject the null if S ≤ critical value.
对于双尾假设，使用非零差值总数（n）将 S 与二项式临界值（或符号检验表）比较。若 S ≤ 临界值则拒绝零假设。
8. Probability, Significance and Degrees of Freedom | 概率、显著性与自由度
In inferential statistics, the p-value is the probability of obtaining the observed result (or more extreme) if the null hypothesis is true. The conventional significance level in psychology is p ≤ 0.05. If p is less than or equal to α, the result is statistically significant and the null hypothesis is rejected.
在推论统计中，p值是在零假设为真时获得当前结果（或更极端结果）的概率。心理学中惯用的显著性水平为 p ≤ 0.05。若 p 小于或等于 α，则结果统计显著，拒绝零假设。
Degrees of freedom (df) reflect the number of values free to vary. In the chi-square test, df = (rows − 1)(columns − 1). For a related t‑test, df = N − 1. Correct df must be used to locate the critical value in statistical tables.
自由度（df）反映可自由变化的数值数量。在卡方检验中，df =（行数 − 1）×（列数 − 1）。对于相关t检验，df = N − 1。在统计表中查找临界值时必须使用正确的自由度。
9. Effect Size: Cohen’s d | 效应量：科恩的d值
Effect size quantifies the magnitude of a difference, independent of sample size. Cohen’s d for two independent means:
效应量量化差异的大小，且不受样本量影响。两独立均值的科恩 d 值：
d = (M₁ − M₂) / SDₚₒₒₗₑₑ
where SDₚₒₒₗₑₑ is the pooled standard deviation. A d of 0.2 is small, 0.5 medium, and 0.8 large. Reporting effect size alongside significance helps demonstrate practical importance.
其中 SDₚₒₒₗₑₑ 为合并标准差。d 值为 0.2 表示小效应，0.5 中等，0.8 大效应。在显著性检验的同时报告效应量有助于体现实际意义。
10. Weber’s Law and Fechner’s Law | 韦伯定律与费希纳定律
Weber’s Law states that the just noticeable difference (JND) between two stimuli is a constant proportion of the initial stimulus intensity. Expressed as:
韦伯定律指出，两个刺激之间的最小可觉差（JND）是初始刺激强度的恒定比例，表达为：
ΔI / I = k
where ΔI is the difference threshold, I is the initial stimulus magnitude, and k is the Weber fraction (different for each sensory modality).
其中 ΔI 为差别阈限，I 为初始刺激大小，k 是韦伯分数（每种感觉通道各不相同）。
Fechner’s Law extends this relationship by linking physical intensity to perceived sensation:
费希纳定律延伸了这一关系，将物理强度与感知感觉幅度联系起来：
S = k log I
where S is the sensation magnitude. This law assumes a logarithmic relationship between stimulus intensity and subjective experience, foundational to psychophysics.
其中 S 表示感觉的幅度。这一定律假设刺激强度与主观体验之间呈对数关系，构成了心理物理学的基础。
11. Yerkes-Dodson Law and Optimal Arousal | 耶克斯-多德森定律与最佳唤醒
The Yerkes-Dodson Law describes the empirical relationship between arousal and performance. Performance increases with arousal up to an optimal point, after which further arousal leads to a decline in performance. Graphically, this produces an inverted-U curve.
耶克斯-多德森定律描述了唤醒与绩效之间的实证关系。绩效随唤醒水平提高而上升，达到一个最佳点后，再增强唤醒将导致绩效下降。这一关系在图形上表现为一条倒U型曲线。
The optimal arousal level depends on task complexity: lower arousal is ideal for difficult or novel tasks, while higher arousal can enhance simple or well-learned tasks. This principle helps explain stress, sports performance, and eyewitness memory.
最佳唤醒水平取决于任务的复杂程度：困难或新异任务需要较低唤醒，而简单或熟练任务在较高唤醒下表现更佳。这一原理有助于解释压力、运动表现和目击者记忆等现象。
12. Classic Memory and Learning Laws | 经典记忆与学习定律
Ebbinghaus’s Forgetting Curve shows that retention declines rapidly soon after learning and then levels off. The decline can be modelled mathematically as:
艾宾浩斯遗忘曲线表明，记忆保持率在学习后很快急剧下降，随后趋于平缓。这种下降可用数学形式描述为：
R = e^(−t / S)
where R is the proportion retained, t is time since learning, and S is the memory stability constant. Regular spaced practice shifts the curve upward.
其中 R 为保持比例，t 为学习后经过的时间，S 为记忆稳定性常数。有规律的间隔练习会使曲线整体上移。
Thorndike’s Law of Effect states that responses followed by satisfying consequences are stamped in, while those followed by discomfort are stamped out. This principle provides the foundation for operant conditioning.
桑代克的效果律指出，伴随满意结果的反应会被打上烙印，而伴随不适结果的反应会被消除。这一原理为操作性条件作用奠定了基础。
Published by TutorHao | Psychology Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导