📚 A-Level CAIE Psychology: Formula and Key Concepts Quick Reference Handbook | A-Level CAIE 心理学：公式定理速查手册
This quick-reference handbook condenses the statistical formulae, experimental designs, ethical principles and key theoretical ideas required for the CAIE A-Level Psychology 9990 syllabus. Use it alongside past papers and the official learner guide to check your calculations and justify your choices in exam responses.
本速查手册浓缩了 CAIE A-Level 心理学 9990 大纲所要求的统计公式、实验设计、伦理原则和核心理论概念。请结合历年真题和官方学习者指南使用，以便在考试中核对计算并论证你的选择。
1. Descriptive Statistics: Central Tendency and Dispersion | 描述统计：集中趋势与离散程度
The mean is the arithmetic average of a set of scores. It is calculated by adding all values and dividing by the number of values, and it is used with interval or ratio data when the distribution is approximately symmetrical.
平均数是一组分数的算术平均值。计算方法是把所有数值相加再除以数值的个数，适用于分布大致对称的等距或比率数据。
x̄ = Σx ÷ n
The median is the middle score when data are arranged in order. It is less affected by extreme scores, so it is preferred when the distribution is skewed or when there are outliers.
中位数是将数据按顺序排列后位于中间的分数。它受极端分数的影响较小，因此在分布偏斜或存在异常值时更适用。
The mode is the most frequently occurring score. It can be used with nominal data, but a data set may have more than one mode or no mode at all.
众数是出现频率最高的分数。它可用于称名数据，但一组数据可能有多个众数，也可能没有众数。
Range measures the spread of data by subtracting the smallest score from the largest score. It is quick to calculate but ignores the distribution between the extremes.
全距通过用最大值减去最小值来衡量数据的离散程度。它计算简单，但忽略了极值之间的分布情况。
Sample standard deviation describes how much scores typically deviate from the mean. In psychology research, the sample formula uses n – 1 as the denominator to estimate the population standard deviation.
样本标准差描述分数通常偏离平均数的程度。在心理学研究中，样本公式用 n – 1 作分母来估计总体标准差。
s = √(Σ(x – x̄)² ÷ (n – 1))
Variance is the square of the standard deviation. It is seldom reported on its own because it is expressed in squared units, but it is an important step in many inferential tests.
方差是标准差的平方。由于它用平方单位表示，所以很少单独报告，但它是许多推断统计检验中的重要步骤。
s² = Σ(x – x̄)² ÷ (n – 1)
2. Choosing an Inferential Test | 推断统计检验的选择
Inferential tests allow researchers to decide whether results are likely to reflect a real effect or chance variation. The choice of test depends on the research design, the level of measurement and the type of question.
推断统计检验可以帮助研究者判断结果是否更可能反映真实效应或随机变异。检验的选择取决于研究设计、测量水平和问题类型。
For a test of difference using nominal data with an independent groups design, the Chi-square test is suitable. For repeated measures data with nominal categories, the Binomial sign test is used.
对于使用称名数据的独立组别差异检验，适合使用卡方检验。对于重复测量设计的称名类别数据，使用二项符号检验。
For ordinal data in an independent groups design, use the Mann-Whitney U test. For ordinal data in a repeated measures or matched pairs design, use the Wilcoxon signed-rank test.
对于独立组别设计中的顺序数据，使用曼-惠特尼 U 检验。对于重复测量或配对设计中的顺序数据，使用威尔科克森符号秩检验。
For a test of correlation or association between two ordinal variables, use Spearman’s rank correlation coefficient. This is not a test of difference but a measure of relationship strength.
对于两个顺序变量之间的相关或关联检验，使用斯皮尔曼等级相关系数。这不是差异检验，而是关系强度的测量。
| Question type | Design | Data level | Test |
|---|---|---|---|
| Difference | Independent groups | Nominal | Chi-square |
| Difference | Independent groups | Ordinal | Mann-Whitney U |
| Difference | Repeated measures | Ordinal | Wilcoxon signed-rank |
| Difference | Repeated measures | Nominal | Binomial sign test |
| Relationship | Pairs | Ordinal | Spearman’s rho |
You must always justify the choice of test in an exam answer by referring to design, level of data and whether the researcher is testing a difference or a relationship.
考试作答时，你必须通过提及设计、数据水平以及研究者是在检验差异还是关系，来论证所选检验的合理性。
3. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s rho measures the strength and direction of association between two sets of ranked data. It produces a coefficient between -1 and +1.
斯皮尔曼等级相关系数衡量两组等级数据之间关联的强度和方向。它产生一个介于 -1 到 +1 之间的系数。
rₛ = 1 – (6Σd²) ÷ (n(n² – 1))
In the formula, d is the difference between the ranks of each pair, and n is the number of paired scores. First rank each variable separately, then find d for every pair and square it.
公式中，d 是每对数据的等级差，n 是配对分数的数量。首先对每个变量分别排序，然后求出每一对的 d 并平方。
A positive coefficient near +1 indicates a strong positive correlation, while a negative coefficient near -1 indicates a strong negative correlation. A value near zero suggests little or no monotonic relationship.
接近 +1 的正系数表明存在强正相关，接近 -1 的负系数表示存在强负相关。接近零的值则表明几乎没有单调关系。
To test significance, compare the calculated rₛ with a critical value from statistical tables using the chosen significance level, usually p ≤ 0.05, and the number of participants.
检验显著性时，将计算出的 rₛ 与统计表中根据所选显著性水平（通常为 p ≤ 0.05）和参与者人数查得的临界值进行比较。
4. Chi-Square Test | 卡方检验
The Chi-square test is used for nominal data in an independent groups design. It compares observed frequencies with expected frequencies to test whether the difference is larger than chance would predict.
卡方检验用于独立组别设计中的称名数据。它比较观察频数与期望频数，以检验差异是否大于随机预期。
Expected frequencies are calculated for each cell using the formula E = (row total × column total) ÷ grand total. The larger the difference between O and E, the larger the value of χ².
每个单元格的期望频数使用公式 E = (行合计 × 列合计) ÷ 总合计 来计算。O 与 E 的差异越大，χ² 值就越大。
χ² = Σ((O – E)² ÷ E)
Degrees of freedom are calculated as df = (number of rows – 1) × (number of columns – 1). For a 2 × 2 contingency table, df = 1.
自由度计算为 df = (行数 – 1) × (列数 – 1)。对于 2 × 2 列联表，df = 1。
The obtained χ² is compared with a critical value. If the obtained value is equal to or larger than the critical value at p ≤ 0.05, the result is statistically significant.
将得到的 χ² 与临界值比较。如果在 p ≤ 0.05 水平上所得值等于或大于临界值，则结果具有统计显著性。
5. Mann-Whitney U Test | 曼-惠特尼 U 检验
The Mann-Whitney U test is used to test for a difference between two independent groups when the data are at least ordinal. It works by ranking all scores from both groups together.
曼-惠特尼 U 检验用于检验两个独立组别之间的差异，数据至少为顺序水平。它通过将两组所有分数合并排序来进行。
U₁ = n₁n₂ + n₁(n₁+1) ÷ 2 – R₁
U₂ = n₁n₂ + n₂(n₂+1) ÷ 2 – R₂
In these formulas, n₁ and n₂ are the group sizes, and R₁ and R₂ are the sums of ranks for each group. The smaller of U₁ and U₂ is taken as the obtained U value.
公式中，n₁ 和 n₂ 是两组人数，R₁ 和 R₂ 是各组的秩和。取 U₁ 和 U₂ 中较小的一个作为所得 U 值。
Compare U with the critical value. Unlike many tests, a result is significant when U is equal to or smaller than the critical value at the chosen probability level.
将 U 与临界值比较。与许多检验不同，当 U 等于或小于所选概率水平下的临界值时，结果显著。
6. Wilcoxon Signed-Rank Test | 威尔科克森符号秩检验
The Wilcoxon signed-rank test is suitable for a repeated measures or matched pairs design with ordinal data. It uses the direction and magnitude of differences between paired scores.
威尔科克森符号秩检验适用于顺序数据的重复测量或配对设计。它利用配对分数之间差异的方向和大小。
First calculate the difference between each pair, then remove zero differences. Rank the absolute differences, attach the original signs, and sum the positive and negative ranks separately.
首先计算每对数据的差值，去掉零差值。对绝对差值排序，附上原始符号，然后分别计算正秩和与负秩和。
The test statistic T is the smaller of the two rank sums. A small T indicates a consistent difference between conditions.
检验统计量 T 是两组秩和中的较小者。较小的 T 值表示条件之间存在一致的差异。
T = min(ΣR⁺, ΣR⁻)
The obtained T must be equal to or smaller than the critical value for significance, using the reduced number of pairs after removing zero differences.
在去掉零差值后使用减少的配对数，所得 T 值必须等于或小于临界值才具有显著性。
7. Binomial Sign Test | 二项符号检验
The Binomial sign test is used for repeated measures designs when data are nominal categories, often recorded as two possible outcomes such as improved or not improved.
二项符号检验用于重复测量设计中数据为称名类别的情况，通常记录为两种可能结果，如改善或未改善。
It considers only the direction of change for each participant, ignoring the size of the change. Count the number of positive changes and the number of negative changes, and exclude ties.
该检验只考虑每个参与者变化的方向，忽略变化的大小。统计正变化数量和负变化数量，并排除不变的情况。
S = min(n⁺, n⁻)
The obtained S is compared with a critical value from a binomial distribution table. Significance is shown when S is equal to or smaller than the critical value at the chosen p level.
将所得 S 与二项分布表中的临界值比较。当 S 等于或小于所选 p 水平下的临界值时，结果显著。
8. Experimental Design and Variables | 实验设计与变量
The independent variable (IV) is the factor manipulated by the researcher. The dependent variable (DV) is the factor measured to see any effect of the IV.
自变量 (IV) 是研究者操纵的因素。因变量 (DV) 是为了观察自变量是否产生影响而测量的因素。
Operationalisation means defining variables clearly so that they can be measured or manipulated. For example, aggression might be operationalised as the number of times a child hits a doll.
操作性定义是指清晰地界定变量，使其能够被测量或操纵。例如，攻击性可以操作化为儿童击打玩偶的次数。
Independent groups design assigns different participants to each level of the IV. Repeated measures design uses the same participants in all conditions. Matched pairs design pairs participants on key traits before assigning them to different conditions.
独立组别设计将不同参与者分配到自变量的各个水平。重复测量设计让同一批参与者经历所有条件。配对设计在关键特质上匹配参与者，然后将其分配到不同条件。
Each design has strengths and weaknesses. Repeated measures controls for individual differences but may suffer from order effects, while independent groups avoids order effects but needs more participants.
每种设计都有优缺点。重复测量可以控制个体差异，但可能存在顺序效应；独立组别可以避免顺序效应，但需要更多参与者。
9. Validity, Reliability and Ethics | 效度、信度与伦理
Validity refers to whether a study measures what it claims to measure. Internal validity is the degree to which the observed effect is due to the IV rather than confounding variables.
效度指研究是否测量了它声称要测量的内容。内部效度是指观察到的效应在多大程度上由自变量而非混淆变量引起。
External validity is the extent to which findings can be generalised to other people, settings and times. Ecological validity is a type of external validity concerned with real-life settings.
外部效度指研究结果在多大程度上可以推广到其他人群、环境和时间。生态效度是外部效度的一种，关注现实生活情境。
Reliability means consistency. A study is reliable if it can be replicated using the same procedures and produce similar results.
信度意味着一致性。如果一项研究采用相同程序重复进行时能得出相似结果，那么它就是可靠的。
Ethical guidelines in psychology include informed consent, right to withdraw, confidentiality, protection from harm, deception avoidance and debriefing. These are especially important when studying sensitive behaviour.
心理学伦理准则包括知情同意、随时退出权、保密、免受伤害、避免欺骗以及事后解释。在研究敏感行为时这些准则尤为重要。
10. Key Approaches and Core Studies Speed Review | 心理学主要流派与核心研究速览
The biological approach explains behaviour through brain structure, hormones and genetics. Core studies include Canli et al. on amygdala activation and emotional memory, Dement and Kleitman on sleep and dreaming, and Schachter and Singer on emotion and adrenaline.
生物学流派通过大脑结构、激素和遗传解释行为。核心研究包括 Canli 等人关于杏仁核激活与情绪记忆、Dement 和 Kleitman 关于睡眠与梦，以及 Schachter 和 Singer 关于情绪与肾上腺素。
The cognitive approach focuses on mental processes such as attention, memory and
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