📚 Year 11 OCR Psychology: Formula & Theorem Quick Reference Guide | Year 11 OCR 心理学公式定理速查手册
Welcome to your go-to quick reference for the essential formulas and key psychological theorems tested in Year 11 OCR Psychology. Whether you are calculating Spearman’s rho or recalling the Yerkes-Dodson Law, this guide will help you revise the core mathematical and conceptual tools needed for your exams. The content focuses on the research methods and statistical techniques required by the OCR GCSE Psychology specification, along with classic psychological principles that explain human behaviour.
欢迎使用这本专为 Year 11 OCR 心理学准备的公式定理速查手册。无论你是在计算斯皮尔曼秩相关系数，还是回忆耶克斯–多德森定律，这份指南都能帮助你复习考试所需的核心数学和概念工具。内容紧扣 OCR GCSE 心理学大纲中的研究方法和统计技术，同时也涵盖了阐释人类行为的经典心理学原理。
1. Measures of Central Tendency & Range | 集中趋势与范围公式
The mean is the arithmetic average of a data set. It is calculated by summing all the values and dividing by the number of values.
平均数是一组数据的算术平均值。计算方法是将所有数值相加，再除以数值的个数。
Mean = Σx / n
The median is the middle value when all scores are arranged in order. If there is an even number of scores, take the mean of the two middle numbers.
中位数是将所有数据从小到大排序后位于中间位置的数值。如果数据个数为偶数，则取中间两个数的平均数。
The mode is the most frequently occurring value in a data set. A set can have more than one mode or no mode at all.
众数是一组数据中出现次数最多的数值。一组数据可以有多个众数，也可以没有众数。
The range is a measure of dispersion, showing the spread of scores. It is found by subtracting the smallest value from the largest value.
范围是衡量数据离散程度的指标，表示数据值的分布幅度。计算公式为最大值减去最小值。
Range = Maximum value − Minimum value
2. Percentages and Proportions | 百分比与比例
In research methods, you often need to express results as a percentage or a proportion. A proportion compares a part to the whole, while a percentage expresses this proportion out of 100.
在研究方法中，我们经常需要将结果表示为百分比或比例。比例是比较部分与整体的关系，而百分比则将这一比例以一百为基准进行表达。
To calculate a percentage, divide the part by the total and multiply by 100.
计算百分比时，用部分数值除以总数，再乘以 100。
Percentage = (Part / Whole) × 100
A proportion is simply the part divided by the whole, without multiplying by 100. Both measures help summarise categorical or frequency data in a meaningful way.
比例则是部分除以整体，不乘以 100。这两种方法都能有效地概括分类数据或频数数据。
3. Spearman’s Rank Correlation Coefficient | 斯皮尔曼秩相关系数
Spearman’s rho (ρ or rₛ) measures the strength and direction of a relationship between two sets of ordinal (ranked) data. It is used when data are not normally distributed or when the relationship is monotonic.
斯皮尔曼秩相关系数 (ρ 或 rₛ) 用于衡量两组顺序（等级）数据之间关系的强度和方向。当数据不服从正态分布或为单调关系时，可采用此系数。
The formula compares the differences (D) between the ranks of each pair of values. D is the difference between rank 1 and rank 2 for the same participant or item.
公式比较了每一对数值的秩次差异 (D)。D 是同一被试或项目在变量1和变量2上的秩次之差。
rₛ = 1 − (6∑D²) / (n(n² − 1))
Steps for calculation: rank the data for each variable separately, giving the highest score rank 1. Find D for each pair, square it, and sum all D² values (∑D²). Substitute n (number of pairs) into the formula. The resulting coefficient can range from −1 (perfect negative correlation) to +1 (perfect positive correlation).
计算步骤：分别对每个变量的数据排序，最高分秩为 1。计算每对数据的 D，平方后求和得到 ∑D²。将配对数量 n 代入公式。所得系数范围从 −1（完全负相关）到 +1（完全正相关）。
Compare the observed rₛ with the critical value from the Spearman rho table at a chosen significance level (usually 0.05). If rₛ is equal to or greater than the critical value, the correlation is statistically significant, and the null hypothesis can be rejected.
将计算出的 rₛ 与所选显著性水平（通常为 0.05）下的斯皮尔曼临界值表进行比较。若 rₛ 大于或等于临界值，则相关性达到统计学显著，可以拒绝零假设。
4. Wilcoxon Signed Ranks Test | 威尔科克森符号秩检验
The Wilcoxon signed ranks test is a non-parametric test used with repeated measures or matched pairs designs when the data are at least ordinal. It determines whether there is a significant difference between two conditions.
威尔科克森符号秩检验是一种非参数检验，用于重复测量或配对组设计，且数据至少为顺序水平。它可检验两种条件之间是否存在显著差异。
Calculate the difference between each pair of scores. Ignore any pairs with a difference of zero and adjust n accordingly. Rank the absolute differences, assigning rank 1 to the smallest difference. Then attach the original sign (positive or negative) to each rank.
计算每对分数的差值。忽略差值为零的对，并相应调整 n。对差值的绝对值进行排序，将最小差值编秩为 1。然后在每个秩前赋予原来的符号（正或负）。
The test statistic W is the smaller of the two sums: the sum of positive ranks (R⁺) and the sum of negative ranks (R⁻).
检验统计量 W 是两组秩和中较小的一个：正秩和 (R⁺) 与负秩和 (R⁻)。
W = min(∑R⁺, ∑R⁻)
Compare W with the critical value from the Wilcoxon table. For a significant result at a given p level, the observed W must be less than or equal to the critical value. This would allow you to reject the null hypothesis.
将 W 与威尔科克森临界值表进行比较。若要在给定 p 水平上达到显著，观测到的 W 必须小于或等于临界值，这样才能拒绝零假设。
5. Mann-Whitney U Test | 曼-惠特尼 U 检验
The Mann-Whitney U test is designed for independent groups designs. It tests whether two independent samples come from the same population by comparing the ranks of the combined data.
曼-惠特尼 U 检验适用于独立组设计。它通过比较合并数据的秩次来检验两个独立样本是否来自相同总体。
Rank all the scores from both groups together, giving rank 1 to the smallest score. Then calculate the sum of ranks for group 1 (R₁) and group 2 (R₂). Let n₁ and n₂ be the sample sizes of the two groups.
将两组的所有数据混合排序，最小值给秩 1。然后计算组1的秩和 (R₁) 和组2的秩和 (R₂)。设 n₁ 和 n₂ 分别为两组的样本量。
U₁ = n₁n₂ + n₁(n₁ + 1)/2 − R₁
U₂ = n₁n₂ − U₁
U = min(U₁, U₂)
The smaller U value is compared against the critical value in the Mann-Whitney table. If the observed U is equal to or less than the critical value, the difference between groups is considered statistically significant.
较小的 U 值与曼-惠特尼临界值表比较。若观测 U 小于或等于临界值，则认为组间差异具有统计学意义。
6. Chi-Square Test (χ²) | 卡方检验
The chi-square test is used with nominal (categorical) data. It can assess goodness of fit (whether observed frequencies differ from expected ones) or test for independence (whether two categorical variables are associated).
卡方检验用于名义（分类）数据。它可以评估拟合优度（观测频数与期望频数是否一致），或检验独立性（两个类别变量是否有关联）。
The core formula compares the observed frequency (O) and the expected frequency (E) in each category.
核心公式将每个类别的观测频数 (O) 与期望频数 (E) 进行比较。
χ² = ∑ ( (O − E)² / E )
For goodness of fit, expected frequencies are based on theoretical distribution, and degrees of freedom (df) equal the number of categories minus 1. For a test of independence with a contingency table, df = (number of rows − 1) × (number of columns − 1).
对于拟合优度检验，期望频数基于理论分布，自由度等于类别数减1。对于列联表的独立性检验，自由度 = (行数 − 1) × (列数 − 1)。
Compare the calculated χ² value with the critical value from the chi-square distribution table at the chosen significance level. If the calculated χ² is larger than the critical value, the result is significant, and the null hypothesis is rejected.
将计算出的 χ² 值与给定显著性水平下的卡方分布临界值进行比较。若计算值大于临界值，则结果显著，拒绝零假设。
7. Sign Test | 符号检验
The sign test is the simplest non-parametric test, used for repeated measures designs with nominal data. It examines whether the direction of change (positive or negative) from one condition to another is systematic.
符号检验是最简单的一种非参数检验，用于重复测量设计中的名义数据。它考察从一种条件到另一种条件的变化方向（正或负）是否具有系统性。
For each participant, record whether their score in condition B is higher (+) or lower (−) than in condition A. Exclude any ties (no change). Count the number of plus signs and minus signs. The test statistic S is the smaller of these two counts.
对每一名被试，记录其在条件 B 的分数比条件 A 高 (+) 或低 (−)。排除无变化的对。计算正号数和负号数。检验统计量 S 取两者中较小的数值。
S = the smaller count of ‘+’ or ‘−’
Compare S with the critical value from the sign test table, using the number of non-zero differences as N. If S is less than or equal to the critical value, the difference between conditions is statistically significant.
将 S 与符号检验临界值表进行比较，以非零差异的个数作为 N。若 S 小于或等于临界值，则条件间的差异具有统计学显著性。
8. Selecting the Right Statistical Test | 选择正确的统计检验
A crucial skill in OCR
Published by TutorHao | Year 11 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