📚 Year 8 OCR Psychology: Formula and Theorem Quick Reference Handbook | Year 8 OCR 心理学：公式定理速查手册
This handbook brings together the essential formulas, rules and principles you will meet in Year 8 OCR Psychology. Whether you are analysing data, planning an investigation or interpreting graphs, having these tools at your fingertips will strengthen your confidence and accuracy. Use it as a quick reference during revision, homework and classwork.
这本手册汇集了你在 Year 8 OCR 心理学课程中会遇到的核心公式、规则和原理。无论是分析数据、规划调查还是解读图表，随时查阅这些工具都能增强你的信心和准确性。请将本文作为复习、作业和课堂练习中的速查宝典。
1. Mean Formula | 平均数公式
The mean is the arithmetic average of a set of numbers. Add all the values together and divide by the total number of values.
平均数是描述一组数据中心趋势的算术平均值。将所有数值相加，然后除以数值的总个数。
Mean = Σx ÷ n
Where Σx (sigma x) represents the sum of all data points and n is the sample size. Always check your sum and count carefully; a small slip can change the mean significantly.
其中 Σx（西格玛 x）表示所有数据点的总和，n 为样本大小。务必仔细核对总和与数量；一个小的疏忽就可能显著改变平均数。
2. Median Rule | 中位数规则
The median is the middle value when data are arranged in order from smallest to largest. If there are two middle numbers, take their mean.
中位数是将数据从小到大排列后位于中间位置的值。如果中间有两个数，则取它们的平均数。
Steps: 1) Order the data; 2) Count the number of values (n); 3) If n is odd, median = the value at position (n+1)/2; if n is even, median = mean of the values at positions n/2 and (n/2)+1.
步骤：1）排序；2）计算数值个数 n；3）若 n 为奇数，中位数 = 第 (n+1)/2 个位置的值；若 n 为偶数，中位数 = 第 n/2 与第 (n/2)+1 个位置数值的平均数。
3. Mode Identification | 众数识别
The mode is the most frequently occurring value in a data set. A set may have one mode (unimodal), two modes (bimodal) or more.
众数是数据集中出现次数最多的数值。数据集可能有一个众数（单峰）、两个众数（双峰）或更多。
Unlike the mean and median, the mode works with categorical data (e.g. favourite colour). Always state the value, not its frequency, when reporting the mode.
与平均数和中位数不同，众数适用于分类数据（如最喜欢的颜色）。报告众数时，始终给出数值本身而不是它的频数。
4. Range Formula | 极差公式
The range measures the spread of data. It is the difference between the largest and smallest values.
极差衡量数据的离散程度。它是最大值与最小值之间的差值。
Range = Highest value − Lowest value
A small range suggests data are tightly clustered; a large range indicates wide variation. Remember the range is easily affected by outliers.
极差小说明数据紧密聚集；极差大表明变动范围很宽。请记住，极差容易受异常值的影响。
5. Percentage Change | 百分比变化
Percentage change shows how much a quantity has increased or decreased relative to the original amount. It is widely used when comparing before-and-after results in experiments.
百分比变化显示一个量相对于原始量增加或减少了多少。在对比实验前后结果时被广泛使用。
Percentage change = (New value − Original value) ÷ Original value × 100%
If the result is positive, there is an increase; if negative, there is a decrease. Always identify the original value correctly, as using the wrong baseline leads to incorrect conclusions.
若结果为正，表示增加；若为负，表示减少。务必正确识别原始值，因为使用了错误的基准值会导致结论错误。
6. Standard Deviation (Introduction) | 标准差（入门）
Standard deviation (SD) is a measure of how spread out numbers are around the mean. A small SD means the data points are close to the mean; a large SD means they are more spread out.
标准差（SD）衡量数据围绕平均数的分散程度。标准差小意味着数据点紧靠平均数；标准差大意味着数据点更分散。
For a population, SD = √[ Σ(x − μ)² / N ], where μ is the population mean and N is the population size. In Year 8 you may not calculate this formula by hand, but understanding its meaning helps interpret graphs and research findings.
对于总体，SD = √[ Σ(x − μ)² / N ]，其中 μ 是总体平均值，N 是总体大小。在 Year 8 你可能不需要亲手计算该公式，但理解其含义有助于解读图表和研究结果。
7. Normal Distribution Essentials | 正态分布要点
Many psychological variables (such as IQ scores) follow a normal distribution: a bell‑shaped curve that is symmetric around the mean. In a perfect normal distribution, the mean, median and mode are equal and lie at the centre.
许多心理学变量（如智商分数）遵循正态分布：一条以平均值为对称中心的钟形曲线。在完美的正态分布中，平均数、中位数和众数相等，都位于中心。
About 68% of data fall within 1 standard deviation of the mean, and roughly 95% within 2 standard deviations. This rule helps researchers decide whether a result is unusual or likely due to chance.
约 68% 的数据落在平均值 ±1 个标准差内，约 95% 落在 ±2 个标准差内。这一规律帮助研究者判断某个结果是异常的还是可能由偶然因素造成的。
8. Hypotheses: Null and Alternative | 零假设与备择假设
A hypothesis is a testable prediction. The null hypothesis (H₀) states there is no effect or no difference; the alternative hypothesis (H₁ or Hₐ) states there is an effect or a difference.
假设是一个可检验的预测。零假设（H₀）声明没有效应或没有差异；备择假设（H₁ 或 Hₐ）声明有效应或有差异。
For example: H₀ — ‘There is no difference in memory recall between silence and music conditions.’ H₁ — ‘There is a difference in memory recall between silence and music conditions.’ In OCR Psychology, you will learn to identify and write both types.
例如：H₀——“安静和音乐条件下记忆回忆没有差异。”H₁——“安静和音乐条件下记忆回忆有差异。”在 OCR 心理学中，你将学会识别并写出这两种假设。
9. Independent and Dependent Variables | 自变量与因变量
The independent variable (IV) is the factor manipulated or changed by the researcher. The dependent variable (DV) is the factor measured to see if it is affected by the IV.
自变量（IV）是研究者操纵或改变的因素。因变量（DV）是被测量的因素，用于观察它是否受自变量影响。
In a simple experiment: ‘Does the amount of sleep affect reaction time?’ The IV is the amount of sleep (e.g. 4 hours vs. 8 hours), and the DV is the reaction time measured. Identifying IV and DV correctly is fundamental to experimental design.
在一个简单实验中：“睡眠时长是否影响反应时间？”自变量是睡眠时长（如 4 小时 与 8 小时），因变量是测量到的反应时间。正确识别自变量和因变量是实验设计的基础。
10. Sampling Methods | 抽样方法
Sampling is the process of selecting participants from a population. Common methods include random sampling (everyone has an equal chance), opportunity sampling (using whoever is available), and systematic sampling (selecting every nth person).
抽样是从总体中选取参与者的过程。常见方法包括随机抽样（每个人被选中的概率相等）、机会抽样（使用最方便找到的人）和系统抽样（每隔 n 人选一个）。
No single method is perfect; each has strengths and weaknesses. Random sampling is representative but difficult to achieve, while opportunity sampling is quick but may be biased. Understanding these trade-offs is key in OCR Psychology.
没有哪种方法完美无缺；每种方法都有优点和缺点。随机抽样代表性强但难以实现，机会抽样快捷但可能带有偏差。理解这些权衡是 OCR 心理学的重要一环。
11. Data Types: Qualitative and Quantitative | 数据类型：定性与定量
Quantitative data is numerical (e.g. scores, reaction times). Qualitative data is non‑numerical and descriptive (e.g. interview transcripts, open‑ended questionnaire responses).
定量数据是数值型的（如分数、反应时间）。定性数据是非数值的、描述性的（如访谈记录、开放式问卷的回答）。
Both types are valuable. Quantitative data can be analysed with means and graphs; qualitative data provides rich detail about thoughts and feelings. Often, researchers collect both to gain a fuller picture.
两种类型都有价值。定量数据可用平均数和图表进行分析；定性数据则提供关于想法和感受的丰富细节。研究者常同时收集两者以获得更全面的了解。
12. Correlation Coefficient Basics | 相关系数基础
A correlation coefficient (often symbolised as r) measures the strength and direction of a linear relationship between two variables. The value of r ranges from −1 to +1.
相关系数（通常用符号 r 表示）衡量两个变量之间线性关系的强度和方向。r 的取值范围在 −1 到 +1 之间。
r = +1 indicates a perfect positive correlation; as one variable rises, the other rises proportionally. r = −1 indicates a perfect negative correlation; as one variable rises, the other falls. r = 0 suggests no linear relationship. In Year 8, you may not calculate r, but you will learn to interpret scatter graphs and describe correlations as positive, negative or zero.
r = +1 表示完全正相关；一个变量上升，另一个成比例上升。r = −1 表示完全负相关；一个变量上升，另一个下降。r = 0 表示没有线性关系。在 Year 8，你可能不需要计算 r，但要学会解读散点图并将相关描述为正相关、负相关或无相关。
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