📚 Year 13 AQA Statistics: Quick Vocabulary Memorisation Guide | Year 13 AQA 统计：词汇术语速记指南
Mastering the precise terminology in Year 13 AQA Statistics is half the battle. This guide pairs every key term with a memory hook and a parallel explanation in Mandarin, making revision faster and deeper. Once you own the language, the techniques follow naturally.
掌握 Year 13 AQA 统计中的精确术语是成功的一半。本指南为每个核心术语配上记忆抓点与中文解释，让复习既快又深。一旦你驾驭了这些语言，统计技巧自然水到渠成。
1. Core Concepts: Statistics, Variables & Data Types | 核心概念：统计、变量与数据类型
The discipline of statistics splits into descriptive methods (summarising data) and inferential methods (drawing conclusions beyond the data). A single numerical fact from a sample is also called ‘a statistic’. Think ‘s’ for sample.
统计学分为描述性方法（汇总数据）和推断性方法（从数据中得出结论）。来自样本的单个数值事实也被称为 “statistic”。用 “s” 关联样本，轻松记忆。
A variable varies. Categorical variables describe qualities (e.g. eye colour), while numerical variables describe quantities. Numerical variables split into discrete (countable, like number of students) and continuous (measurable, like height). Remember: ‘discrete’ = distinct countable steps; ‘continuous’ = continuum.
变量就是变化的量。分类变量描述品质（如眼睛颜色），数值变量描述数量。数值变量又分为离散型（可数，如学生人数）和连续型（可测，如身高）。记法：discrete 有清晰可数的台阶，continuous 是一条连续的线。
2. Populations, Samples & Parameters | 总体、样本与参数
The population is the complete collection of individuals we want to know about. A sample is a subset drawn from it. A census measures the whole population, but is often impractical.
总体是我们想要了解的全体个体的总集。样本是从中抽出的子集。普查测量整个总体，但往往难以实现。
A parameter is a numerical summary of a population (e.g. population mean μ, population standard deviation σ). A statistic is a numerical summary calculated from a sample (e.g. sample mean x̄, sample standard deviation s). The ‘p’ in parameter pairs with population; ‘s’ in statistic pairs with sample.
参数是描述总体的数值指标（如总体均值 μ、总体标准差 σ）。统计量是从样本计算出的数值指标（如样本均值 x̄、样本标准差 s）。parameter 中的 “p” 对 population，statistic 中的 “s” 对 sample。
| Population (总体) | Sample (样本) |
|---|---|
| Parameter (参数) μ, σ² | Statistic (统计量) x̄, s² |
| Fixed but usually unknown | Varies from sample to sample |
3. Sampling & Sampling Distributions | 抽样与抽样分布
Common sampling methods: simple random sample (everyone equally likely), stratified (split into groups and sample proportionally), cluster (sample whole groups), systematic (every k-th item). Bias arises when some parts of the population are systematically over- or under-represented.
常见抽样方法：简单随机抽样（每人等可能）、分层抽样（按组比例抽）、整群抽样（整群抽取）、系统抽样（每隔 k 个抽一个）。当总体的某些部分被系统性高估或低估时，就会产生偏差。
The sampling distribution of a statistic is the distribution of that statistic over all possible samples of the same size from the same population. Its spread is measured by the standard error. Knowing the sampling distribution unlocks inference.
抽样分布是一个统计量在所有同规模样本上的分布。它的离散程度由标准误衡量。掌握了抽样分布，就打开了推断的大门。
4. Central Limit Theorem | 中心极限定理
The Central Limit Theorem (CLT) states: for a random sample of size n from any population with mean μ and variance σ², the sampling distribution of the sample mean x̄ becomes approximately normal as n grows, with mean μ and variance σ²/n. The magic number is usually n ≥ 30.
中心极限定理(CLT)指出：无论总体分布如何，只要样本量 n 足够大（通常 n ≥ 30），样本均值 x̄ 的抽样分布就近似正态，均值为 μ，方差为 σ²/n。
x̄ ~ N(μ, σ²/n) approximately
This result justifies using normal-based confidence intervals and hypothesis tests for means even when the raw data are not normal. The standard error of the mean is σ/√n, which shrinks as n increases.
这个定理让我们即便原始数据不正态，也能用基于正态的方法去构建置信区间和做均值假设检验。均值的标准误为 σ/√n，样本越大，标准误越小。
5. Point Estimates & Confidence Intervals | 点估计与置信区间
A point estimate is a single value used to guess a parameter. We want it to be unbiased (centred on the truth) and consistent (gets closer with more data). A confidence interval (CI) gives a range of plausible values. The confidence level (e.g. 95%) describes how often the method captures the parameter in repeated sampling.
点估计是猜测参数的单一值。我们希望它无偏（以真值为中心）且一致（数据越多越精准）。置信区间(CI)则给出一段可信的范围。置信水平（如 95%）描述在重复抽样中，该方法捕获参数的频率。
A 95% CI for μ (when σ is known): x̄ ± z* × σ/√n. When σ is unknown, use the t-distribution: x̄ ± t* × s/√n, with degrees of freedom n − 1. Note: ‘s’ represents the sample standard deviation.
当 σ 已知，μ 的 95% 置信区间为 x̄ ± z* × σ/√n。σ 未知时，用 t 分布：x̄ ± t* × s/√n，自由度为 n − 1。这里 “s” 是样本标准差。
Confidence interval = point estimate ± margin of error
6. Hypothesis Testing Fundamentals | 假设检验基础
A hypothesis test assesses evidence against a null hypothesis H₀. The alternative hypothesis H₁ is what we suspect might be true. A test statistic measures how far the observed data fall from what H₀ predicts. A critical region (or rejection region) is the set of values of the test statistic that lead to rejecting H₀.
假设检验评估反对原假设 H₀ 的证据。备择假设 H₁ 是我们怀疑可能正确的说法。检验统计量衡量观测数据偏离 H₀ 预期的程度。临界域（拒绝域）是检验统计量取值的集合，落入其中则拒绝 H₀。
Structure: State H₀ and H₁, choose significance level α, calculate test statistic, compare with critical value or use p-value, then conclude in context. One-tailed tests look for an effect in one direction; two-tailed tests look for any difference.
步骤：写出 H₀ 和 H₁，确定显著性水平 α，计算检验统计量，与临界值比较或使用 p 值，最后在上下文中结论。单尾检验关注单一方向的效果；双尾检验检测任何差异。
7. P-Values, Significance Levels & Critical Regions | P值、显著性水平与临界域
The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming H₀ is true. A small p-value indicates strong evidence against H₀. The significance level α is the threshold we set in advance (commonly 0.05). Reject H₀ if p-value < α.
p值是在 H₀ 为真的前提下，得到至少与观测值同样极端的检验统计量的概率。p 值越小，反对 H₀ 的证据越强。显著性水平 α 是事先设定的门槛（通常 0.05）。若 p < α，则拒绝 H₀。
The critical value marks the boundary of the critical region. If the test statistic falls in the critical region, the result is statistically significant. Memorise: ‘If p is low, H₀ must go.’
临界值是临界域的边界。若检验统计量落入临界域，结果就具有统计显著性。记住口诀：”p 小则拒 H₀”。
8. Type I & II Errors, Power | 第I类与第II类错误及检验功效
A Type I error occurs when we reject a true H₀ (a false positive). Its probability is α, the significance level. A Type II error occurs when we fail to reject a false H₀ (a false negative), with probability β. Power = 1 − β is the probability of correctly rejecting a false H₀.
第I类错误是 H₀ 为真却被拒绝（假阳性），概率为 α。第II类错误是 H₀ 为假却没有拒绝（假阴性），概率为 β。检验功效 = 1 − β，即正确拒绝假 H₀ 的概率。
Trade-off: reducing α makes it harder to reject H₀, which increases β unless sample size is increased. Use a mnemonic: ‘Type I cries wolf (false alarm), Type II misses the wolf (false reassurance).’
取舍：降低 α 会让拒绝 H₀ 更难，从而可能增大 β，除非增大样本量。记忆法：”第一类误报警，第二类漏敌情”。功效受样本量、效应大小和 α 影响。
| H₀ True (H₀ 真) | H₀ False (H₀ 假) | |
|---|---|---|
| Reject H₀ (拒绝) | Type I error (α) | Correct (Power 1−β) |
| Do not reject (不拒绝) | Correct | Type II error (β) |
9. Correlation & Regression Terminology | 相关与回归术语
Correlation measures the strength and direction of a linear relationship. The product-moment correlation coefficient (PMCC), r, ranges from −1 to +1. Spearman’s rank correlation uses ranked data and is robust to outliers. Correlation does not imply causation.
相关衡量线性关系的强度与方向。积矩相关系数 (PMCC) r 取值在 −1 到 +1 之间。斯皮尔曼秩相关使用秩次数据，对异常值稳健。相关不等于因果。
In linear regression, we model the response variable y using an explanatory variable x: y = a + bx. The residual is the difference between observed y and predicted y. Interpolation (within data range) is reliable; extrapolation (outside data range) is risky.
在线性回归中，我们用解释变量 x 对响应变量 y 建模：y = a + bx。残差是观测值 y 与预测值之差。内插（数据范围内）可靠；外推（数据范围外）有风险。
residual = observed y − predicted y
10. Chi-Squared Tests for Independence & Goodness of Fit | 卡方检验：独立性与拟合优度
The χ² goodness-of-fit test checks whether a single categorical variable follows a claimed distribution. The χ² test for independence examines whether two categorical variables are associated in a contingency table. Both compare observed (O) and expected (E) frequencies.
χ² 拟合优度检验检验单个分类变量是否符合声称的分布。χ² 独立性检验检查列联表中两个分类变量是否有关联。两者都对比观测频数 (O) 与期望频数 (E)。
Test statistic: χ² = Σ (O − E)² / E. Expected frequencies are calculated under H₀. Degrees of freedom: for goodness-of-fit, df = number of categories − 1 − (number of estimated parameters); for independence in an r×c table, df = (r−1)(c−1). The test is approximate, requiring expected counts ≥ 5.
检验统计量：χ² = Σ (O − E)² / E。期望频数在 H₀ 下计算得出。自由度：拟合优度为类别数 − 1 − 估计参数个数；r×c 独立性检验自由度为 (r−1)(c−1)。该检验为近似法，要求所有期望频数 ≥ 5。
11. Common Distributions & Notation Quick Reference | 常见分布与符号速查
Binomial distribution: X ~ B(n, p). Conditions: fixed n independent trials, two outcomes, constant p. Mean = np, variance = np(1−p). Used for count of successes.
二项分布：X ~ B(n, p)。条件：固定 n 次独立试验、两种结果、p 不变。均值 = np，方差 = np(1−p)。用于成功次数。
Poisson distribution: X ~ Po(λ). Conditions: events occur singly and independently at a constant average rate λ. Mean = λ, variance = λ. Often models rare events.
泊松分布：X ~ Po(λ)。条件：事件独立
Published by TutorHao | Year 13 统计 Revision Series | aleveler.com
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