Selecting Any Inference Procedure · 选择任意推断程序
The whole toolbox
- By now you've met four families of inference — this lesson picks among all of them.
- Proportions ($z$), means ($t$), chi-square (categorical counts), and slopes ($t$).
- The right choice comes from the type of data and the structure of the question.
- Master this and you can attack any inference problem on the exam.
整个工具箱
- 到现在你已见过四大类推断——这节课在所有这些之间选择。
- 比例（$z$）、均值（$t$）、卡方（分类计数）和斜率（$t$）。
- 正确的选择来自数据类型和问题的结构。
- 掌握了它，你就能攻克考试中任何推断问题。
Start with the data type
- Categorical, and you want a proportion / count? → a $z$-procedure (proportions) or chi-square (tables).
- Quantitative average? → a $t$-procedure for means.
- Two quantitative variables, a linear trend? → slope $t$-inference.
- The data type narrows it to a family immediately.
先看数据类型
- 分类，且你要一个比例 / 计数？ → $z$ 程序（比例）或卡方（表格）。
- 数值型的平均？ → 均值的 $t$ 程序。
- 两个数值变量，一个线性趋势？ → 斜率 $t$ 推断。
- 数据类型立即把它缩小到一个族。
Then count samples and variables
- One or two groups? Independent or paired?
- One categorical variable vs. a distribution → goodness-of-fit; two variables / several groups → homogeneity/independence.
- A relationship between two quantitative variables → slope inference.
- These structural questions pin down the exact procedure.
再数样本和变量
- 一个还是两个组？独立还是配对？
- 一个分类变量对照一个分布 → 拟合优度；两个变量 / 几个组 → 齐性/独立性。
- 两个数值变量之间的关系 → 斜率推断。
- 这些结构性问题锁定确切的程序。
Implement and communicate
- Interval or test? — estimate a value, or judge a claim.
- State hypotheses/parameter, check conditions, compute, and conclude in context.
- Name the procedure and justify why the data fit it.
- Clear reasoning earns as much credit as the right number.
实施与沟通
- 区间还是检验？——估计一个值，或判断一个主张。
- 陈述假设/参数，检查条件，计算，并结合语境下结论。
- 点名程序并论证数据为什么适合它。
- 清晰的推理与正确的数字赢得同样多的分。
Two features decide everything: the DATA TYPE and the STRUCTURE. Categorical count → $z$-proportion or chi-square; quantitative average → $t$-mean; two quantitative variables' trend → slope $t$. Then: how many samples/variables, and interval or test. Nearly every lost mark on inference is a wrong choice, not wrong arithmetic — decide deliberately.
两个特征决定一切：数据类型和结构。分类计数 → $z$ 比例或卡方；数值型平均 → $t$ 均值；两个数值变量的趋势 → 斜率 $t$。然后：几个样本/变量，以及区间还是检验。推断上几乎每一处丢分都是选错，而非算错——要审慎地决定。
"Is there a linear relationship between temperature and ice-cream sales?"
- Data: two quantitative variables; the question is about a linear trend.
- → slope $t$-inference (a test of $H_0: \beta = 0$, or an interval for $\beta$).
- (Had it compared mean sales on hot vs. cold days → a two-sample $t$; proportions of days → a $z$ or chi-square.)
“温度与冰淇淋销量之间有线性关系吗？”
- 数据：两个数值变量；问题是关于一个线性趋势。
- → 斜率 $t$ 推断（$H_0: \beta = 0$ 的检验，或 $\beta$ 的区间）。
- （若比较热天对冷天的平均销量 → 两样本 $t$；若是天数的比例 → $z$ 或卡方。）
Choose from all the course's methods by data type (proportion → $z$; mean → $t$; categorical table → chi-square; two quantitative variables' trend → slope $t$) and structure (samples, variables, interval-vs-test). Then implement fully and communicate the reasoning and conclusion clearly, in context.
从所有课程方法中按数据类型（比例 → $z$；均值 → $t$；分类表 → 卡方；两个数值变量的趋势 → 斜率 $t$）和结构（样本、变量、区间对检验）来选择。然后完整地实施，并结合语境清晰地沟通推理与结论。
One family among many · 众多族中的一族
Two quantitative variables' trend → slope t-inference. · 两个数值变量的趋势 → 斜率 t 推断。
A question about a linear relationship between two quantitative variables calls for... · 关于两个数值变量之间线性关系的问题需要……
Two quantitative variables + a trend → slope inference. · 两个数值变量 + 一个趋势 → 斜率推断。
Comparing the mean of a measured quantity for two independent groups calls for... · 比较一个测量量在两个独立组的均值需要……
Measured average, two independent groups → two-sample t. · 测量出的平均、两个独立组 → 两样本 t。
Two categorical variables in one sample, testing association, calls for... · 一个样本里两个分类变量、检验关联，需要……
Two categorical variables, one sample → independence. · 两个分类变量、一个样本 → 独立性。
Which questions help you pick the right inference procedure? · 哪些问题帮助你挑选正确的推断程序？
Data type, structure, and goal — not the graph's color. · 数据类型、结构和目标——而非图的颜色。
Most lost marks on inference come from choosing the wrong procedure, not from arithmetic. · 推断上大多数丢分来自选错程序，而非算术。
Decide the procedure deliberately from data type and structure. · 根据数据类型和结构审慎地决定程序。