IB地理 IA 田野调查 抽样 统计检验 图表
IB 地理的内部评估（internal assessment，通称 IA）是一份基于田野调查的书面报告，上限 2,500 词，满分 25 分。它和笔试的区别在于数据要自己到现场收，同一个田野问题，两组学生可能得出完全相反的结论，评分看的不是结论站在哪一边，而是问题、方法、数据与分析这条链条有没有扣上。下面按野外工作的真实顺序，把分值分布、田野问题的写法、抽样与测量口径、三个常用统计检验的算式、词数与图表规则逐项拆开，算例都给出具体数字，可以直接照着核。IB 官方 Geography guide（2017 年 2 月发布，2022 年 11 月更新，2017 年 9 月起施教、2019 年 5 月首次评估）是以下全部口径的依据。
Internal assessment is the one component where the data belongs to you, and the rubric is identical for SL and HL, so only the weighting differs at 25 per cent of the final grade for SL and 20 per cent for HL. Criteria A to F carry 25 marks between them, and the guide suggests roughly 300, 300, 500, 850, 200 and 300 words for the six report sections, which adds to about 2,450 against the 2,500 word ceiling. Because written analysis alone is worth 8 marks, examiners reward a report that explains patterns and anomalies rather than one with tidy graphs and no argument.
IA 的 25 分与六项标准的分值分布
两级用的是同一套标准，差别只在权重，SL 占最终成绩 25%，HL 占 20%，田野时间都按 20 小时计。报告 25 分的分布是 A 田野问题与地理情境 3 分、B 调查方法 3 分、C 数据质量与处理 6 分、D 书面分析 8 分、E 结论 2 分、F 评价 3 分。官方给的建议词数是 A 300 词、B 300 词、C 500 词、D 850 词、E 200 词、F 300 词，合计约 2,450 词，剩下 50 词的余量正好卡住上限。D 一项独占 8 分，接近三分之一的分落在分析这一段文字上，图画得再整齐也换不来这个分。IB 官方 Examiner Instructions 2026 提醒阅卷人，教师的评分只要合理就接受，明显偏差时才调整，校内的第一稿反馈因此基本决定了最终分数。很多学生以为标准 A 的三分最好拿，实际上地图缺少比例尺、图例或指北针，一样会掉到 2 分。
Criterion A to F together carry 25 marks, and the weighting is the only thing that separates the two levels; SL takes 25 per cent of the final grade and HL 20 per cent, with 20 hours of fieldwork assumed for both. Written analysis is worth 8 marks on its own, so a well argued analysis of a modest data set beats a beautiful set of graphs with no interpretation attached. Note the split across assessment objectives as well, since criteria A and D cover knowledge and analysis while B and C carry the skills objective and D, E and F carry evaluation.
田野问题与地理情境的落笔口径
标准 A 的三分全部压在聚焦两个字上：田野问题必须写成问句，必须指向一个能步行到达的具体地点，并且能用一手数据回答。"这座城市是否可持续发展"范围太大，两小时田野收不回任何可分析的数据；"某河段从上游桥到下游堰的流速与河床粒径是否随距离变化"才落在可测量的范围里。地理情境部分要交代为什么选这里、它有什么位置特征，并写明这个问题对应考纲的哪个主题或哪条地理理论，理论挂钩之后才谈得上提出假设。位置图是这一项失分最集中的地方，一张从网上直接截下来的地图通常只值 2 分，比例尺、图例、指北针与边框不全，实际调查点也没标出来。带标注的照片和手绘图都算加分材料，前提是每张图有编号和标题。常见的错误是把地图塞进附录，附录里的插图不计分，判分只认正文中出现的图。
Criterion A is usually lost on the map rather than the wording; a screenshot lifted from an online source carries no scale, key, north arrow or border and does not mark the survey points, so it scores 2 at best. A question such as whether a city is sustainable cannot be answered with two hours of primary data, whereas the downstream change in velocity and bedload size between two fixed structures gives variables you can actually measure. State the syllabus topic or geographical theory the question links to, because that link is what makes a hypothesis possible.
随机 系统 分层抽样与样本量的取舍
抽样方法决定了数据能代表谁。随机抽样用随机数表配编号网格，好处是把个人偏好彻底排除；系统抽样按固定间隔取点，比如每 20 米一个测点，重复起来最快；分层抽样按子区域或类别的比例分配样本量，适合街区之间差异明显的城市题目。机会抽样最省时间，偏差也最大，用了它就必须在 F 项承认局限。样本量的经验下限是每个测点至少 30 个读数，秩相关这一类检验在样本少于 5 对时多数表格已经没有临界值可查。样方面积容易被忽略：0.5 米见方的样方只有 0.25 平方米，30 个合计 7.5 平方米，在 100 平方米的样地里只覆盖 7.5%，要凑到 10% 得布 40 个样方。学生最常把测点选在桥边或停车场，因为下车就到，这属于系统性偏差而不是随机抽样，评阅时会被直接点出来。
Random, systematic, stratified and opportunistic sampling each buy something different; random sampling through a numbered grid removes personal choice, systematic sampling at a fixed interval is quick to repeat, and stratified sampling keeps sub-areas in proportion to their size. Opportunistic sampling is the fastest and the most biased option, so a report that relies on it has to admit the limitation under criterion F. Thirty readings per site is the working floor in most fieldwork handbooks, and forty quadrats of 0.5 m by 0.5 m are needed to cover ten per cent of a hundred square metre plot.
流速 流量与河床粒径的野外测法
流速通常在 10 米测段上用浮标测三次取平均，读数记的是水面流速，比垂线平均流速偏大，教材惯例乘 0.8 到 0.9 的系数换算，水面 0.42 m/s 换算后约 0.36 m/s。流量由横断面推出来：按等距垂线测深，比如每 0.5 米一根，平均水深乘宽度得断面面积，8.0 米宽、平均水深 0.45 米对应 3.6 平方米，再乘平均流速 0.35 m/s，流量约 1.3 立方米每秒。河床粒径量中间轴，不是最长轴，长轴会把片状砾石算得偏大；圆度用 Powers 圆度指数，按 0.5 为间隔分成六类，判读时看同一测点 30 颗以上的分布而不是单颗。很多学生以为流量测一次就够，同一断面在不同水位下差别很大，报告里要写清测量日期与当天水位条件，否则第二年重复调查根本对不上。
Velocity is normally taken over a ten metre stretch and repeated three times before averaging, and because a float rides the surface it overstates the true mean flow; a correction factor of about 0.8 to 0.9 is standard practice, so 0.42 m/s becomes roughly 0.36 m/s. Discharge follows from the cross-section, where an 8.0 m wide channel with a mean depth of 0.45 m gives 3.6 m squared and a discharge of about 1.3 cubic metres per second. Measure bedload on the intermediate axis rather than the longest, and record the date and water level, because the same cross-section behaves very differently at different stages.
海岸剖面与沿岸输沙的测量口径
海滩剖面用两根标杆加皮尺测量，从后滨向低潮线每 0.5 米读一次高程，遇到滩肩、滩槽这类坡度突变处加密到 0.25 米，剖面上标出每个采样点编号，图上再对回数据表。沿岸输沙用漂浮物追踪，在固定位置放入，记录 4 分钟漂移 12 米，换算成 3 米每分钟，也就是每小时约 180 米。风向、潮位与浪级要一并记录在同一张表里，因为不同潮位的剖面不能直接叠在一张图上比较。常见的错误是把高潮时测的剖面和低潮时测的剖面画成同一组曲线，那张图上升的不是地形变化而是潮差。采样点的选择也要交代清楚，只测游客最多的那段海滩，结论只能限定在那一段。
Beach profiles are surveyed with ranging poles and a tape, reading elevation every half metre and closing in to a quarter metre where a berm or trough interrupts the slope. Longshore drift is tracked with a float released at a fixed point, where twelve metres in four minutes is three metres per minute, or about 180 metres an hour. Wind direction, tide height and wave conditions belong in the same table, because profiles taken at different states of tide cannot be compared directly.
数据层级决定统计检验的选择
数据分四层：名义数据是类别，比如土地用途；顺序数据是排名或等级，比如环境质量 1 到 5 分；等距与比率数据带单位，比如流速与距离。层级决定了能算什么：类别配频数用卡方检验，顺序配顺序用 Spearman 秩相关，两个地点的连续数据比差异用 Mann-Whitney U，点状要素的空间格局用最近邻指数，读数本身的离散程度用标准差。检验选错，D 项基本进不了 7 到 8 分那一档，因为分析的解释力从第一步就断了。学生最常把百分比直接送进卡方公式，期望频数必须由实际计数推出来，先还原成样本数才能往下算。植被或生物多样性类的题目还会用到多样性指数，N(N-1) 除以各类 n(n-1) 之和，100 个个体按 50、30、20 分布时约等于 2.68。
The level of measurement decides which test is defensible: nominal categories go to chi-squared, ordinal ranks to Spearman's rank or Mann-Whitney U, and interval or ratio data to means and standard deviations. Point patterns call for the nearest neighbour index, while vegetation studies often use a diversity index such as N(N-1) divided by the sum of n(n-1), which gives about 2.68 for a hundred individuals split 50, 30 and 20. Feeding percentages into a chi-squared calculation is a frequent error, since expected frequencies have to be built from counts.
Spearman 秩相关的算法与判读
Spearman 秩相关的公式是 rs = 1 - 6Σd² / (n(n² - 1))，d 是两列变量在同一测点上的秩之差。十对数据、Σd² 等于 44.5 时，分母是 10 乘 99 等于 990，分子 6 乘 44.5 等于 267，rs = 1 - 267/990，约等于 0.73。算出系数只是半程，还要拿它和临界值比：n 等于 10 时，5% 显著性的临界值在 0.56 上下，不同版本的表略有差异，以随卷附的那张为准，0.73 大于它才能说存在显著的正相关。秩并列要取平均秩，直接按原始数值排名会算错。系数本身不说明因果，写结论时只能说相关，不能说 A 导致了 B 这一类判断。阅卷时常见的失分是只报一个数字就收笔，既没有回答关系是正还是负，也没有交代强度和显著性。
Spearman's rank coefficient is 1 minus 6 times the sum of squared rank differences, divided by n(n squared minus 1); with ten pairs and a sum of squared differences of 44.5 the coefficient comes to about 0.73. Reporting that number alone is not enough, because a coefficient only means something beside the critical value for the sample size, which sits near 0.56 at the five per cent level when n equals 10. Tied values take the mean of the ranks they would have occupied, and a negative coefficient describes an inverse relationship rather than a weak one.
卡方检验的期望频数算法
卡方统计量是 Σ(O - E)² / E，期望频数 E 用行合计乘列合计再除以总样本数。一个 2 乘 2 的例子里，地点 A 有植被 40 个、无植被 20 个，地点 B 有植被 25 个、无植被 35 个；四个格子的期望值分别是 32.5、27.5、32.5、27.5，代入公式后卡方值约 7.55。自由度按 (行数 - 1) 乘 (列数 - 1) 算，2 乘 2 表只有 1，1 自由度在 5% 水平的临界值是 3.84，1% 水平是 6.63，7.55 两个都超过，可以说两个地点的植被分布差异显著。期望频数低于 5 的格子占太多时结论不稳，通常要把相邻类别合并再算一次。错得最多的是把自由度按格子数算成 4，自由度错，整段结论都站不住。
Chi-squared compares observed counts with expected counts, where each expected value is the row total multiplied by the column total and divided by the grand total. In a two by two table with 40 and 20 observed at one site against 25 and 35 at the other, the expected values are 32.5 and 27.5 and the statistic comes to about 7.55 on one degree of freedom. That degree of freedom has a critical value of 3.84 at five per cent and 6.63 at one per cent, so the difference is significant at both levels, although cells with expected counts below five make the conclusion unreliable.
最近邻指数与点状分布的判读
最近邻指数 Rn = 2 d̄ √(n / A)，d̄ 是每个点到最近邻点的平均距离，n 是点数，A 是研究区面积。20 个零售点、平均最近邻距离 0.12 公里、研究区 5.0 平方公里时，Rn = 2 乘 0.12 乘 √(20/5)，等于 0.24 乘 2，也就是 0.48，明显小于 1，说明点状要素呈聚集分布。Rn 等于 1 表示随机分布，大于 1 表示规则或均匀分布，判断之前先确认面积口径一致。面积要用实际调查的范围算，把整张行政区图的面积套进去会人为压低指数，凭空造出一个聚集的结论。这一步最容易出的错是把 d̄ 和点点之间的最小距离混为一谈，d̄ 是全部最近邻距离的平均值，不是最小的那一个。
The nearest neighbour index is two times the mean nearest neighbour distance, multiplied by the square root of the number of points divided by the study area; twenty outlets across five square kilometres with a mean spacing of 0.12 km give 0.48. Values below one indicate clustering, a value close to one indicates a random pattern, and values above one indicate regularity. The area must be the area actually surveyed, since borrowing a whole administrative boundary shrinks the index and invents clustering that is not there.
2500 词的计数规则与图表整合
计入 2,500 词的是全部正文，田野问题、分析、结论与评价一个都跑不掉。不计入的清单很窄：标题页、致谢、目录、大小标题、参考文献、每条 15 词以内的脚注、图例与地图键、10 词以内的标注、数据表格、计算过程，以及只放原始数据的附录。超限的后果很直接，官方口径是教师与审核人停止阅读，E 与 F 两项基本拿不到分，D 项的尾部论证也会被拦腰截断。附录只能放原始数据或问卷样张，把二手资料整篇塞进附录会被当成规避词数限制。每张图都要编号、有标题，并嵌在相关段落旁边，不能堆在文末当图集。
The 2,500 word limit covers the whole body of the report, including the fieldwork question, the analysis, the conclusion and the evaluation. Excluded material is narrow and specific: title page, acknowledgements, contents page, headings, references, footnotes of up to 15 words, map keys, labels of up to 10 words, tables of data, calculations and an appendix of raw data only. Exceeding the limit is not a minor deduction, because moderators are instructed to stop reading, which usually costs the marks attached to criteria E and F.
结论 评价与 20 小时田野的时间分配
结论 2 分，要的是一句清楚的回答，并且与分析一致，数据不支持最初的假设时如实写出来同样得分。评价 3 分看的是方法层面的反思：浮标高估流速、环境质量打分带主观性、人流只在一个时段计数、样本量偏小，这些都要指出，并给出可执行的改进办法和预期影响，只写设备有限属于空泛。20 小时的田野时间可以按采集 6 小时、整理与录入 4 小时、分析与作图 6 小时、写作 4 小时分配，整理放在采集之后尽快做完，避免现场笔记失去上下文。正式提交的版本必须是定稿，因为校内一般只对第一稿给一次反馈。阅卷时最能分出高下的不是结论写得多漂亮，而是评价里有没有具体、可执行的改进方案。
The conclusion carries 2 marks and asks only for a clear answer that the analysis supports, and a report that honestly rejects its own hypothesis can still score full marks there. The evaluation carries 3 marks and looks at method, so float velocity overstating flow, subjectivity in environmental quality scoring, counts taken at a single time of day and small samples all belong here with a realistic improvement and its likely effect. Twenty hours is the recommended fieldwork commitment, and splitting it across collection, data entry, analysis with graphing and writing keeps the field notes usable when the analysis begins.
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