Module 2 Lesson: Variables, Measurement, Samples, and Bias
Classroom Explanation
Before any summary, three things have to be settled: what one row represents, what each column measures, and who is missing. Getting the first wrong makes every count wrong; getting the third wrong makes every generalisation wrong.
In this module, the goal is to identify units, variables, samples, populations, missing evidence, and likely bias. The important part is not only the calculation. The important part is the thinking before and after the calculation.
Why This Matters
The common mistake is treating the available rows as if they represent everyone. People who did not complete the survey or missed the exam may differ from those who did. This mistake can make a report sound more confident than the evidence deserves.
Key Ideas
1. The unit of analysis is the thing each row describes.
The unit is the thing one row describes. If the unit is unclear, the analysis can accidentally mix people, sessions, orders, classrooms, or months.
2. Variable type decides which summaries and comparisons are suitable.
A variable type is not a small detail. It decides whether an average, percentage, count, rank, or chart is a sensible choice.
3. A sample can be biased even when every recorded value is correct.
Bias can appear before analysis begins. If the people or records included are not like the people or records missing, a neat calculation can still mislead.
Worked Example
In the student study sample, each row is one survey respondent. Weekly study hours is numeric, preferred resource is categorical, and missing exam scores are evidence to investigate.
Here is the dataset used in this module.
| respondent_id | cohort | weekly_study_hours | preferred_resource | completed_survey | exam_score | missing_score_reason |
|---|---|---|---|---|---|---|
| S01 | A | 3 | video | yes | 62 | |
| S02 | A | 5 | practice | yes | 71 | |
| S03 | A | 2 | notes | yes | 58 | |
| S04 | A | 7 | practice | yes | 78 | |
| S05 | A | 4 | video | yes | 67 | |
| S06 | B | 6 | practice | yes | 74 |
Read the columns before the numbers. For each one ask what type it is, because the type decides what you may do with it — an average of a 1-to-5 opinion scale assumes the gap between 1 and 2 equals the gap between 4 and 5, which nothing about the question guarantees.
How To Think Through It
- Name what one row is.
- Classify every column by type.
- Note any column whose meaning is ambiguous.
- Identify who is absent from the data.
- Decide which summaries the types allow.
Common Mistake
The common mistake is treating the available rows as if they represent everyone. People who did not complete the survey or missed the exam may differ from those who did.
How To Write The Result
The table describes the learners who responded and have recorded scores; it may not represent learners who skipped the survey or missed the exam.
Practice Prompt
Mark the unit, variable types, sample, intended population, and missingness risks in the student study sample.
Takeaway
The unit of analysis and the measurement type constrain every number you can honestly report.