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Teaching video
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Grade 11 chapters and video availability01 · Read and understand
What you will learn
- Recognize a confounder and use random allocation to address it.
- Justify the conclusion "Random assignment supports a more comparable treatment contrast" using the stated assumptions.
Before you start
Averages, groups, and study design.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A voluntary study finds students choosing a new study app score higher. Why does that alone not isolate the app's effect?
Why this math matters
Recognize a confounder and use random allocation to address it. This worked micro-lesson connects a precise mathematical condition to a conclusion you can check. The transfer task asks you to change the setting and decide which parts of the reasoning still apply.
Set up the model
A useful answer starts with clear assumptions:
- The original comparison is observational.
- The outcome and app participation are measured consistently.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Separate an association from a controlled comparison
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A voluntary study finds students choosing a new study app score higher. Why does that alone not isolate the app's effect?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Build the model
App choice may be related to prior motivation or preparation
The groups can differ before the app is used.
Work through the mathematics
Those background factors may also affect scores
A common cause can generate an association without the app producing all of it.
Check the conclusion
Random assignment supports a more comparable treatment contrast
Randomization balances confounders in expectation, while the actual study still needs sound measurement and implementation.
The result
Random assignment supports a more comparable treatment contrast
Randomization balances confounders in expectation, while the actual study still needs sound measurement and implementation.
Common mistakes to catch
- Correlation alone does not establish causation.
- Randomization does not guarantee perfectly identical groups in every finite sample.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Does a larger voluntary sample automatically remove this bias?
Show a hint
More data can repeat the same selection pattern.
Reveal answer and explanation
No
Sample size reduces some random error but does not guarantee removal of systematic confounding.
Practice 2
What is the role of a pretest?
Show a hint
Measure starting differences.
Reveal answer and explanation
It can describe and help adjust for measured baseline differences
It does not reveal every unmeasured confounder.
Take the idea with you
Propose an ethical randomized comparison with a clear outcome and a documented assignment procedure.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Predict how rescaling measurements changes their spread
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