Keep an Observational Association Qualified
An observational score difference can reflect preexisting differences between groups as well as an intervention.
About 25 minutes, plus any extended practice
Supplied materials
- Paper or a browser scratch area; a calculator is optional unless rounding is requested.
- Supplied teaching case: In fictional observational study 2, students choosing a practice app have higher scores. What conclusion fits? Candidate answers: (A) Every app user must score above every nonuser (B) Random sampling alone proves the app effect (C) The app caused the whole score difference (D) The groups differ in scores; motivation or other differences may explain part of it.
- Independent check inputs: In fictional observational study 3, students choosing a practice app have higher scores. What conclusion fits? Candidate answers: (A) Every app user must score above every nonuser (B) Random sampling alone proves the app effect (C) The app caused the whole score difference (D) The groups differ in scores; motivation or other differences may explain part of it.
Learn the idea
Evidence quality depends on how participants and conditions are selected. Random sampling supports population generalization, random assignment supports treatment comparisons, and uncertainty summaries do not repair biased recruitment or uncontrolled causal differences. An observational score difference can reflect preexisting differences between groups as well as an intervention. Without random treatment assignment or a justified alternative design, the whole difference cannot be assigned cleanly to one cause.
Here is the method on the supplied teaching case. App choice was not randomly assigned. Existing motivation, prior preparation or other differences may affect both app use and scores. The observed association is evidence to investigate, not a clean estimate of a treatment effect.
Random sampling alone does not randomize treatment. Name plausible confounders and bound the claim to the observed association; additional design evidence would be needed to isolate a causal effect.
- Write or sketch the supplied teaching case, labeling its quantities and restrictions.
- Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
- Solve the independent check with its changed inputs before revealing feedback.
- Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
See the method in action
Teaching case: In fictional observational study 2, students choosing a practice app have higher scores. What conclusion fits? Candidate answers: (A) Every app user must score above every nonuser (B) Random sampling alone proves the app effect (C) The app caused the whole score difference (D) The groups differ in scores; motivation or other differences may explain part of it. Solution: App choice was not randomly assigned. Existing motivation, prior preparation or other differences may affect both app use and scores. The observed association is evidence to investigate, not a clean estimate of a treatment effect. The final answer is The groups differ in scores; motivation or other differences may explain part of it. Random sampling alone does not randomize treatment. Name plausible confounders and bound the claim to the observed association; additional design evidence would be needed to isolate a causal effect.
Check your reasoning
Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.
Helpful tips
- An observational score difference can reflect preexisting differences between groups as well as an intervention.
- Random sampling alone does not randomize treatment.
See the answer and explanation
The groups differ in scores; motivation or other differences may explain part of it
App choice was not randomly assigned. Existing motivation, prior preparation or other differences may affect both app use and scores. The observed association is evidence to investigate, not a clean estimate of a treatment effect.
Take it further
Changed-input task: In fictional observational study 9, students choosing a practice app have higher scores. What conclusion fits? Candidate answers: (A) Every app user must score above every nonuser (B) Random sampling alone proves the app effect (C) The app caused the whole score difference (D) The groups differ in scores; motivation or other differences may explain part of it. Show the mathematical reason, not only the selected answer. Expected result: The groups differ in scores; motivation or other differences may explain part of it. App choice was not randomly assigned. Existing motivation, prior preparation or other differences may affect both app use and scores. The observed association is evidence to investigate, not a clean estimate of a treatment effect.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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