A researcher randomly assigns 40 university students to a treatment or control group, then measures anxiety after a 6-week therapy program. After the study, she finds the treatment group had significantly lower anxiety. She also notes she did not use random sampling from any population. Which conclusion is most justified?
ANeither causation nor generalization — without random sampling, the study is invalid
BCausation within this sample, but limited generalization to the broader population
CBroad generalization to all adults, because the finding was statistically significant
DCausation only if the two groups happened to be identical on all pre-existing characteristics
Random assignment enables causal inference (the treatment likely caused the anxiety reduction) by eliminating systematic confounds. Without random sampling, generalizability is limited — the finding may not extend beyond university students or this particular population. But the absence of random sampling does not invalidate the causal conclusion within the study. Random assignment controls internal validity; random sampling controls external validity. They are independent, and a study can have one without the other.
Question 2 Multiple Choice
After random assignment, a researcher checks her two groups and finds that, by chance, the treatment group has slightly higher baseline anxiety than the control group. What does this reveal about random assignment?
AThe random assignment was done incorrectly and must be redone
BRandom assignment guarantees perfect group equivalence, so this finding indicates a procedural error
CRandom assignment prevents systematic bias but does not guarantee identical groups — chance imbalances are still possible, especially with small samples
DThis imbalance is impossible if true randomization was used
Random assignment ensures that no characteristic systematically concentrates in one condition — assignment is determined by chance, not by any property of the participant. But chance itself can produce imbalances, particularly with small samples. In a study of 40 participants, a few unlucky assignments could leave one group slightly higher on a variable. This is not an error; it is the expected variability of random processes. Random assignment controls systematic bias, not sampling error. Large samples reduce but never eliminate this possibility.
Question 3 True / False
A study that uses random assignment but not random sampling can still support causal conclusions about the effect of the independent variable.
TTrue
FFalse
Answer: True
Causal inference depends on internal validity, which random assignment provides by distributing pre-existing differences evenly across groups. External validity (generalizability) depends on how the sample was selected — random sampling improves it, but its absence does not undermine causation. A laboratory study using convenience sampling with random assignment can validly conclude that the treatment caused the observed difference within that study, even if generalization to other populations requires caution.
Question 4 True / False
Random assignment eliminates most confounding variables, ensuring that any group difference in outcomes is expected to be caused by the independent variable.
TTrue
FFalse
Answer: False
Random assignment eliminates systematic confounds — pre-existing characteristics that would otherwise concentrate in one group due to how participants were selected or self-selected. But it cannot eliminate chance imbalances on specific variables, and it does not control for procedural confounds introduced during the study (e.g., experimenter expectancy effects). The correct claim is that random assignment eliminates *systematic* bias in group composition, which is what enables causal inference on average and across replications.
Question 5 Short Answer
Why does random assignment enable causal conclusions in a way that correlational research cannot, regardless of how large the correlational sample is?
Think about your answer, then reveal below.
Model answer: In correlational research, any observed association between X and Y might be explained by a third variable Z that causes both — a confound. Increasing sample size cannot rule out this explanation; it only provides more precise estimates of the association. Random assignment breaks the connection between participant characteristics and group membership: because assignment is determined by chance, no participant characteristic can systematically differ between groups. Before the manipulation, groups are equivalent on average on all variables (measured and unmeasured). Any post-treatment difference therefore cannot be explained by pre-existing group differences, leaving the treatment as the only systematic explanation.
This is the logical structure that gives experiments their privileged status for causal inference. The logic is: (1) groups were equivalent before treatment by design, (2) groups were treated identically except for the IV, (3) one group shows better outcomes — therefore the IV caused the difference. Step 1 is only guaranteed by random assignment. No statistical technique applied to correlational data can fully replicate this guarantee, because unmeasured confounds always remain possible.