Distinguishing Correlation and Causation - Statistics
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What is the definition of correlation in a statistical study?
What is the definition of correlation in a statistical study?
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Association between variables; not necessarily a cause-and-effect link. Correlation measures relationship strength, not whether one causes the other.
Association between variables; not necessarily a cause-and-effect link. Correlation measures relationship strength, not whether one causes the other.
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What is the definition of causation in a statistical study?
What is the definition of causation in a statistical study?
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A change in one variable directly produces a change in another variable. Causation requires one variable to be the reason for changes in another.
A change in one variable directly produces a change in another variable. Causation requires one variable to be the reason for changes in another.
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Which option indicates causation: observational study or randomized experiment?
Which option indicates causation: observational study or randomized experiment?
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Randomized experiment. Random assignment controls confounders, enabling causal conclusions.
Randomized experiment. Random assignment controls confounders, enabling causal conclusions.
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Which option usually supports only correlation: observational study or randomized experiment?
Which option usually supports only correlation: observational study or randomized experiment?
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Observational study. Without random assignment, confounders may explain observed relationships.
Observational study. Without random assignment, confounders may explain observed relationships.
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What does the phrase "correlation does not imply causation" mean?
What does the phrase "correlation does not imply causation" mean?
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An observed association alone is insufficient to conclude cause and effect. Other factors may explain the relationship between correlated variables.
An observed association alone is insufficient to conclude cause and effect. Other factors may explain the relationship between correlated variables.
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Identify the term: a correlation caused by chance, bias, or confounding rather than a real link.
Identify the term: a correlation caused by chance, bias, or confounding rather than a real link.
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Spurious correlation. The association exists but lacks a genuine causal mechanism.
Spurious correlation. The association exists but lacks a genuine causal mechanism.
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What is the direction problem when interpreting a correlation?
What is the direction problem when interpreting a correlation?
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It is unclear which variable influences the other, if either does. With correlation alone, we can't determine if A causes B or B causes A.
It is unclear which variable influences the other, if either does. With correlation alone, we can't determine if A causes B or B causes A.
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What is the lurking variable problem when interpreting a correlation?
What is the lurking variable problem when interpreting a correlation?
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An unmeasured variable may be causing the observed association. Hidden third variables can create apparent relationships.
An unmeasured variable may be causing the observed association. Hidden third variables can create apparent relationships.
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Which feature is essential for a causal claim: random assignment or a large sample size?
Which feature is essential for a causal claim: random assignment or a large sample size?
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Random assignment. Random assignment eliminates confounding, unlike sample size alone.
Random assignment. Random assignment eliminates confounding, unlike sample size alone.
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Which option best reduces confounding in a study: random assignment or voluntary response?
Which option best reduces confounding in a study: random assignment or voluntary response?
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Random assignment. Randomly assigning treatments balances known and unknown confounders.
Random assignment. Randomly assigning treatments balances known and unknown confounders.
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Identify whether this is correlation or causation: "Students who sleep more score higher." (observational)
Identify whether this is correlation or causation: "Students who sleep more score higher." (observational)
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Correlation only. Observational data can't establish if sleep causes higher scores.
Correlation only. Observational data can't establish if sleep causes higher scores.
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Identify whether this is correlation or causation: "Randomly assigned tutoring increased scores."
Identify whether this is correlation or causation: "Randomly assigned tutoring increased scores."
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Causation supported. Random assignment allows causal inference about tutoring's effect.
Causation supported. Random assignment allows causal inference about tutoring's effect.
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Identify the best conclusion: A study finds $r=0.80$ between $x$ and $y$ in observational data.
Identify the best conclusion: A study finds $r=0.80$ between $x$ and $y$ in observational data.
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Strong correlation; causation cannot be concluded. High $r$ shows strong association, but observational data can't prove causation.
Strong correlation; causation cannot be concluded. High $r$ shows strong association, but observational data can't prove causation.
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Which statement is valid: "$x$ causes $y$" or "$x$ is associated with $y$" for observational data?
Which statement is valid: "$x$ causes $y$" or "$x$ is associated with $y$" for observational data?
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"$x$ is associated with $y$". Observational data supports association claims, not causal claims.
"$x$ is associated with $y$". Observational data supports association claims, not causal claims.
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Find and correct the claim: "Because $r=-0.6$, increasing $x$ will cause $y$ to decrease."
Find and correct the claim: "Because $r=-0.6$, increasing $x$ will cause $y$ to decrease."
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Correct: $r=-0.6$ shows association, not causation. Correlation coefficient describes association strength, not causal effect.
Correct: $r=-0.6$ shows association, not causation. Correlation coefficient describes association strength, not causal effect.
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Identify the confounder type: Ice cream sales and drownings rise together due to hot weather.
Identify the confounder type: Ice cream sales and drownings rise together due to hot weather.
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Confounding (lurking) variable: temperature. Temperature affects both variables, creating spurious correlation.
Confounding (lurking) variable: temperature. Temperature affects both variables, creating spurious correlation.
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Choose the correct interpretation: In a randomized experiment, treated group mean $>$ control mean.
Choose the correct interpretation: In a randomized experiment, treated group mean $>$ control mean.
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The treatment likely caused an increase in the response. Randomization allows causal interpretation of group differences.
The treatment likely caused an increase in the response. Randomization allows causal interpretation of group differences.
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Identify whether reverse causation is plausible: More firefighters at fires correlates with more damage.
Identify whether reverse causation is plausible: More firefighters at fires correlates with more damage.
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Yes; severity can cause both more firefighters and more damage. Fire severity could cause both more responders and more damage.
Yes; severity can cause both more firefighters and more damage. Fire severity could cause both more responders and more damage.
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Which design best supports causation: match subjects only, or randomize subjects to treatments?
Which design best supports causation: match subjects only, or randomize subjects to treatments?
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Randomize subjects to treatments. Randomization eliminates confounding; matching alone doesn't.
Randomize subjects to treatments. Randomization eliminates confounding; matching alone doesn't.
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Choose the correct conclusion: an observational study finds $r=0.80$ between $X$ and $Y$.
Choose the correct conclusion: an observational study finds $r=0.80$ between $X$ and $Y$.
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Strong association, but causation is not established. Observational studies can't prove causation regardless of $r$.
Strong association, but causation is not established. Observational studies can't prove causation regardless of $r$.
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Identify the likely issue: ice cream sales and drowning deaths increase together in summer.
Identify the likely issue: ice cream sales and drowning deaths increase together in summer.
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Confounding by season/temperature. Both variables are influenced by hot weather, not each other.
Confounding by season/temperature. Both variables are influenced by hot weather, not each other.
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Which design change best supports causation: random assignment to treatments or increasing sample size only?
Which design change best supports causation: random assignment to treatments or increasing sample size only?
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Random assignment to treatments. Random assignment eliminates confounding variables.
Random assignment to treatments. Random assignment eliminates confounding variables.
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Identify the likely issue: people with higher stress report less sleep; a headline says stress is caused by low sleep.
Identify the likely issue: people with higher stress report less sleep; a headline says stress is caused by low sleep.
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Reverse causation is possible. Sleep loss might cause stress, not vice versa.
Reverse causation is possible. Sleep loss might cause stress, not vice versa.
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Identify the correct interpretation: a scatterplot shows a curved pattern but $r,\approx,0$.
Identify the correct interpretation: a scatterplot shows a curved pattern but $r,\approx,0$.
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There may be a non-linear association despite near-zero $r$. $r$ only detects linear patterns, not curves.
There may be a non-linear association despite near-zero $r$. $r$ only detects linear patterns, not curves.
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What is reverse causation in an observed association?
What is reverse causation in an observed association?
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The supposed effect actually causes the supposed cause. The direction of causation is backwards from what's assumed.
The supposed effect actually causes the supposed cause. The direction of causation is backwards from what's assumed.
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Which feature of a randomized experiment helps eliminate confounding: random assignment or self-selection?
Which feature of a randomized experiment helps eliminate confounding: random assignment or self-selection?
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Random assignment. Randomization eliminates systematic differences between groups.
Random assignment. Randomization eliminates systematic differences between groups.
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What is the purpose of a control group in a randomized experiment?
What is the purpose of a control group in a randomized experiment?
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To provide a baseline for comparison against the treatment group. Shows what happens without the treatment.
To provide a baseline for comparison against the treatment group. Shows what happens without the treatment.
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Which option best indicates a causal claim: “is associated with” or “causes”?
Which option best indicates a causal claim: “is associated with” or “causes”?
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“Causes”. Direct causal language indicates cause-effect claims.
“Causes”. Direct causal language indicates cause-effect claims.
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Identify the study type: researchers assign a new drug or placebo by chance and compare outcomes.
Identify the study type: researchers assign a new drug or placebo by chance and compare outcomes.
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Randomized experiment. Random assignment of treatments defines an experiment.
Randomized experiment. Random assignment of treatments defines an experiment.
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Identify the study type: researchers record exercise and blood pressure without assigning exercise levels.
Identify the study type: researchers record exercise and blood pressure without assigning exercise levels.
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Observational study. No manipulation of variables means it's observational.
Observational study. No manipulation of variables means it's observational.
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