Correlation vs. Causation - Algebra-1

1. Fundamental Concepts

Correlation: Refers to a statistical association between two or more variables, meaning changes in one variable tend to be accompanied by changes in another (e.g., positive, negative, or no correlation). This association only reflects a trend in data and does not involve a causal relationship between variables.
Causation: Occurs when a change in one variable directly leads to a change in another, with a clear causal logic (e.g., "watering" directly causes "plant growth").
Core difference: Correlation describes the phenomenon of variables "changing together," while causation emphasizes the necessary relationship where "the cause leads to the effect."

Correlation does not imply causation: Even if two variables have a strong correlation, it cannot be directly inferred that there is a causal relationship between them. There may be other factors (third variables) affecting both (e.g., "ice cream sales" and "drowning accidents" are positively correlated, but both are actually influenced by "rising temperatures").
Conditions for verifying causation: Three conditions must be met—correlation between variables, the cause occurs before the effect, and other interfering factors are excluded (through experimental design or logical reasoning).
Common misunderstanding: It is easy to mistake correlation for causation, ignoring potential third variables or coincidental factors.

Correlation: "The number of students wearing sports shoes" is positively correlated with "average math test scores" (possibly because classes with active sports have a better overall learning atmosphere, but wearing sports shoes does not directly lead to higher scores).
Causation: "Memorizing 10 words every day" and "increasing vocabulary" (the act of memorizing words directly leads to an increase in vocabulary).

Correlation: "The number of streetlights in a city" is negatively correlated with "crime rate" (possibly because areas with more streetlights have more developed economies and better security measures, rather than streetlights directly reducing crime).
Causation: "Smoking" and "lung cancer incidence" (numerous studies have proven that harmful substances in cigarettes directly increase the risk of lung cancer).

Correlation: "Annual chocolate sales in a region" are positively correlated with "the number of Nobel Prize winners" (in fact, it may be because residents in economically developed regions have stronger consumption capacity and higher education levels; there is no causation between chocolate sales and the number of winners).
Causation: "Flu vaccination" and "decreased flu incidence" (vaccines directly reduce the probability of illness by stimulating immunity, verified by scientific experiments).

Identify correlation: Use tools such as scatter plots and correlation coefficients to determine whether there is an association between variables, and clarify the direction (positive/negative) and strength of the correlation.
Question causation: If a correlation is found, ask "Is there a reasonable causal mechanism?" and "Does the cause occur before the effect?"
Look for third variables: Analyze whether there are unconsidered factors affecting both variables (e.g., the third variable between "ice cream sales" and "drowning accidents" is "temperature").
Verify through experiments: For potential causal relationships, design controlled experiments (e.g., control other variables and observe whether the "effect" changes when only the "cause" variable is altered) to exclude interfering factors.