## Key Ideas > [!abstract] Core Concepts > > - **Association versus causation**: Variables can be statistically related without one causing the other > - **Control groups required**: Establishing causal relationships needs experimental design with proper controls > - **Third variables**: Confounding factors often explain apparent causal relationships ## Definition **Correlation Does Not Equal Causation**: Fundamental principle that statistical association between variables doesn't prove one causes the other (causal relationships require controlled experimental evidence). ## Connected To [[What Research can you Trust]] | [[Replication Crisis]] | [[Jean Piaget]] | [[Learning Disabilities]] --- ## Core principle Just because two variables are associated with each other doesn't mean one variable causes the other to change (Mill, 1843). This error is common in interpreting research and everyday observations. To establish causal relationship between variables, a [[What Research can you Trust|control group]] is required (Campbell & Stanley, 1963). Without experimental control, correlation remains merely suggestive, not conclusive. ## Classic example ### Ice cream and shark attacks This absurd example illustrates how third variables create spurious correlations. As ice cream sales increase, shark attacks also increase (a clear correlation that seems meaningful until examined critically). One might conclude that ice cream sales cause shark attacks, but this interpretation is nonsensical. The actual explanation involves a third confounding factor: both ice cream sales and ocean swimming increase during summer months. The correlation between ice cream and shark attacks is real, but attributing causation misses the actual relationship. ## Educational applications Educational research frequently confuses correlation with causation, leading to misguided interventions based on misinterpreted associations. ### Brain differences and learning Brain scans show differences between dyslexic and typical readers (Gabrieli, 2009; Shaywitz et al., 2008), suggesting that brain differences cause reading difficulties. However, this represents correlation, not causation. Brain differences could result from different teaching methods or reading experiences rather than causing them. The brain changes in response to what we learn, meaning that [[Learning Disabilities|brain differences might be a consequence rather than a cause]] of reading difficulties (Vellutino et al., 2004). Without experimental manipulation of brain structure or controlled comparison of identical brains with different reading experiences, the causal direction remains unclear. ### Piaget's stages Piaget observed that children of certain ages show specific cognitive patterns (Piaget, 1952), leading to the conclusion that age causes cognitive abilities. However, [[Jean Piaget|prior knowledge and experience]], rather than age, likely determine performance (Chi et al., 1981). Children of the same age with different educational experiences show vastly different cognitive abilities, undermining age-based stage theories. Age correlates with cognitive abilities because it generally correlates with accumulated experience, but chronological age itself does not cause development (the learning and experience accumulated over time do). ## Why correlation doesn't imply causation There are two potential problems with drawing causal inferences from correlational evidence (Stanovich & Stanovich, 2003). ### The third-variable problem The third-variable problem occurs when the correlation between two variables does not indicate a direct causal path between them but arises because both variables are related to a third variable that has not been measured. The ice cream and shark attacks example illustrates this problem: the third variable (summer weather) causes both increased ice cream sales and increased ocean swimming, creating a spurious correlation between ice cream and shark attacks. In educational research, third variables frequently confound interpretations. Students who receive music lessons often achieve higher academic scores. However, music lessons correlate with family socioeconomic status, which independently predicts academic achievement. The correlation between music lessons and academic achievement may result entirely from the third variable of socioeconomic status rather than any causal effect of music instruction. ### The directionality problem The directionality problem creates interpretive difficulties because even if two variables have a direct causal relationship, the direction of that relationship is not indicated by the mere presence of the correlation. A correlation between variables A and B could arise because changes in A are causing changes in B or because changes in B are causing changes in A. The mere presence of the correlation does not allow us to decide between these possibilities. Consider the correlation between reading skill and vocabulary knowledge. This correlation could arise because reading causes vocabulary growth (exposure to written language teaches new words), or because vocabulary knowledge causes reading improvement (knowing more words makes reading easier), or both. Correlational evidence alone cannot distinguish between these alternatives. ## The logic of the experimental method The heart of the experimental method lies in manipulation and control (Stanovich & Stanovich, 2003). In contrast to a correlational study, where the investigator simply observes whether the natural fluctuation in two variables displays a relationship, the investigator in a true experiment manipulates the variable thought to be the cause (the independent variable) and looks for an effect on the variable thought to be the effect (the dependent variable) whilst holding all other variables constant by control and randomisation. This method removes the third-variable problem because, in the natural world, many different things are related. The experimental method may be viewed as a way of prying apart these naturally occurring relationships. It does so because it isolates one particular variable (the hypothesised cause) by manipulating it and holding everything else constant through control. ### Random assignment When manipulation is combined with a procedure known as random assignment (in which the subjects themselves do not determine which experimental condition they will be in but, instead, are randomly assigned to one of the experimental groups), scientists can rule out alternative explanations of data patterns. By using manipulation, experimental control, and random assignment, investigators construct stronger comparisons so that the outcome eliminates alternative theories and explanations. Random assignment ensures that groups are equivalent before the experimental manipulation. Any pre-existing differences between individuals are distributed equally across experimental and control groups. If groups differ after the manipulation, the difference can be attributed to the experimental treatment rather than pre-existing characteristics of the participants. ### Control groups Control groups provide the comparison necessary to isolate the effect of the independent variable. Without a control group, we cannot determine whether changes in the dependent variable result from the experimental manipulation or from other factors such as the passage of time, practice effects, or external events that affect all participants. For example, if students receive a new reading programme and their reading scores improve, we cannot conclude the programme caused the improvement without a control group. Students might have improved due to maturation, other aspects of schooling, or external factors. A control group that receives standard instruction allows us to compare the improvement in the experimental group against the natural rate of improvement, isolating the programme's effect. ## Research implications Understanding correlation versus causation changes how we evaluate research claims and educational practices (Pearl, 2009). Randomised controlled trials are the gold standard for establishing causation because they control for confounding variables (Shadish et al., 2002). By randomly assigning participants to treatment and control conditions, researchers can isolate the causal effect of a specific intervention. Observational studies, by contrast, can reveal correlations but cannot prove causal relationships. These studies track existing patterns without manipulating variables, leaving open the possibility of confounding factors that explain observed associations. 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