Eyeball theorem

The eyeball theorem is an informal rule that a trend or difference can be judged by visually inspecting a graph instead of applying a formal statistical test.

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Statistical hypothesis test: A procedure that evaluates data against a null hypothesis using a test statistic and a probability model. It replaces visual judgment with an explicit rule for assessing evidence.
Scatter plot: A graph that displays paired observations as points on two axes. It is a common display for judging whether two variables appear associated.
Exploratory data analysis: The use of summaries and visualizations to discover structure, anomalies, and hypotheses in data. Eyeballing is most defensible as an exploratory step that generates questions.
Confirmation bias: The tendency to favor information that supports existing beliefs or expectations. Expectations can guide which plotted features appear meaningful.
Confidence interval: A range produced by a statistical method that captures uncertainty about an unknown parameter. It expresses uncertainty that an apparent graph difference cannot reveal by itself.
Line chart: A graph that connects data values in sequence, often to show change over time. Its connected shape makes apparent trends especially easy to judge by eye.
Regression analysis: A set of methods for modeling relationships between a response variable and predictors. A plotted association may motivate a regression model, but cannot establish its adequacy.
P-hacking: The selective use of analyses or reporting choices to obtain statistically significant results. Repeated visual searching can encourage unreported choices that make a pattern seem stronger.
P-value: The probability, under a specified null hypothesis, of results at least as extreme as those observed. It quantifies evidence against a null model rather than relying on apparent separation.
Visual perception: The processes by which the visual system organizes and interprets sensory information. Pattern judgments depend on how people perceive position, slope, grouping, and contrast.