= Solution
Use \b[<one-way analysis of variance>] to compare a quantitative <response variable> across levels of one categorical factor; for example, compare task accuracy across three independently assigned teaching methods. The ordinary independent-groups procedure tests the <null hypothesis> that all group <population means> are equal. Its <F-test> compares variation associated with the group factor against within-group error variation; a significant result indicates that not all <population means> are equal, without identifying which groups differ.<One-Way ANOVA by National Institute of Standards and Technology>[Handbook Section 3.2.3.1, Description and Model]{ref}
The classical <one-way normal linear model> assumes independent observations and within-group errors approximately following a <normal distribution> with a common <variance>. Repeated observations on the same people require a different dependence structure; pronounced unequal <variances> may call for <Welch's one-way analysis of variance>. Planned <contrasts> or appropriately controlled follow-up comparisons identify scientifically relevant differences. Report the <means>, differences and <confidence intervals>, not just significance. Causal interpretation depends on the <design of experiments>, particularly <randomization>, rather than on the <F-test> alone.
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