Problem

A randomized study reports new-method minus control mean gain \(=~+6~\text{points}\), \(p~=~0.02\), and \(\text{alpha}~=~0.05\). Interpret the direction, statistical evidence, causal scope, and limits on generalization and practical importance.

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What this problem is really about

Interpret the signed contrast before considering statistical evidence: its order determines direction, and its size with units describes the observed magnitude. Then compare p with alpha and use random assignment to bound any causal conclusion to the experimental participants under the design assumptions. Population generalization depends on recruitment, while practical importance requires a separate context-based standard.

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The observed gain is 6 points higher and p < alpha, so there is statistical evidence of an increase and the p-value proves the effect is practically important.

The observed gain is 6 points higher and p < alpha, so there is evidence the method increases mean gain among randomized participants under design assumptions.

The observed gain is 6 points higher and p < alpha, so there is evidence the method increases mean gain and the result automatically generalizes to every population.

The observed gain is 6 points lower because control is subtracted from treatment; p < alpha, so there is evidence the method reduces mean gain among participants.

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A randomized study reports new-method minus control mean gain \(=~+6~\text{points}\), \(p~=~0.02\), and \(\text{alpha}~=~0.05\). Interpret the direction, statistical evidence, causal scope, and limits on generalization and practical importance.

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