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To clarify: If as the sample size rose the variance assignable to the block effect due to pretrial preference were to drop and then level off (which is what one would expect) it would either level off at a statistically significant or statistically insignificant value. At an insignificant value that would indicate that the diver's (and I'd look at this by diver rather than in the aggregate) fin choice had no bearing on the most efficient fin for the diver. If, on the other hand, the variance remained significant that would indicate that the fin the diver used before the experiment was a predictor of the outcome of the experiment and would also permit a quantification of how important this influence was.