Sample size too large ?

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    Under what conditions should sample sizes be considered too large ? 
    Other than the practical considerations like time, cost, etc, at what point do too many samples result in an overly  narrow estimate of the confidence interval – eg a dataset of 200,00-300,000 samples showed a correlation between an automated measurement vs phase of the moon, as the ANOVA had narrowed the CIs down to a fraction of a mm.
    I have heard anecdotaly that this may occur with sample sizes greater than 300-500, but havent found any reference to this.

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