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Sample Size

Sample Size. How many replications, n, do I need? What size effects do you want to detect? We will focus on detecting effects of a pre-specified magnitude. Sample Size. Researchers have difficulty articulating the magnitude of both effects and experimental error

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Sample Size

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  1. Sample Size • How many replications, n, do I need? • What size effects do you want to detect? • We will focus on detecting effects of a pre-specified magnitude

  2. Sample Size • Researchers have difficulty articulating the magnitude of both effects and experimental error • Have them specify a range and then use the empirical rule to estimate noise • Provide sample sizes for a range of effects

  3. Sample size • We rewrite the t-statistic to replace MSPE* with a general estimator of experimental error (assume the effect of interest is A): *Mean Square Pure Error

  4. Sample Size • If A is distinguishable from background noise, the absolute value of the t test statistic is larger than the t critical value • The t-critical value for 5% risk is approximately 2, so in order to detect an effect of magnitude A, we need:

  5. Sample Size • This can be rewritten

  6. Sample Size • If we have all the data from a replicated experiment, we can just use MSPE:

  7. Sample Size • If we have an unreplicated pilot experiment, or only the effects from a pilot experiment, we can do the following: • Let E1,…,Em be the set of negligible effects from a pilot experiment with n* reps (often the experiment is unreplicated so n=1) .

  8. Sample Size • We can construct an estimate as:(Recall that m is the number of negligible effects.)

  9. Sample Size • We can use other methods to obtain an estimate • Empirical rule • sc from centerpoint design • Combine MSPE and negligible effects

  10. Sample Size • Regardless of the estimate, in order to detect an effect of size A, we use as a lower bound:

  11. Sample Size • U-do-it exercise: Estimate experimental error from the probability plot you obtained from the violin example. Suppose the violinist wanted to detect effects equal to .5 decibels; how many replications are needed?

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