Sample Size

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 n1) .

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?