After plotting the CDF of the probabilities of type 1 error for a test at alpha=0.05 and n=15 i am getting the given plot. It it ok to say "there is evidence that the Type I error rate of the test has poor control in small sample settings"? enter image description here

closed as unclear what you're asking by whuber Oct 11 at 16:36

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  • Because "poor control" is unspecific, it's essentially meaningless. Could you elaborate on what you intend that to mean? – whuber Oct 11 at 16:35
  • I just want to comment on the low type 1 error rate for the test. Should i rather say "the test is under rejecting" – Show Oct 11 at 18:07
  • That's evidently the case for $n=15.$ Because you don't describe the test, we have no information to draw conclusions about any other $n.$ – whuber Oct 11 at 18:08
  • Type I error rates for larger sample sizes are closer to the true nominal alpha-level of 0.05. For example n = 30, the estimated Type I error rate is 0.047807, For n = 50 the estimated Type I error rate is 0.050416 and For n = 150 the estimated Type I error rate is 0.04958. – Show Oct 11 at 18:20