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One Sample t Test
What do you know about the one-sample t test? Did you know that it is considered to be very robust for non-normal data? What does "very robust" mean? Many contend that if your sample size is large (say 30 or more), you need not be concerned about normality of the data.
In the example shown here, the test accepts the null hypothesis that the mean is equal to the known population mean almost 95% of the time for samples of size 25 or more (at 30, the rate is 94.3%). When you run the test, you are assuming a 95% rate of acceptance. The distribution used in the simulation is highly skewed, yet there is little affect on the test acceptance rate. This is why the test is considered to be "very robust" for non-normal data. You should have a high rate of confidence using this test with most samples, especially if you have the recommended 30 or more observations.
We have developed a macro that allows you to check the acceptance rate for various degrees of skew, with a target sample size, and to change the number of samples used in the simulations.
|One-sample t test simulation|
|Wilcoxon test simulation|