Data Analysis with R, Second Edition - Second Edition

Assumptions of the one sample t-test

There are two main assumptions of the one sample t-test are as follows:

• The data is sampled from a normal distribution. This actually has more to do with the sampling distribution of sample means being approximately normal than the actual population. As we know, the sampling distribution of sample means for sufficiently large sample sizes will always be normally distributed, even if the population is not. In reality, this assumption can be violated somewhat and the results will be valid, especially for sample sizes of over 30. We have nothing to worry about here. Usually, people check this assumption by plotting the sample means and making sure it's kind-of normal, though there are more formal ways of ...