For a given test, the only way to reduce both error rates is to increase the sample size, and this may not be feasible.
A test statistic is robust if the Type I error rate is controlled.
Tabularised relations between truth/falseness of the null hypothesis and outcomes of the test:): "Adding water does not make toothpaste more effective in fighting cavities." This null hypothesis is tested against experimental data with a view to nullifying it with evidence to the contrary.
A type I error occurs when detecting an effect (adding water to toothpaste protects against cavities) that is not present.
Thus a type I error is a false positive, and a type II error is a false negative.
When comparing two means, concluding the means were different when in reality they were not different is a type I error; concluding the means were not different when in reality they were different is a type II error.
In statistical hypothesis testing a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding or conclusion), while a type II error is the non-rejection of a false null hypothesis (also known as a "false negative" finding or conclusion).
In statistics, a null hypothesis is a statement that one seeks to nullify (that is, to conclude is incorrect) with evidence to the contrary.
Due to the statistical nature of a test, the result is never, except in very rare cases, free of error.
Two types of error are distinguished: type I error and type II error.