I recently read about contrasts and how to code them. Contrasts can be orthogonal which means that they are independent and the statistical tests for them are not correlated. Normally, when doing multiple tests on the same data the family-wise error rate increases. It is possible to calculate this increase if the tests are not correlated (then the alpha-levels of each test can be multiplied to get the new probability of making a type 1 error). However, I read in Field (2018) that if contrasts are orthogonal then Type 1 error-rate is controlled. Does this mean that the family-wise error rate does not increase when you test the orthogonal contrasts with a statistical test? As I said before, I thought there was always an increase when multiple tests are done on the same data. So I am a little bit confused.
- Discovering Statistics using IBM SPSS Statistics, Field, 2018, 5th edition (see chapter 12 and specifically page 544-546)