Contents
What are orthogonal contrasts in statistics?
Orthogonal contrasts for analysis of variance are independent linear comparisons between the groups of a factor with at least three fixed levels. The contrasts are orthogonal because they have a zero sum of the products of their coefficients (2×0 + -1×1 + -1x-1 = 0).
What is a family wise type 1 error?
What is the Familywise Error Rate? The familywise error rate (FWE or FWER) is the probability of a coming to at least one false conclusion in a series of hypothesis tests . In other words, it’s the probability of making at least one Type I Error. The FWER is also called alpha inflation or cumulative Type I error.
When do you use orthogonal contrasts in math?
If A 1 is a control and A 2 and A 3 are treatments, then the contrasts test respectively for a difference between the control and the pooled treatments, and for a difference between the treatments. The contrasts are orthogonal because they have a zero sum of the products of their coefficients (2×0 + -1×1 + -1x-1 = 0).
How is the family wise error rate calculated?
The family-wise error rate would be calculated as: Family-wise error rate = 1 – (1-α)c = 1 – (1-.05)5 = 0.2262. In other words, the probability of getting a type I error on at least one of the hypothesis tests is over 22%! There are several methods that can be used to control the family-wise error rate, including: 1. The Bonferroni Correction.
When to rearrange contrast coefficients without losing orthogonality?
If the control belongs to a different level of A, then the rows of the contrast coefficients can be rearranged accordingly without losing orthogonality. These two contrasts can be analysed in GLMwith sequential SSby requesting the terms: B + C(B) as fixed factors.
Why does Hochberg’s step up procedure control the family wise error rate?
The reason why this procedure controls the family-wise error rate for all the m hypotheses at level α in the strong sense is, because it is a closed testing procedure. As such, each intersection is tested using the simple Bonferroni test. Hochberg’s step-up procedure (1988) is performed using the following steps: