Follow up Tests Flashcards
What do follow up tests tells us?
The differences among means or sets of means; they decrease the probability of making a type 1 error
What is the difference between a priori & post hoc tests?
A-priori are planned before the test (bonferroni t & linear contrasts) & post hoc tests (scheffé) are performed afterwards, to control the familywise error rate
What is the primary advantage of linear contrasts over pairwise tests?
They’re planned before data is collected so not influenced by the data; they don’t require a significant overall F; they’re more powerful & allow us to compare averages of multiple groups means
What rules should you follow to assign linear weights?
Choose sensible comparisons (2 chunks at a time); groups coded with positive values compared against groups with negative values; the sum of weights must equal zero; if a group isn’t involved in the comparison it gets a weight of zero; weights assigned to 1 chunk of variation need to equal the number of groups in the other chunk
What are orthogonal contrasts?
They ask independent questions of the data set; use non-redundant information; get more information with fewer amount of tests (more power); explains in simplest terms
What rules should you follow to check orthogonality
Each comparison needs to be a valid linear contrast (sum of weights must equal zero); contrasts must be independent/orthogonal (sum of ajbj = 0) maximum possible number of orthogonal contrasts is k-1 (df treat)
What should the sum of SS contrasts be equal to?
SS treatment
What if we don’t have orthogonal contrasts?
We can do non-orthogonal contrasts but need to be aware that there may be overlapping information & may have less power in the set
What is the Bonferroni t (Dunn’s) test based on?;
What’s the formula for this?
Bonferroni inequality - probability of type 1 error in a set of comparisons won’t exceed the sum of probability of type 1 error for each test;
alpha prime = alpha/c; i.e. significance level per comparison = overall alpha level/number of comparisons (alpha level is shared among comparisons)
What are the statistical hypotheses when using Bonferroni t test?
Null: mew 1 = (mew 2 + mew 3) / 2
Alternative: mew 1 /= (mew 2 + mew 3 ) / 2
We can either square t prime to find F value or…
Take the square root of F to find t prime (depending on which calculations we use)
How does the Tukey test differ to the Scheffé test?
The tukey test adjusts alpha as though we’re doing all possible pairwise comparisons; The scheffé test adjusts alpha as though we’re doing all possible pairwise & non-pairwise comparisons (more flexible)
When are follow up tests used?
With quantitative data, comparing differences between multiple independent groups in a one-way ANOVA
How do you calculate Fcrit in the scheffé test?
Multiply the original omnibus Fcrit x k-1 (number of levels in the full data set)
Which is more conservative; bonferroni or scheffé test?
Scheffé test (harder to reject null)
