module 3 Flashcards
(20 cards)
What is the main aim of an ANOVA test?
To explain why people are different by assigning them to categories or groups and analysing variance.
What does SSTotal represent in a One-Way ANOVA?.
The total variance in the data
What do SSWithin and SSBetween represent in One-Way ANOVA?
SSWithin = variance within groups (null hypothesis variance), SSBetween = variance between groups (model variance).
What does a significant F-ratio in ANOVA indicate?
There is at least one significant difference between group means.
Why can’t you just run multiple t-tests instead of ANOVA?
A: Because multiple t-tests increase the chance of Type 1 error (false positives) due to family-wise error inflation.
What is family-wise error?
A: The probability of making one or more Type 1 errors when performing multiple comparisons.
How does family-wise error increase with the number of comparisons?
A: Each additional test adds a 5% chance of Type 1 error, so the overall error rate increases cumulatively.
What are planned comparisons (contrasts) in ANOVA?
A: Hypothesis-driven tests decided before data collection to break down variance into specific components.
What are the rules for planned contrasts?
A: 1) Once a group is used in one contrast, it cannot be used in another.
2) Each contrast compares only two “chunks” of variation.
3) The number of contrasts equals the number of groups minus one (k-1).
What is a post-hoc test?
A: A test performed after finding a significant ANOVA result, comparing all groups pairwise using stricter alpha values to control Type 1 error.
How many planned contrasts should be run if there are 3 groups?
A: Two planned contrasts (3 - 1 = 2).
What variance components are involved in ANOVA with planned contrasts?
A: SSWithin (residual variance), SSBetween (model variance), and how SSBetween is broken down by planned contrasts.
What is the purpose of planned contrasts in ANOVA?
A: To test specific, hypothesis-driven comparisons between groups, defined before data collection.
What rules must weights in planned contrasts follow?
A: Sum of weights must equal zero; groups not in the contrast get zero weight; weights on one side equal the number of groups on the opposite side.
What is an orthogonal contrast?
A: A contrast that compares unique chunks of variance, independent of other contrasts.
Name two common types of standard planned contrasts.
A: Helmert contrasts and Difference contrasts.
What does Tukey’s HSD post-hoc test do?
A: Compares all pairs of group means while controlling the overall Type 1 error rate.
How do planned contrasts differ from post-hoc tests?
A: Planned contrasts test specific hypotheses set before data collection; post-hoc tests explore all pairwise group differences after finding a significant ANOVA.
What is the consequence of using non-orthogonal contrasts?.
A: They overlap in variance, require careful interpretation, and increase the risk of Type 1 errors
What is the difference between Helmert and Difference contrasts?
A: Helmert contrasts compare each group to the mean of subsequent groups; Difference contrasts compare each group to the mean of previous groups.
