Week Eleven - ANOVA Flashcards
WHAT IS ANOVA USED FOR?
Used for testing hypotheses involving multiple means in a single test
DEFINE A ONE-WAY ANOVA
One IV (factor) with two or more levels One-way ANOVA is an omnibus test
WHAT IS THE NULL HYPOTH IN REGARDS TO ONE-WAY ANOVA
Null hypothesis: all means are equal
H0 : μ1 = μ2 = μ3
Rejecting null means deciding some means differ.
A one-way, between-groups ANOVA is appropriate when your study design has what characteristics?
The DV is interval or ratio
The IV is categorical with three or more levels
Your hypothesis is whether there are differences among the means of the group
ANOVA partitions variance of data into what types?
Total variance: Variance of all scores around grand mean.
Between-groups: Variance due to the independent variable
- MSbetween
Within-groups (error): Variance that is unaccounted for
- MSwithin
WHAT ARE THE ASSUMPTIONS OF A ONE-WAY ANOVA? (4)
Independence
Normality
Homogeneity of variance
Absence of outliers
A KEY THING TO REMEMBER ABOUT OWA AND NULL
HE NULL-HYPOTHESIS THAT IS TESTED BY ANOVA IS THAT THE MEANS OF ALL GROUPS ARE EQUAL. IF THE ANALYSIS REVEALS A STATISTICALLY SIGNIFICANT RESULT, YOU ARE ONLY ABLE TO CLAIM THAT THERE IS A DIFFERENCE SOMEWHERE AMONG THE MEANS. YOU DON’T KNOW YET WHICH PAIRS OF MEANS DIFFER SIGNIFICANTLY.
TWO WAYS TO ACCOUNT FOR VARIABILITY IN ONE-WAY ANOVA.
Some of the total variance can be accounted for by differences among subjects (within-groups variance)
Random variance
Some of the total variance can be accounted for by effects of conditions (between-groups variance)
This is variance due to condition
PERFORMING MULTIPLE T-TESTS RESULTS IN WHAT?
Performing multiple tests increases the risk of making at least one Type I error (assuming that the null is actually true)
- family-wise error rate
WHAT ARE THE 3 WAYS TO CONTROL FOR A FAMILY WISE ERROR RATE?
BONFERRONI TEST
TUKEY’S HONESTLY SIGNIFICANT DIFFERENCE (HSD) TEST
FISHER’S PROTECTED LEAST SIGNIFICANT DIFFERENCE TEST
WHAT DO CONSERVATIVE TESTS DO? BENEFITS & DRAWBACKS
Maximally control Type I errors (false positives)
Benefit: Risk of making at least one Type I is no greater than 5%
Drawback: Minimising type 1 errors increases the risk of Type II errors (false negatives)
WHAT DO LIBERAL TESTS DO? BENEFITS & DRAWBACKS
Reduce the risk of Type I errors, but not as much as conservative tests.
Benefit: Greater statistical power to detect a true effect
Drawback: Risk of a false positive is higher than for conservative tests.
DESCRIBE BONFERRONI TEST
Most conservative of all multiple-comparison tests
Simple and effective
Adjusts p-value required for statistical significance by dividing desired alpha-level by the number of tests performed
- IV with four levels
- Six pairwise comparisons to test all possible differences
- Bonferroni-adjusted p = .05/6 = .008
Only p-values less than adjusted p are declared significant.
Adjustment is severe when many comparisons are required, so best used when the number of comparisons is small.
DESCRIBE TUKEY’S HONESTLY SIGNIFICANT DIFFERENCE (HSD) TEST
Moderately conservative
Very popular
Required p-value calculated using the Studentized range statistic.
The test is performed by determining difference between means required for significance
Excellent choice when number of required comparisons is relatively large
DESCRIBE FISHER’S PROTECTED LEAST SIGNIFICANT DIFFERENCE TEST
Most liberal
No adjustment to p-value
Controls Type 1 error rate by requiring a statistically significant omnibus test (ANOVA) before interpreting results.
(Bonferroni and Tukey do not require ANOVA to be significant).
LSD is a series of t-tests, but SE is calculated using all available groups.
Use when ANOVA is significant and there are only three means.
