Analysis of Variance Flashcards
Sample Distribution Outlines
Normal distribution. Mean of sample distribution is same as pop mean. Sample error of distribution is equal to standard deviation of pop
When are t-tests used
When measuring sample means from 2 independent groups
Average t-test Outline
Both groups come from normally distributed populations and both populations have equal variance
Welch’s t-test
Both groups come from normally distributed populations with unequal variance
Variance Definition
Squared average distance from the mean
How do you determine if there’s significant variance between groups
Levene’s Test (Equal to F-value) or do t-tests for mean comparisons from independent samples (by observation)
Type 1 Error
Alpha inflation. Risk of dismissing valid null-hypothesis. Too many false positives
Relationship between alpha inflation and groups number
Group numbers increase, increasing alpha inflation
Analysis Variance Test Outline
Way to combat alpha inflation. Tests the equality of all group means in 1 go
Within Group variability Outline
Differences between 2 means in a group
Between Group Variability Outline
Difference between mean of sample and grand mean
Grand Mean Def.
Average of means across independent groups being compared
What is the F value expected to be in the case of variance equality
~1
How F Value is Evaluated
(Between Group Diff.)/(within group diff.) = (effects of group +error)/(error)
F-distribution
Non-symmetrical (must be positive). Shape depends on degrees of freedom of denom/numerator (squared measurements eg variance). Groups of distributions need to be compared. MStotal/MmsWithin group
Sum of Squares (SS) Total
Total variation between sum of all squared differences between individual values (within group) and grand mean (between groups)
SS Between
Variation between groups. Squared diff, between group means and grand mean
SS within
Variation within groups. Squared diff. between each individual value (result) in group and the mean value of the group
Post-hoc comparison
Used to find exactly where mean diff lies if F value is significant
Method of post-hoc comparison
Bonferroni Correction. Divides alpha by no. of pair wise comparisons (note if there are 4 means there are 6 times you have to subtract mean values from eachother (pair wise comparison))
