Chapter 39-Analysis of Variance Flashcards
What is ANOVA used for?
ANOVA is used to test differences between 2 or more (usually more) means.
How are the comparisons of an ANOVA made?
The comparisons are made by “analyzing variance.”
How is the variance analyzed in ANOVA?
ANOVA test compares different components of variation and also can be considered a comparison of models, for example, a model in which all groups share the same mean vs groups with different means.
What is the null hypothesis for ANOVA test?
The null hypothesis is that all the groups share the same mean.
What is the alternative hypothesis for ANOVA test?
The alternative hypothesis is that all the groups have different means.
What is the grand mean?
The grand mean is the mean of all values from all groups.
ANOVA Instead of a t test null model:
SS distances from the grand mean
ANOVA Instead of alternative model:
SS distances to group means
MS is a _________.
variance
The P value represents what in ANOVA test?
The P value represents the probability that the F ratio would be so extreme if the null hypothesis (single mean) were true.
Why doesn’t comparing three means work for t test?
You cannot run multiple t tests due to problem of multiple comparisons, but you can ask if the model of 3 means is better than 1 mean.
What is the traditional approach for ANOVA test?
The traditional approach is to partition the variation (SS) into different components.
What is total variation?
Total variation is the difference in the SS of all values from the grand mean.
Some of the variation in the traditional approach of an ANOVA comes from what?
Comes from difference among the group means.
What is it called when the rest of the variation is in the groups?
Error SS or residual SS
What does df equal?
df equals the number of samples minus the number of groups (parameters)
Total variation=?
Between groups SS + within groups SS
What is the MS?
The MS is the variance of the source of variation.
What would it mean if the null hypothesis were true?
It would mean the variance would be the same for all of the different partitions.
Null:
Total group variance=between group variance=within group variance
F ratio
between group variance/within group variance
What is would the F ratio equal if the null hypothesis was true?
1, but could differ from 1 by chance even if null is true
What is the P value?
The P value is the probability of such an extreme F if null is true
What is effect size?
The fraction of the variation explained by the groupings
Skim over the last slide of anova tests.
Skim over the last slide of anova tests.
