ANOVA Derivations Flashcards
What is the equation for Variance?
๐๐๐ซ๐ข๐๐ง๐๐=
(๐๐ฎ๐ฆ ๐จ๐ ๐ฌ๐ช๐ฎ๐๐ซ๐๐ ๐๐๐ฏ๐ข๐๐ญ๐ข๐จ๐ง๐ฌ)
divided by
(๐๐๐ ๐ซ๐๐๐ฌ ๐จ๐ ๐๐ซ๐๐๐๐จ๐ฆ)
DF (Degrees of freedom) is the number of distinct โquantitiesโ that are used to describe?
Your data (sample size)
minus all the โconstraintsโ that the data must satisfy
DF
Within-groups:
Number of subjects in each group (the quantities) in each group
if the F Ratio is large enough it suggests what about the treatment condition?
The treatment effect does not exist.
๐ = number of groups
๐ = number of subjects in each group
so, ๐ฆ_(๐ด๐,๐) =
a single participant score
in one group
of 2 iv conditions
๐ = number of groups
๐ = number of subjects in each group
so, ๐ฆ(๐ด๐) =
mean score across one group
of the 2 iv conditions
Name 3 assumptions of ANOVA:
Independence
Normality
Homogeneity of variance
Assumptions of independence:
Random Sampling
Treatment levels are randomly assigned to subjects; i.e., there is
no systematic difference in how they are assigned
Assumptions of Homogeneity of variance:
All the treatment populations have the same variance
(i.e., only the means differ)
Assumptions of Normality:
The DV is normally distributed
in the population
Name the tests for Homogeneity of Variance:
Between-group design is:
Bartlett test
Mixed or Within-group designs:
Boxโs M
Both tests are sensitive to departures from normality
(Only valid if the normality assumption is met)
or you cannot reliably interpret results
Name the 3 common tests for normality:
Skewness
Kolmogorov-Smirnov
Shapiro-Wilk
Tests for Normality:
Compare the sample data distribution to a theoretical normal distribution
Very sensitive with large samples
What does Skewness mean?
Values are more probable on one side of the mean than the other
A perfectly normal distribution has a skewness of 0
A skewness that deviates substantially from zero violates the normality assumption
A perfect normal distribution has a skewness of?
0
