ANOVAs Flashcards
Analysis of Variance
Comparison between 2 or more groups
One-way ANOVA
An anova with multiple groups where one factor is being tested
Two-way anova (three way four way etc)
An ANOVA where more than one operational definition or “factor” is being tested
Between subjects ANOVA
An ANOVA where two independent groups are compared
Within subjects ANOVA
An ANOVA with two groups whos data are dependent on each other
n, N, K
n=number of participants in a group
N=number of participants in a study
k=number of groups (levels in a factor, for instance one two or three majors etc)
Quasi-Experimental assignment
An assignment of participants to groups based on a pre-decided factor, “you’re with your group based on this particular aspect”
Experimental Assignment
where all participants are randomly assigned to groups
Between groups variation
How different are people overall in a group from overall another people in another?
Within group variation
How different are people from each other within a particular group in a study
F-Distro
A positively skewed one-tailed-test used to test ANOVAs
F-statistic (F-obtained)
Test Statistic for ANOVA: mean square between groups divided by mean square within groups (error)
(variance between groups (numerator))/(variance within groups(denominator))
F-Statistic Equation
Fobt=MSbg/MSe
Numerator
differences between groups
Denominator
differences within groups (error)
Overall Degrees of Freedom
N-1
Between Groups Degrees of Freedom (Numerator Degrees of Freedom)
number of groups -1, or k-1
Degrees of freedom error (within groups df) (Denominator degrees of freedom)
The overall number of participants - the number of groups N-k
ANOVA assumptions
The data in a population is normally distributed, the data was randomly sampled, one person performing in your study will not affect another person’s performance in your study, the amount of variability that exists within a single group is the same as exists in the other groups being measured
ANOVA (Analysis of Variance)
A statistical method for testing hypotheses about the variance between k≥2 (greater than two group means) (variance in one or more populations is unknown)
Between-persons variation
Variation that cannot be explained by having different groups; variation between individual person means within a single group
Degrees of freedom between groups
The degrees of freedom aligned with the variance of the numerator group means (K-1)
F Distribution
A positively skewed sampling distribution of f-ratios
Fobt (F obtained)
Test statistic for ANOVA
Fobt Formula
Fobt-MSbg/MSe OR variance between groups/variance within groups
degrees of freedom error
synonym for degrees of freedom within groups or degrees of freedom denominator
degrees of freedom between persons (dfBP)
df associated with the variance of person means averaged across groups
(n-1) (usually written n sub 1, n sub 2, and so on)
One-way between subjects ANOVA
A specific type of ANOVA with ONE factor and two + INDEPENDENT groups.
Levels of the factor
k, or the number of different ways an independent/quasi-indep factor is observed (measuring emotionality, one level might be negative emotionality/affect and another might be positive affect)
One-way repeated-measures ANOVA
Used to test hypotheses for one factor with two + levels, where the same participants are observed more than once, once at each level
Mean square error
vairance related to differences within a specific group, the denominator of the test statistic
Mean square within groups
The mean square error associated with the denominator
One-way within-subjects ANOVA
An ANOVA conducted on a single group tested at multiple levels of the same factor
Post Hoc Test
“After-the-fact” test measuring pairwise comparisions, or all the different possible pairs of group means.
Pairwise comparisions
Comparing every possible pairing of groups to find where significant differences lie
Experimenwise alpha
The alpha level, usually .05, for multiple tests on the same data. Put another way, the probability of committing a type I error across all tests.
Testwise alpha
The alpha level for each individual post-hoc test
Types of Conservative Post-Hoc Tests
Sheffe test, Bonferroni. Conservative here means, “least power, can only find large differences.”
Liberal post hoc-tests
Tukey’s HSD test, SNK test, Fisher’s LSD test (Liberal here means aimed at finding smaller, more nuanced differences between groups)
