ANOVA Flashcards
What is S^2 within?
The within-groups estimate of the population variance
What is S^2 between?
Between-groups estimate of the population variance
What is SStotal?
Total sum of squares
What is SSbetween?
Between-groups sum of squares
What is SSwithin?
Within-groups sum of squares
What is dftotal?
Total degrees of freedom
what is dfbetween?
Between-group degrees of freedom
Is dfbetween always on the numerator or denominator?
Numerator
What is dfwithin?
Within-groups degrees of freedom
Is dfwithin always on the numerator or denominator?
Denominator
How many IV’s are in a one way ANOVA?
One
Nominally scaled
Three or more levels
What do you assume about the populations in a one way ANOVA?
They’re normal, have equal variances and independent scores
How many dependent variables does a one way ANOVA have?
One
What scale of measurement does the DV have in a one way ANOVA?
Equal interval
Step one of one way ANOVA
Restate the question as a research and null hypothesis
What is the null hypothesis in a one way ANOVA?
Mew1 = mew2 = mew3
What is the research hypothesis for a one way ANOVA?
The population means differ in some way
- cannot be written in symbols
What is type 1 error in a one way ANOVA?
The probability of rejecting the null hypothesis when it is true
S^2 within in a one way ANOVA
Looks at variance within each sample to estimate population variance
S^2 between in one way ANOVA
Looks at variance between samples to estimate population
What happens in a one way ANOVA if there’s no treatment effect and the null is true?
S^2 within = S^2 between
What happens in a one way ANOVA if there’s a treatment effect and the null is false?
S^2 between > S^2 within
What is an F ratio in a one way ANOVA?
Comparison of the two population variances
What will the F ratio be when there’s no treatment effect and the null is true?
Close to 1
What will the F ratio be when the null is false and there’s no treatment effect?
Greater than 1
Numerator of the F ratio dfbetween
N groups - 1
Denominator of the F ratio dfwithin
Df1 + df2 +df3
What is a grand mean
The overall mean of the means
How to measure SSbetween
How much does each mean deviate from the grand mean?
Calculate SSwithin
How much do individual scores deviate from the mean of each group?
Calculate SStotal
SSbetween + SSwithin
How to calculate SStotal from cell means in a one way ANOVA
Find the grand mean of all individual scores by finding the mean of the means of each column
. (X - GM) = subtract the grand mean from each individual score
. (X - GM)^2 = Square that answer
. Add up all of them squares to get SStotal
Calculate SSbetween
(M - GM)^2
Calculate SSwithin
(X - M)^2
How to calculate S^2 from SS and df values
SS / df = S^2
How to calculate F ratio
S^2 between / S^2 within
How to use F table
Numerator F = dfbetween
Denominator F = dfwithin
If the F ratio is more extreme than cutoff reject the null
When do you reject the null in a one way ANOVA?
When the F ratio is more extreme than the F cutoff
Effect size symbol
R^2
R^2
The proportion of variance in the dependent variable that can be accounted for by the independent variable
R^2 conventions
.01 = small
.06 = medium
.014 = large
Using a power table
How many groups do you have?
What is the effect size?
How many effects are you assessing in a two way ANOVA?
Three
What are the three effects you assess in a two way ANOVA?
Main effect of x
Main effect of y
Interaction effect
What is the null hypothesis in a two way ANOVA?
No main effect of x, no main effect of y, no interaction effect
How do we determine if there’s a main effect of the row factor?
Assess marginal means for row factor
What is a marginal mean?
The mean of the cell means for each row and column
How do we determine if there’s a main effect for the column factors?
Assess marginal means for column factors
How do we determine if there’s an interaction effect?
Assess the difference between all cell means
What is the row factor in a two way ANOVA?
The factor down the side of the table, so the information goes across the rows
What is the column factor in a two way ANOVA?
The top factor along the top, so the information goes down the columns
Graphing a two way ANOVA
When independent variables are normal use a bar graph
SSwithin
(X - GM)^2
SSbetween
(M - GM)^2
How to calculate the SSbetween value in a two way ANOVA
SScolumn + SSrow + SSinteraction
How to calculate SSinteraction
SStotal - (SSwithin + SSrow + SScolumn)
Calculate SSrow in two way ANOVA
SSrow = (Mrow - GM)^2
- Mrow is the row mean (mean of means in the row)
Calculate SScolumn in a two way ANOVA
SScolumn = (Mcolumn - GM)^2
For a one way ANOVA, how is dfbetween calculated?
groups - 1
How to calculate dfcolumns in a two way ANOVA
columns - 1
How to calculate dfrows in a two way ANOVA
rows -1
How to calculate dfinteraction in a two way ANOVA
(# rows - 1) x (# columns - 1)
For a one way ANOVA, how is dfwithin calculated?
Df of each group added together
For a two way ANOVA, how is dfwithin calculated?
Dfwithin = the sum of the df of each cell
Df1 + df2 + df3 + df4
For a one way ANOVA, how is dftotal calculated?
Total # of participants - 1
For a two way ANOVA, how is df total calculated?
Total # of participants - 1
How is F ratio calculated for one way ANOVA?
S^2 between / S^2 within
How many F ratios are there in a two way ANOVA?
Three
- three effects so three F ratios
What is always the denominator of an Fratio for a two way ANOVA?
S^2 within
F column equation for a two way ANOVA
S^2 column / S^2 within
F row equation for a two way ANOVA
S^2 row / S^2 within
F interaction equation for a two way ANOVA
S^2 interaction / S^2 within
Determining F cutoff in two way ANOVA
The df in the denominator will always be the same dfwithin
- df column / df within
- df row / df within
- df interaction / df within
Determining effect size (R^2) in a one way ANOVA
SS between / SStotal
Determining effect size (R^2) for a two way ANOVA
Use R^2 equations on the sheet given
