Lecture 3: Independent One-Way ANOVA Flashcards
What is an ANOVA?
An analysis of variance
When is an ANOVA used?
It is used when we have 1 IV with more than 2 levels.
What do ANOVAs test?
Whether the population means under the different levels of the IV are different based on sample means.
How is an ANOVA an extension of a t-test?
f= t^2
How do you calculate the f ratio?
The variance between IV levels/ Variance within IV levels
What does an f value close to 0 tell us?
That there is a small difference between IV levels relative to within IV levels
What does an f ratio further from 0 tell us?
That there is a large difference between IV levels relative to within IV levels
When p is < .05 what do we do?
Reject the null hypothesis (i.e., heterogeniety)
What contributes to variance BETWEEN IV levels?
- Manipulation of IV
- Individual difference
- Experimental error (random and constant)
What contributes to variance WITHIN IV levels?
- Individual differences
- Experimental error (random)
How do we partition variance?
- Calculate means for each IV level
- Calculate grand mean: sum of IV level means/ no. of IV levels
- Calculate IV level variance: sum of squared differences between individual values and the corresponding IV level means
- Calculate between IV level variance: sum of squared differences between each IV level mean and the grand mean
What are the one-way ANOVA assumptions?
- Normality
- Homogeneity of variance
- Equivalent sample size
- Independence of observations
What is the normality assumption in accordance to One-Way ANOVAs?
DV should be normally distributed, under each level of the IV
What is homogeneity of variance, in accordance to one-way ANOVAs?
Variance in DV, under each IV level, should be roughly equivalent
What is equivalent sample size, in accordance to one-way ANOVAs?
Sample size under each IV level should be roughly equivalent
What is independence of observations, in accordance to one-way ANOVAs?
Scores under each level of the IV should be independent.
Which statistic will correct for homogeneity of variance, if the assumption is violated?
Welch’s F
Which test does SPSS use to check homogeneity of variance?
Levene’s test.
If data violates all the one-way ANOVA assumptions, which non-parametric equivalent should be used?
Kruskal-Wallis test, although less powerful and proposes a greater risk of Type II error
How do you report the F statistic?
F(df^m, df^r) = F-value, p(italicised) = p-value
When do you use a Welch’s F test?
When Levene’s is significant
What happens to the degrees of freedom in a Welch’s F test?
Gets adjusted as a ‘penalty’.
Should you report degrees of freedom as a decimal?
No.
What is the Model Sum of Squares?
Sum of squared differences between IV level means and grand means (i.e., between IV level variance)
What is the Residual Sum of Squares?
The sum of squared differences between individual values and corresponding IV level mean (i.e., within IV level variance)
What is the equation for the Mean Square for Model?
SSm / dfM
What is the equation for Mean Square for Residual?
SSr / dfR
How do you calculate the dof between IV levels?
df(model) = K-1
k= number of IV levels
How do you calculate dof within IV levels?
df(residual) = N-k
n= total sample size
k= number of IV levels
How do you calculate dof for an independent one-way ANOVA?
number of measurements - number of parameters estimated
What is a posthoc test?
A secondary analysis used to assess which IV level mean pairs differ
When should a posthoc test be used?
When the F-value IS significant
What are the 3 corrections, and which one do we usually use?
Bonferroni, Least Significant Difference (LSD), Tukey Honestly Significant Difference (HSD). HSD is the one we usually use
How can bonferroni be classified, and what are the error risks does it pose?
It is classified as “very conservative”, for Type I risk, it poses a very low risk, whereas poses a very high Type II error risk.
How can Least Significant Difference be classified, and what are the error risks it poses?
It is classified as “liberal”, and poses a high Type I error risk, whereas has a low Type II error risk
How can Tukey Honestly Significant Difference be classified and what are the error risks it poses?
It is classified as “reasonably conservative”, and poses a low Type I error risk, whereas a high Type II error risk.
Which error are we happy to risk over the other?
We are happy to risk Type II error over Type I error.
What is partial ETA squared?
How much variance in the DV is explained by the manipulation of the IV overall
How can partial ETA squared values be classified?
Small = > .01
Medium = > .06
Large = > .14
What is the equation for partial ETA squared?
SSm / SSm + SSr
