Lecture 3: Independent One-Way ANOVA Flashcards
(40 cards)
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)
