ANOVA Flashcards
When do you use ANOVA (Analysis of Variance)?
When you wish to compare the means of MORE than 2 populations as t-test can only test for equality of means from 2 populations
How do you analyse variances?
1) Measure the total variation by summing squares of differences between each mean and the overall mean
2) Measure between group variation by summing squares of the differences between each group mean and the overall mean
3) Measure the difference between group variation by summing squares of the differences between each measurement and the group mean
SStotal = SSbetween + SSWithin
ANOVA compares the within group variability and between group variability to see if there is evidence that the means of each group differ
If SSbetween/SSwithin is high= There is evidence that the means are different
What is the appropriate test-statistic for ANOVA and how do you calculate it?
F-statistic: shows ratio of variability between groups mean square and the within groups mean square
1) Calculate the appropriate degrees of freedom which indicate how much independent data were used to calculate the SS values
•If you are looking at N data values in total: Total df= N-1
•If you are comparing means across M groups then between groups df= M-1
•Like SS, the df also sum the within groups df= (N-1)- (M-1)= N-M
•2) Calculate the mean square for the between and within components
The mean square: The sum of squares divided by corresponding df
•The MS is simply the SS divided by corresponding df
F-distribution needs 2 degrees of freedom to work
What are the null and alternative hypothesis associated with ANOVA?
Null: The mean of all groups are equal AND the variance in the data is the same for all groups
Alternative: The mean of at least one group is different or the variances differ
If null is true: F is around 1 or 2
What probability does the ANOVA table give in SPSS?
Probability that an F value would be > or equal to the F-value calculated IF the null hypothesis was true
If probability is