W8 Flashcards
How do you quantify the null hypothesis that all groups are the same?
By calculating the sum of squares total (SStotal).
What is a multi-group hypothesis?
It’s a hypothesis designed to test more than one group, where the null hypothesis states that all groups are the same or that all means are the same.
How do you quantify the alternative hypothesis that each group has its own means?
By calculating the sum of squares within (SSwithin).
How do you calculate the total variance in the data?
By subtracting SSwithin from SStotal, which gives SSbetween.
How do we normalize sums of squares by degrees of freedom within subjects?
By dividing SSwithin by the degrees of freedom within subjects, which is the number of observations minus the number of groups, resulting in MSEwithin.
How do we normalize sums of squares by degrees of freedom between subjects?
By dividing SSbetween by the degrees of freedom between subjects, which is the number of groups minus 1, resulting in MSEbetween.
What is the test statistic, the core of ANOVA?
It’s F = MSEbetween/MSEwithin.
What does F tell us and how do you interpret it?
A large F suggests a large MSEbetween, indicating that the data should be modeled with individual means. A small F suggests a small MSEbetween, indicating not much variability in the data and that all groups can share an overall mean.
When ANOVA is presented in a table, what are df1 and df2?
df1 represents the number of groups, while df2 represents the number of observations.
What does the ANOVA p-value suggest?
If p < 0.05, it suggests that the data is significant and that we would be very unlikely to observe this data if there were no true differences between the means of these groups, thus accepting the alternative hypothesis that groups have different means.
What are post-hoc tests?
They are used because the ANOVA F statistic suggests differences, but we can’t determine what the differences actually are. Post-hoc tests run t-tests for every comparison combination of the groups.
What are factors and levels?
A factor is a categorical or nominal variable containing labels of a set group, while levels are the different groups within a factor.
What are the assumptions of ANOVA?
Independence, normal distributions, equality of variance, categorical factors, and interval or ratio data.
