Week 8 day 1 Flashcards
When do we use a chi-squared test?
when the outcome data is nominal. Here we are looking at frequency tables.
The test can be a chi-squared goodness of fit or chi-square test of independence (where two frequency tables are compared to each other - are they the same?).
What is the simplest form of ANOVA?
One-way ANOVA.
There are multiple groups (more than two) and there is only one outcome variable, e.g. treatment outcome for placebo, dose 1 of drug, dose 2 of drug.
Similar to a t-test, but there are more than two groups.
What is null hypothesis of a one-way ANOVA?
That the means of each group are the same.
H0: mean 1= mean 2 = mean 3.
Alternative says they are different.
What is the grand mean in reference to an ANOVA?
It is the mean for all the data from all the groups.
What are the two kinds of variability taken into account in an ANOVA?
Between groups variability and within groups variability.
What is between groups variability?
How different are the groups from each other?
This is measured as how different the groups means are from the grand mean.
What is the within groups variability?
How much do individuals within the groups differ from the group mean?
In an ANOVA, what is the total variability?
The total variability in an ANOVA is the combination of within groups and between groups variability.
What is the between groups degrees of freedom?
Number of groups - 1.
What is the within groups degrees of freedom?
Total sample size - number of groups.
What is the test statistic for an ANOVA?
The F statistic.
It is calculated as follows:
F=(SS between/G-1)/(SS within/N-G)
where SS between = variability between groups
SS within = variability within groups
N=total sample size
G=number of groups.
Is it true, that the larger F is the more different means of the groups are?
Yes.
Or another way to say it is that the higher F is the more unlikely we would see this data if the null was true.
Can F ever be negative?
No.
What is the difference between a one-way and two-way ANOVA?
What does it mean if the F stat is 1, less than 1, or more than 1?
What does ANOVA stand for?
Analysis of variance.
What is the measure of effect size for an ANOVA?
Eta-squared.
Eta-squared is calculated by taking the between groups variability and dividing by the total variability.
What does it mean if we have an eta-squared of 1?
This means that the between groups variability accounts for the total variability and therefore, this is a large effect.
The smaller eta-squared gets, the less of an effect is being observed, because the between groups variability is accounting for less of the total variability, which in turn means that there must be higher levels of within groups variability.
What does it mean if the between groups variability is low?
It means that the means of the groups are very close to each other and very close to the group mean.
Can eta=squared be interpreted as the proportion of variance explained by the grouping variable?
If so, what does an eta-squared of 0.20 mean?
Yes.
20% of the variance in the outcome variable is explained by the grouping variable.
