Week 8 day 1

Question 1

When do we use a chi-squared test?

Answer 1

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?).

Question 2

What is the simplest form of ANOVA?

Answer 2

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.

Question 3

What is null hypothesis of a one-way ANOVA?

Answer 3

That the means of each group are the same.
H0: mean 1= mean 2 = mean 3.

Alternative says they are different.

Question 4

What is the grand mean in reference to an ANOVA?

Answer 4

It is the mean for all the data from all the groups.

Question 5

What are the two kinds of variability taken into account in an ANOVA?

Answer 5

Between groups variability and within groups variability.

Question 6

What is between groups variability?

Answer 6

How different are the groups from each other?

This is measured as how different the groups means are from the grand mean.

Question 7

What is the within groups variability?

Answer 7

How much do individuals within the groups differ from the group mean?

Question 8

In an ANOVA, what is the total variability?

Answer 8

The total variability in an ANOVA is the combination of within groups and between groups variability.

Question 9

What is the between groups degrees of freedom?

Answer 9

Number of groups - 1.

Question 10

What is the within groups degrees of freedom?

Answer 10

Total sample size - number of groups.

Question 11

What is the test statistic for an ANOVA?

Answer 11

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.

Question 12

Is it true, that the larger F is the more different means of the groups are?

Answer 12

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.

Question 13

Can F ever be negative?

Answer 13

No.

Question 14

What is the difference between a one-way and two-way ANOVA?

Question 15

What does it mean if the F stat is 1, less than 1, or more than 1?

Question 16

What does ANOVA stand for?

Answer 16

Analysis of variance.

Question 17

What is the measure of effect size for an ANOVA?

Answer 17

Eta-squared.
Eta-squared is calculated by taking the between groups variability and dividing by the total variability.

Question 18

What does it mean if we have an eta-squared of 1?

Answer 18

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.

Question 19

What does it mean if the between groups variability is low?

Answer 19

It means that the means of the groups are very close to each other and very close to the group mean.

Question 20

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?

Answer 20

Yes.

20% of the variance in the outcome variable is explained by the grouping variable.