ANOVA

Question 1

In a one-way ANOVA, what is the general premise of the null?

Answer 1

That there is no difference between the groups.

All population means are the same.

Question 2

What are the characteristics of a one-way ANOVA?

Answer 2

One outcome varaible (numeric), and one grouping varaible (categorical)

The grouping variable contains 2+ subgroups.

Question 3

What four steps are needed to construct a test?

Answer 3

1. Diagnostic test statistic, t
2. Sampling distribution of t if null is true
3. The observed t in data
4. A rule that maps every value of t onto a decision

Question 4

What does having having significantly difference between among groups depend upon?

Answer 4

Varaibility. SSb and SSw.

Question 5

What are the two kinds of varaiblity an ANOVA is concerned with?

Answer 5

Between groups (how different are the group means from the grand [total] mean - SSb)
Within group (how much to values differ from the mean in each group - SSw)

Both varaibilities depend on Sum of Squares (SS).

Question 6

what is the equation for SSb? (one way)

Answer 6

weighted_by_n_of each group
(group#mean - grandMean)^2 and summed over all groups

Question 7

What is SSw calculating, and what is the equation?

Answer 7

Calculating the residuels, or how far away each data point is from the group mean.
(dataPoint - group mean)^2 summed over all items in group, and across all groups.

Question 8

Why don’t we just add SSb and SSw to get a our variance number?

Answer 8

Because we are only interested low SSw and high SSb. Therefore a fraction is between

degrees of freedom needs to be corrected for.

Question 9

How do you calculate variability using SSw and SSb?

Answer 9

You cannot cacluate using these exact figures, both need correct for df:
MSw = SSw / (n - G),
MSb = SSb / (G -1)
Varability, F = MSb / MSw

High F = means are different

Question 10

F-distribution.

Answer 10

Made out of the F-values if the null was true. Positively skewed.

Question 11

What are the key features of a one-way stat block.

Answer 11

F(df-SSb, df-SSw) = f-stat, p-value

Question 12

Why don’t we run combinations of t-tests to see which group is sig’ different with ANOVA ?

Answer 12

Possible combinations grow exponentially as group number increases. Also increaes Type 1 error rate. Each t-test has 5% T1 error rate. More tests grows this significantly.

We want to keep Family-wise T1 erorr at 5%

Question 13

How do post-hoc tests keep family wise T1 error at 5%?

Answer 13

They adjust the p-values for the combinations t-test being run on ANOVA groups.

Question 14

What are residuels also know as?

Answer 14

Within group variation (SSw)

Question 15

What are residuels also know as?

Answer 15

Within group variation (SSw)

Question 16

What is the output of a Kruskal-Wallis test, and why is it run?

Answer 16

A Kruskal-Wallis test is run if residuels are not normally distributed. The output is a chi-squared (because it ranks values), df, and p-value (most important)

Question 17

How are is varaibility different in two-way ANOVA?

Answer 17

SSb = (SSa, SSb): This is now how different are the grand means from one another (of both grouping variables)
SSw = SSR: how much variation is left AFTER you take into account variation associated with both groups

Question 18

How are is varaibility different in two-way ANOVA?

Answer 18

SSb = (SSa, SSb): This is now how different are the grand means from one another (of both grouping variables)
SSw = SSR: how much variation is left AFTER you take into account variation associated with both groups

Question 19

How does MSR differ from SSR?

Answer 19

releates to degrees of freedom. in a two way, the residuels need to take into account df of both groups
MSR = SSr / (N - R - C + 1)

Question 20

How is a two-way anova different from a one-way?

Answer 20

Two grouping variables.
(outcome ~ groupingV + groupingV2)
Variance.
Df correction.

Question 21

How does does the output of a two-way ANOVA look?

Answer 21

SSb for each group. Residuels. df for SSb(G-1), df for SSr (N-R-C+1)

Question 22

Why does an f-statisic differ when performing a one one- two-way ANOVA on the same grouping varaibles?

Answer 22

Because of the **residuals **! In a two-way ANOVA your residuals are what’s left of the variance after the groups are considered. If you add a group that captures more variance, your residuals in a two-way will be smaller.

Question 23

What is an interaction effect.

Answer 23

The effect of factor A depends on what is going on with factor B

Question 24

What is an interaction sum of sqaures (SSA:B).

Answer 24

This is another kind of varation that can be considered. This is: How much variation is accounted for by taking into account memebership in both groups at once.

Interaction therefore results in three kind of variation .

Question 25

What is eta^2?

Answer 25

This is the effect size of each grouping variable give the other grouping variables exist. So how much each grouping variable influences the outcome variable.