ANOVA Flashcards
In a one-way ANOVA, what is the general premise of the null?
That there is no difference between the groups.
All population means are the same.
What are the characteristics of a one-way ANOVA?
One outcome varaible (numeric), and one grouping varaible (categorical)
The grouping variable contains 2+ subgroups.
What four steps are needed to construct a test?
- Diagnostic test statistic, t
- Sampling distribution of t if null is true
- The observed t in data
- A rule that maps every value of t onto a decision
What does having having significantly difference between among groups depend upon?
Varaibility. SSb and SSw.
What are the two kinds of varaiblity an ANOVA is concerned with?
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).
what is the equation for SSb? (one way)
weighted_by_n_of each group
(group#mean - grandMean)^2 and summed over all groups
What is SSw calculating, and what is the equation?
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.
Why don’t we just add SSb and SSw to get a our variance number?
Because we are only interested low SSw and high SSb. Therefore a fraction is between
degrees of freedom needs to be corrected for.
How do you calculate variability using SSw and SSb?
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
F-distribution.
Made out of the F-values if the null was true. Positively skewed.
What are the key features of a one-way stat block.
F(df-SSb, df-SSw) = f-stat, p-value
Why don’t we run combinations of t-tests to see which group is sig’ different with ANOVA ?
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%
How do post-hoc tests keep family wise T1 error at 5%?
They adjust the p-values for the combinations t-test being run on ANOVA groups.
What are residuels also know as?
Within group variation (SSw)
What are residuels also know as?
Within group variation (SSw)
What is the output of a Kruskal-Wallis test, and why is it run?
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)
How are is varaibility different in two-way ANOVA?
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
How are is varaibility different in two-way ANOVA?
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
How does MSR differ from SSR?
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)
How is a two-way anova different from a one-way?
Two grouping variables.
(outcome ~ groupingV + groupingV2)
Variance.
Df correction.
How does does the output of a two-way ANOVA look?
SSb for each group. Residuels. df for SSb(G-1), df for SSr (N-R-C+1)
Why does an f-statisic differ when performing a one one- two-way ANOVA on the same grouping varaibles?
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.
What is an interaction effect.
The effect of factor A depends on what is going on with factor B
What is an interaction sum of sqaures (SSA:B).
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 .
What is eta^2?
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.
