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PWS 633 Midterm 2

Terms in this set (28)

When to use an ANOVA?
- when comparing the means of more than 2 groups
What is an ANOVA?
- analysis of means relative to variances
Multiple comparison problem
- when running multiple comparisons, just by chance you will have 5% of them be significant
- you can avoiv this problem by using an f-protected t-test (Tukey, BonFerroni)
Assumptions for ANOVAs
- normally distributed populations
- homoscedasticity (similar spread)
- independent samples (both within and
between groups)
F-test
- The test used to statistically evaluate the differences between the group means in ANOVA
- named for Fisher
- 2 different degrees of freedom:
- i-1 (i is the number of groups)
- n-1 (n is the total number of observations)
full model vs. reduced model
- the reduced model is a special case or restricted version of the full model
- the full model assumes that each group has a different mean (aka separate means model, assumes that Ha is true)
- the first reduced model is that all groups have the same mean (called the equal means model, assumes that Ho is true)
- get 2 separate sets of residuals (bigger residual for reduced model)
What are residuals?
- difference between actual value and predicted value based on the model
- there's a residual for each observation
Key point of residuals
If a model fits the data well, the residuals should be small - and things like the sum of squared residuals should be small
sum of squares residual
- Single summary of how well a model fits the data
- The reduced model will always have the larger residual sum of squares
Is the reduction in the residual sum of squares from the reduced model to the full model large enough that the extra complexity of the full model is worthwhile?
- use an F-test to figure this out
- F-stat must be compared to a table to get any sense out of it
random effects model
- The random effects model assumes that the groups are a random sample of a larger population AND THAT WE ARE INTERESTED IN THE LARGER
POPULATION
Fixed vs. random effects
1. Fixed effects: With fixed effects, the treatments are chosen by the experimenter.They are not a random subset of all possible treatments. (e.g., specific drug treatments, specific diets, season...)

2. Random effects: With random effects, the treatments are a random sample from all possible treatments. (e.g., family, location, ...)

***For single-factor ANOVAs, there is no difference in the statistics for fixed or random effects.
degrees of freedom
The number of individual scores that can vary without changing the sample mean. Statistically written as 'N-1' where N represents the number of subjects.
Residual sum of squares
the sum of each residual squared for all the observations in the sample. This reflects the amount of variation in the dependent variable not explained by the regression equation
PSEUDOREPLICATION AND THE DESIGN OF ECOLOGICAL FIELD EXPERIMENTS by Hurlbert
Pseudoreplication was disocvered to be happening in 47% of observational studies. They suggest ways to avoid this problem
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