Ch 26 - Follow-up tests and two-way ANOVA Flashcards
If that overall test showed statistical significance, then a detailed follow-up analysis can examine ____
all pair-wise parameter comparisons to define which parameters differ from which and by how much.
- pairwise multiple comparisons
Pairwise multiple comparisons among ___ groups are variants of the _____. However, ____
k
two-sample t procedures
1) they use the pooled standard deviation sp =√MSE
2) the pooled degrees of freedom DFE = N – k
3) they compensate for the multiple comparisons.
We can calculate simultaneous level C confidence intervals for all pairwise differences
(µi – µj) between population means:
m* depends on
1) the confidence level C
2) the number of populations k
3) the total number of observations N
Use technology or Table G
To carry out simultaneous Tukey tests of the hypotheses _____
H0: μi = μj
Ha: μi ≠ μj
0 NOT in CI - reject)
These tests have an overall significance level
no less than 1 − C.
That is, 1 − C is the probability that, when all of the population means are equal, any of the tests incorrectly rejects its null hypothesis.
In a two-way design
2 factors are studied in conjunction with the response variable.
There is thus two ways of organizing the data, as shown in a two-way table.
two way design
When the response variable is quantitative, the data are analyzed with____ A ____ is used instead if the response variable is categorical.
a two-way ANOVA procedure.
chi-square test
Advantages of a two-way ANOVA model
1) It is more efficient to study two factors at once than separately.
2) Including a second factor thought to influence the response variable helps reduce the residual variation in a model of the data.
3) Interactions between factors can be investigated.
Advantage of a two-way ANOVA model
It is more efficient to study two factors at once than separately.
Smaller samples sizes per condition are needed because the samples for all levels of factor B contribute to sampling for factor A.
Advantage of a two-way ANOVA model
Including a second factor thought to influence the response variable helps reduce the residual variation in a model of the data.
In a one-way ANOVA for factor A, any effect of factor B is assigned to the residual (“error” term). In a two-way ANOVA, both factors contribute to the fit part of the model.
Advantage of a two-way ANOVA model
Interactions between factors can be investigated.
The two-way ANOVA breaks down the fit part of the model between two main effects and an interaction effect.
We record a quantitative variable in a two-way design with
R levels of the row factor and C levels of the column factor.
The two-way ANOVA SRSs
have independent SRSs from each of R x C Normal populations. Sample sizes do not have to be identical (although some software only carry out the computations for equal sample sizes ó “balanced design”).
The two-way ANOVA all peramaters
are unknown.
The population means may be different but all populations have the same standard deviation σ.
(Two way ANOVA) Each factor is represented by a ____ : this is the ___
main effect
impact on the response variable of varying levels of that factor, regardless of the other factor (i.e., pooling together the levels of the other factor).
There are two main effects, one for each factor.
In two way ANOVA, the interaction of both factors is also studied and is described by the ____
interaction effect.
how much one variable impacts another variable
In two way ANOVA, when there is no clear interaction, the ____
main effects are enough to describe the data. In the presence of interaction,
the main effects could mask what is really going on with the data
Major types of two-way ANOVA outcomes
(two way anova) Two variables interact if
a particular combination of variables leads to results that would not be anticipated on the basis of the main effects of those variables.
(two way ANOVA) An interaction implies
that the effect of one variable differs depending on the level of another variable.
Interpreting 2 way ANOVA plots
A one-way ANOVA tests the following model of your data:
A two-way design breaks down the “fit” part of the model into more specific subcomponents, so that:
Main effects: ____
Interaction: ___
Error: ____
Main effects: P-value for factor R, P-value for factor C.
Interaction: P-value for the interacting effect of R and C.
Error: It represents the variability in the measurements within the groups. MSE is an unbiased estimate of the population variance s2.
