Week 4 & 5 Flashcards
What is an ANOVA?
Statistical method to decide whether an observed difference in sample scores represents a “real” difference in the population…. vs. just sampling error, but with 3 or more groups/levels of 1 IV and or 2 or more IVs
What is the question asked in an ANOVA?
Are observed differences in whole set of means greater than would be expected by chance alone?
What statistic is looked at for ANOVA?
An f- statistic
What is an F-statistic?
The between group variability divided by the within group variability
What is the null hypothesis in the ANOVA?
All of the population means are even
What is the alternative hypothesis in the ANOVA?
At least one pair of samples is significantly different, but we don’t know which one
What are the basic assumptions for ANOVA?
- Samples are randomly drawn from populations
- Population is normally distributed
- Homogeneity of variance (roughly)
- Data from ratio or interval (i.e. continuous) scales
What does one need to be careful with when randomly drawing samples from the population?
Generalization
How can the normal distribution of a population be tested?
- Statistically
- Graphically
- Common sense
When is the homogeneity of variance especially important?
When there is an unequal group size
How is the homogeneity of variance usually tested?
Statistically
The types of ANOVA concern what…?
- Whether they are one way (1 IV) or multiple ways
- Whether the IV are between subjects(independent groups) or within subjects (repeated measure) or a mixed model
What is a mixed model?
Where there is 1 IV that is between subject and 1 IV that is within subjects
What are the types of ANOVA?
- One way ANOVA: independent samples
- Two way ANOVA: independent samples
- One way ANOVA: Repeated measures samples
- Two way ANOVA: Repeated measures samples
What is the characteristic of a one way ANOVA: independent variable?
1 IV with 3 or more levels
What does the result of an ANOVA show?
Whether or not there is a difference overall, but not where the difference is
What is the characteristic of a two way ANOVA: independent variable?
2 or more IV
What are the things you’re interested in when performing a two way ANOVA: independent variable?
- Main effect of IV A
- Main effect of IV B
- Main effect of IV A & B (interaction effect)
What is the interaction effect?
Saying that the scores across one of the IV depends on the levels of the other IV
It is really helpful to look at ____ when talking about interaction effects
It is really helpful to look at graphs when talking about interaction effects
What does it mean when the lines of an interaction effect graph are parallel?
There is no interaction
What does it mean when the lines of an interaction effect graph are not parallel?
There is an interaction
What is a disordinal interaction?
When the lines cross and significant main effects cannot be interpreted
What is an ordinal interaction?
When the lines don’t cross and significant main effects can be interpreted
The one way ANOVA: Repeated measures samples is more powerful that the independent ANOVA because ___
The one way ANOVA: Repeated measures samples is more powerful that the independent ANOVA because it has less error variance
What is the homogeneity of variance in the one way ANOVA: Repeated measures samples?
Sphericity
What is sphericity?
The homogeneity of variance of differences
How is sphericity tested?
Test with Mauchly’s Test of Sphericity
What is a non-significant finding of sphericity mean?
No difference in variance
If sphericity assumption is failed, what happens?
Use correction/adjusted p-value
What is a multiple comparison test used for?
To determine where the difference is
The multiple comparison test is also called the ____
The multiple comparison test is also called the pairwise comparisons
What are the different strategies of performing a multiple comparison test?
- Post-hoc
2. Planned comparison
When is a post-hoc performed?
Performed after ANOVA
___ multiple comparison strategy is the most common
Post-hoc multiple comparison strategy is the most common
The post hoc test ___ and therefore are exploratory
The post hoc test every difference and therefore are exploratory
When is a planned comparison performed?
Performed instead of ANOVA (a priori)
What does a planned comparison focus on?
Focused only on specific comparisons
How do you calculate the family wise type 1 error rate that is used for the one way ANOVA?
Add up all the alpha values
When the family wise type 1 error rate is too high, what do you do?
A Bonferroni Correction can be done
How is a Bonferroni Correction done?
Divide alpha by the number of statistical tests to be performed and use that for each post hoc test
What is the downside to the Bonferroni Correction?
Because it has less power and a higher chance of a type 1 error, must balance risk of Type 1 and Type 2 error
What are the types of post hoc test to perform in the order of least conservative/most likely to find a significant difference?
- Fisher’s least significant difference
- Duncan multiple range test
- Newman-Keuls method
- Tukey’s honestly significance difference
- Bonferroni t-test
- Scheffe’s comparison
What are the post-hoc test that are performed the most?
- Fisher’s least significant difference
- Tukey’s honestly significance difference
- Bonferroni t-test
What is the Fisher’s least significant difference test?
Essentially and unadjusted t-tes (LSD)
Why is the Tukey’s honestly significance difference important?
“Middle of the road” in
terms of risk and most
commonly used
What does the Bonferroni t-test do?
Simply divides α by # of
comparisons
When is the Fisher’s least significant difference test, Tukey’s honestly significance difference important, and Bonferroni t-test suitable for use?
When an independent groups type test is being performed
What are the multiple comparison test to be used for repeated measures?
- LSD
- SIdak
- Bonferoni correction
LSD is an _____
LSD is an unadjusted paired t-test
Sidak is ___
Sidak is adjusted, but good balance of type 1 & type 2 error protection
The LSD test has a high risk of ___, type 1 error meaning it is less conservative
The LSD test has a high risk of high, type 1 error meaning it is less conservative
The bonferoni correction test has a high risk of ___ error and is more conservative
The bonferoni correction test has a high risk of type 2 error and is more conservative
What is an ANCOVA?
(Analysis of covariance) is a statistical technique that is used when you cannot control a variable through research design and sampling
What does the ANCOVA do?
It statistically adjust the dependent variable based on the covariate
ANCOVA produces ____
ANCOVA produces adjusted means
ANCOVA is a combination of ___ and _____
ANCOVA is a combination of ANOVA and linear regression
What are the assumptions of ANCOVA?
- Usual parametric assumptions
- Linear relationship between CoV and DV (with r>.6)
- Homogeneity of slopes
You can also use ANCOVA to adjust for ____ scores
You can also use ANCOVA to adjust for baseline scores
