Module 4: Multiple Levels of IVs Flashcards
What is a single-factor experiment?
An experiment with one independent variable with multiple conditions/levels
Also known as a one-way ANOVA
What is a two-factor experiment?
An experiment with two independent variables with multiple conditions/levels
Also known as a two-way ANOVA
State the null hypothesis of a one-way ANOVA
All mean levels of the independent variable are equal H0:µ1=µ2=µ3=µ3
State the alternative hypothesis of a one-way ANOVA
At least one mean level is different from the others
For the t-test calculations, the means are inputted into the calculation whereas in the ANOVA calculation, means are not inputted ____________ are instead
Variances
In ANOVA we assess….
The amount of variability and explain source of the variability
If we compare a single score drawn from each of two conditions (between treatments variability) the two scores may vary due to… (3 reasons)
- Treatment effect
- Individual differences
- Experimental error
If we compare two scores drawn from the same condition (within treatments variability) the scores may vary due to… (2 reasons)
- Individual differences
2. Experimental error
Why do we not need to worry about treatment effects in within treatment designs?
Treatment effect is a constant within conditions
Conceptually the F ratio is defined as…
The ratio of the variance in the scores
f = between subjects variability / within subjects variability
Factors that influence F ratio to be larger?
- Large treatment effect
- Small values for individual differences and experimental error
Denominator of the F-test
Measures unsystematic variability in scores (i.e., individual differences and experimental error)
Numerator of the F-test
Measures same unsystematic variability in scores AND systematic variability (i.e., treatment effects)
If the null hypothesis is true…
The variance associated with treatment effects should be zero or nearly equal to 1
If the null is false…
The variance associated with treatment effects should be larger than 1
Analysis of variability involves two parts:
- Analysis of sums of squares (SS)
2. Analysis of degrees of freedom (df)
A posteriori tests aka post hoc tests
Follow-up tests that are not based on prior planning or clear hypotheses
Only considered when the F-test is significance
A priori tests aka planned tests
Planned or theoretically driven follow-up tests
Family-wise error
Cumulative likelihood of making a type I error
Post hoc tests control for this error
The more post hoc tests hold down the family-wise error, the more ____ also goes down
Power (likelihood of making a type II error increases)
Least Significant Difference (LSD)
Common post hoc test
Does not control for family-wise error
Planned contrast
Specifying a very specific comparison based on research question
In a planned contrast, comparisons are specified by the _________ ___________
Contrast weights
Contrast weights must sum to…
Zero
Non-orthogonal contrasts
Results of contrasts overlap and are NOT independent of one another
Orthogonal contrasts
The results of one contrast are completely independent of the other
Bonferroni adjustment
Not necessarily a post hoc test, rather an adjustment to alpha depending on number of comparisons
Alpha / number of comparisons
Going beyond 3 or 4 comparisons will make power very poor
Tukey’s HSD
Common post-hoc test
Tests all pairwise comparisons while controlling for family-wise error
Good when testing lots of comparisons
