Psych Stats Exam #3 Flashcards
What is ANOVA used for?
Comparing more than two means (i.e. 3+ levels of an IV)
Pros and cons of within groups design
pro: reduced variability within participants
con: participants may figure out the experiment and change behavior
Why don’t we just do a bunch of t-tests?
The false alarm rate (finding an effect that is not there, type I error) becomes extremely high
- have to multiply probability for each test (95% CI = 5% false alarm x 3 tests = 0.95 x 0.95 x 0.95 = 85% CI, 15% error)
What does ANOVA stand for?
analysis of variance
Looking for overall significant differences (One way ANOVA)
look for omnibus anova: see if there is a difference
- compare p to alpha to do this
- if there is a difference: run post hoc testing
- no difference: you are done, fail to reject the null
Post hoc tests (one way ANOVA)
tells us which specific conditions are statistically different
F statistic
ANOVA: same logic as NHST – testing against sampling dsitribution to see how unlikely / likely your results are
- use F distribution
effect size for ANOVA
eta squared (η2)
Eta squared cutoffs
0.01 = small effect
0.06 = medium effect
0.14 = large effect
F distribution
one tailed - rejection region is only in one of the tails
Measures of degrees of freedom in ANOVA
1) df between group
2) df within group
F statistic formula
F = (between group variance) / (within group variance)
Between group variance
- the variance from our IV (difference from manipulation)
Grand mean: mean of all the data - found by averaging each condition means
- between condition mean: measures how much the condition means differ from the grand mean
- “MS between” + “condition”
- large: more likely to reject the null hypothesis
Within group variance
variability not due to our manipulation (individual differences, error)
- small: more likely to reject null (want less error)
expected value under F statistic
1 (if it is 1, we fail to reject the null hypothesis)
Writing an Omnibus Anova
Overall: there is/is not an effect of the IV on the DV (F stat, p, eta squared)
Writing Post hoc tests
Condition A (M, SD) showed higher / lower levels of DV then condition B (M, SD) (t, p , d)
- For ALL comparisons
Degrees of freedom between (one way between groups ANOVA)
- first number
- conditions in the study minus 1
Degrees of freedom within (one way between groups ANOVA)
- second (usually larger) number
- participants in each condition - # of conditions
Assumptions of ANOVA
1) DV is scale
2) IV is nominal / ordinal
3) homogeneity of variances
4) DV is normally distributed in population
Homogeneity of Variances
the amount of variability within each condition should be similar across all conditions
- check this: if the p value is less than alpha, you have to run a correction
calculating residual (MS within)
sum of squares (within) / degrees of freedom (within)
calculating condition (MS between)
sum of squares (between) / degrees of freedom (between)
If you have more between condition variance…
you are more likely to reject the null (as experiment had more influence on the difference you saw)
Within condition study allows researchers to…
more likely to find an effect if one exists (more power) - less participant variance
Within groups ANOVA degrees of freedom
1) Df between
2) Df within
Df between (one-way repeated measures ANOVA)
of conditions-1
- same as between groups ANOVA
Df within (one-way repeated measures ANOVA)
(conditions-1) * (participants -1)
- Different from between groups ANOVA
Factorial ANOVA
2+ independent variables each with 2+ levels
- used to see an interaction
Interaction definition
when the effect of one independent variable depends on the other independent variable
Main effect
the effect of one IV by ignoring/averaging the other IV
- calculated using marginal means
Marginal Means
the mean for one level of the IV (down a column or across a row)
- used to find main effects
Simple Effect
the effect of one IV at a specific level of the other IV
- found by looking across each row (or down each column) and seeing if there is a difference
How to identify an interaction
Compare simple effects: see if they differ in effect size (magnitude) or direction
Quantitative interaction
difference in effect size not direction
Qualitative interaction
difference in direction not effect size
Can you have no main effects and still a qualitative interaction
YES
When to use a t-test
- 1 nominal IV (2 levels)
- Scale DV
- independent or paired samples
When to use a One-way ANOVA
- 1 nominal IV (3+ levels)
- Scale DV
- Between groups or repeated measures
Factorial ANOVA
- 2+ nominal IV (2+ levels)
- Scale DV
- Between groups, repeated measures, or mixed design
What does a 2x2x3 design mean?
there are 3 independent variables, the first with 2 levels, the second with 2 levels and the third with three levels
Write up example for interaction
“The effect on test performance of using a mnemonic device changes depending on whether or not the student was trained in mnemonic use: mnemonic use improves test performance with and without training but is more beneficial with training than without”
3 Patterns of an interaction
1) An effect is larger at one level than the other, but they are in the same direction
2) An effect is present at one level but not the other (i.e. one simple effect is null)
3) An effect is reversed at one level compared to the other (i.e. the simple effects are in opposite directions)
Number of simple and main effects in a 2x2 interaction
- 2 main effects
- 4 simple effects
Manual Bonferroni correction:
We run multiple sets of t-tests then we divide our original alpha by the number of post hoc tests we ran
ex: If 2 post hoc tests and original alpha of 0.05
- 0.05/2 = 0.025 → this becomes a new alpha that we compare the p values of the t-test to this
