Section #3 for Midterm Flashcards
ANOVA use and non-parametric alternative
For continuous data from 3 or more groups (analysis of variance)
Non-parametric alternative is Kruskal-Wallis test
F-test
df in F-test
for ANOVA: (variation between means)/(variation within means)
rejects H0 when variability between groups > variability within groups
Large ratio → significant p-value
df1 = k - 1
df2 = n - k
Assumptions in ANOVA
Normally distributed variable
Errors are normally distributed (compares actual with expected, tbd in regressions)
Cases are independent
Variance homogeneity (without this you CANNOT use ANOVA) → Levene’s test
- Robust with minor violations of assumptions
ANOVA means plot
gives an idea of relationships between groups without significance
How to report ANOVA means
Mean ± SD, F(df1, df2) = #, p = #
Post-Hoc Tests
How it changes power
Following ANOVA - multiple comparison tests to determine which means differ significantly
Tukey’s (common)
Least squared difference (LSD)
Dunnett’s
Bonferroni (strict)
More tests done ↓ power - ↑ likelihood of finding something which correlates (AKA family-wise error)
Can be corrected for by reducing p-value cutoff
Factors for: One-way ANOVA, repeated measures, MANOVA, factorial and ANCOVA
One-way: 1 independent, 1 dependent w/ independent groups
Repeated measures: 1 independent, 1 dependent w/ dependent groups over time
MANOVA: 1 independent, 2+ dependent w/ independent groups
Factorial: 2+ independent, 1 dependent w/ independent groups
ANCOVA: covariables
Repeated measures one-way ANOVA:
considers dependency between multiple measurements
If were to compare two groups before and after → t test, but if the effect of time is added, becomes a repeated measure ANOVA
MANOVA
Benefits and drawbacks
MANOVA has predictor (independent)-outcome (dependent) dynamic
Benefits: Can protect against type I error (⍺)
- Combination can better represent phenomenon than individual factors
- May reveal differences ANOVA does not catch
Drawbacks:
- Complicated
- Loss of df with each dependent variable included
Factorial:
Effect of 2+ factors on an outcome
2x2 factorial design
Interactions between factors could demonstrate emergent outcomes
Parallel implies no interaction, but large slope implies eventual interaction
Interaction factor an be insignificant while individual factors are significant
Two-way ANOVA most common
ANCOVA benefits
Control for effects of other relevant variables
Mitigate confounding variables
Chi-squared test of independence:
Test for significant association between 2+ categorical variables
Goodness of fit test between observed and expected values (if there were an association….etc)
df = k -1
Uses cross-tabulation table (2xk table for number of groups)
If significant → make graph to visualize group differences because test does not specific which differences are significant
Assumptions for Chi-squared test
Variables are ordinal or nominal
Groups are independent
- Other use McNemar for dependent groups
Expected count >5 –>
Expected count less than 5 indicates use of Fisher’s exact test instead
Test for Trend theory
Linear by linear association: Best for ordinal data
Tests for trends in contingency table >2x2 using odds (not probability)
Assumes: change in rank does not affect odds
df = 1
Odds are 1/5 - will either get 1 or one of the other 5
Shows association ≠ difference
