7. Independent groups One Way ANOVA Flashcards
Why use an ANOVA?
To show whether there are differences among groups (IVS) on a variable of interest (DV) … do the means VARY?
What does an ANOVA compare a ratio of?
Systematic variance to Unsystematic variance (error)
In ANOVA speak what is Systematic variance and unsystematic variance written as?
Variance Between Groups
Variance Within Groups
What is the total mean of means called in an ANOVA?
The Grand Mean (the simplest model)
Why is the grand mean important in ANOVA?
The regression ANOVA model must be a sig. better fit than the grand mean
What does b0 represent in the regression line equation?
the coefficient of the intercept
What does b1 represent in the regression line equation?
the slop of the line
What happens as the coefficient of the regression line (b1) gets bigger?
The difference between the model and the mean gets bigger
When would we expect that the regression model is a better fit than the mean?
When the group means are sig. different
What is the grand mean represented as in the regression output?
The Total Sum of Squares
SST
(The Total Variance)
What is the variance from the model represented as in the regression output?
The Model Sum of Squares
SSM/B
(Variance Between Groups)
What is the residual variance represented as in the regression output?
Residual Sum of Squares
SSW
(Variance Within Groups)
What do we need to do in an ANOVA if we have more then 2 levels in a categorical IV?
Dummy code the levels to create new dummy variables
How many Dummy variables do you need?
1 less than the number of levels with a baseline variable of 0
(e.g. with 4 levels you would have 0, 1, 2, 3)
To create the dummy variables, how many times do you need to code them if you have four levels?
3 times… e.g. baseline (0) and dummy variable 1, then baseline (0) and DV2, then baseline (0) and DV3
CODED as 0 AND 1 each time (with the other non-used variables as 0 as well)
What does OLS stand for?
Ordinary Linear Squared (regression)
What are the degrees of freedom for SSB/M?
k - 1
k = number of groups
What are the degrees of freedom for SSW (error)?
N - k
(N = total sample size
k = number of groups)
What are the degrees of freedom for SST or Grand Mean?
N - 1
N = total sample size
How do you calculate the effect size for an ANOVA?
Take the square root of
Rsq = SSM / SST
= r (Cohen’s conventions)
What is the effect size normally reported as?
Eta squared (based on the SS sample not SS population = issue)
What should we used instead of Eta Squared?
Omega Squared
What is Omega Squared?
A less biased measurement of effect size
How is Omega Squared calculated?
ωSq (omega squared)
= SSB - (k - 1)*MeanSqSSW /
SST+MeanSqSSW
How is Omega Sq interpreted?
Using Cohen’s RSq conventions: 1%, 9%, 25%
What are the 2 ways you can test for group differences?
Planned comparisons (planned contrasts)
or
Post-hoc tests
What is the difference between using contrasts and post-hoc tests?
Contrasts = one-tailed for specific priori hypotheses Post-hoc = two-tailed for non directional hypotheses
What are the 5 rules for planned contrasts?
number of contrasts = k - 1
(e.g. 0 v. 1,2&3; 1 v. 2&3; 2 v. 3)
Orthogonal
if group not in contrast = 0
two chunks of variance contrasted
sum of weights = 0
(coefficients balance out e.g. if using 0 v.1,2,3 then 0 has a coefficient of 3 because it is being compared to 3 other variables with coefficients of 1: 1+1+1=3)
What does orthogonal mean?
Unrelated
Why do contrasts need to be orthogonal?
To compare two unique chunks of variance (t-tests)
What are the 5 options for testing planned contrasts and are they orthogonal or not?
Deviation (non-orthogonal). Simple (non-orthogonal).
Repeated (non-orthogonal).
Helmert (orthogonal).
Difference (orthogonal).
What does the deviation planned contrasts do?
Compares the effect of each group (except the first) to the overall experimental effect
2 v. (1, 2, 3, 4)
3 v. (1, 2, 3, 4)
4 v. (1,2, 3, 4)
What does the simple planned contrasts do?
Compares each category to the first category.
1 v. 2
1 v. 3
1 v. 4
What does the repeated planned contrasts do?
Compares each category (except the first) to the previous category
1 v. 2
2 v. 3
3 v. 4
What does the Helmert planned contrasts do?
Compares each category (except the last) to the mean effect of all subsequent categories
1 v. (2, 3, 4)
2 v. (3, 4)
3 v. 4
What does the difference planned contrasts do?
Compares each category (except the first) to the mean effect of all previous categories
4 v. (3, 2, 1)
3 v. (2, 1)
2 v. 1
How do you calculate t?
Mean Diff/ SE
What is the post-hoc process that looks for differences that might exist between groups called?
Data Mining
or
Data Snooping
What are the two types of error rates that are important in post-hoc tests?
Error rate per comparison (PC)
Family wise error rate (FW) … probability of containing Type I Error
What is Type I Error?
The incorrect rejection of the null hypothesis (a “false positive”: finding something that’s not there)
What is Type II Error?
The failure to reject a null hypothesis (a “false negative”: not finding something that’s there)
What is the most popular way to control the error rate in post-hoc tests?
Bonferroni Correction
What determines which post-hoc procedure you should use?
If groups have equal numbers
or
If groups have equal variance
What are the 6 types of post-hoc tests you can do?
Tukey HSD Bonferroni Levene's Gabriel Hochberg's GT2 Games-Howell Brown-Forsythe F
When should you use Tukey?
To compare differences among group means when:
Equal variances
Equal sample sizes
When should you use Levene’s test?
When testing the equality of group variances on the DV in an ANOVA
When should you use Brown-Forsythe F?
To compare differences among group means when: Unequal variances
When should you use Bonferroni?
To adjust for the error rate when multiple post-hoc tests are performed
When should you use Gabriel test?
Post-hoc test when comparing groups with:
Equal variances
Slightly different sizes
When should you use Hochberg’s GT2?
To compare differences among group means when:
Equal variances
Markedly different sizes
When should you use Games-Howell?
To compare differences among group means when: Unequal variances
What is the difference between post-hoc tests and contrasts?
Post-hoc = compare each group mean again each other group mean on DV Contrasts = comparing different pairs
What df do you use when reporting the t-tests for post-hoc tests?
Within Subjects: N - k
(N = total sample size
k = number of groups)
How many df do you need to report when reporting on t-tests?
1
How many degrees of freedom do you need to report when reporting F?
2
What can you use other than Bonferroni to correct for error rate?
Fisher’s LSD
What is the formula for the effect size of contrasts and comparisons?
sqrt (tsq / tsq +df)
(Using cohen’s r conventions)
Only computed for sig. contrasts/ comparisons
What are the 3 assumptions for an independent group ANOVA?
Normal distributions (6 sub checks) Homogeneity of variances (Non sig. Levene's) Independence
What are the 6 sub checks for normality?
Symmetry (Mean= medium = mode) Modality Skew Kurtosis Outliers 95%, 5%, 3% Non sig. S-W
How often does normality need to be checked in an independent groups ANOVA?
Once for each group/ level
Violations of normality are only problematic in an independent groups ANOVA if?
The populations are dramatically skewed
The populations are skewed in opposite directions from each other
Which Levene’s test do you read from?
“Based on Mean”
When is an independent groups ANOVA okay even when Levene’s is sig.?
When the largest variance isn’t more than 4x the smallest
AND
Sames sizes approach equal
What should you use if normality is violated in an independent groups ANOVA?
Kruskal-Wallis
Non-parametric test
What should you use if homogeneity of variance is violated in an independent groups ANOVA?
Brown-Forsythe
or
Welch F
What should you use if BOTH normality AND homogeneity of variance is violated in an independent groups ANOVA?
Kruskal-Wallis
Non-parametric test
What should you use if your design is oneIVwith3ormore
unrelated groups and one DV?
An Independent groups one-way ANOVA
What should you do if after running an Independent groups one-way ANOVA, you DON’T get a sig. F?
STOP
What should you do if after running an Independent groups one-way ANOVA, you GET a sig. F?
Planned contrasts (directional hypothesis) Post-hoc tests (non-directional hypothesis)
What post-hoc test should you use if you have equal groups and equal variance?
Tukey HSD
What post-hoc test should you use if you have unequal group sizes?
Gabriel
or
Hochberg’s
What post-hoc test should you use if you have unequal variances?
Games Howell
