Week 11 (ANOVA) Flashcards
What is ANOVA used for?
Testing hypotheses involving multiple means in a single test
What is the simplest ANOVA
One way ANOVA
One IV with two or more levels
What is the null hypothesis of ANOVA?
All means are equal
H0= u1 = u2 = u3
Rejecting this means some means differ
One way ANOVA partitions variance how?
Into several types Total variance: variance of all scores around grand mean Between-groups: variance due to the independent variable (MS between) Within groups (error): variance that is unaccounted for
What is the ANOVA statistic?
F
What are the assumptions of one way ANOVA?
Independence: each participant only contributes one score
Normality: data within groups should be normally distributed
Homogeneity of variance: variance of scores within groups should be equal for all groups
Absence of outliers
How is homogeneity of variance assessed in one way ANOVA?
Levene’s test
Based on p values
If p is not statistically significant do not reject the null
Concluding homogeneity of variance is still intact
And augment with Harley’s f Max test
What is Hartley’s f max test?
Tests homogeneity of variance assumption
Find group with either the largest and smallest SD or variance (SD^2)
Assume equal variance if:
SD^2 ratio = <4.0
SD critical ratio = 2
ANOVA involves calculating the sum of squares (SS). What does this mean?
It is a measure of variation or deviation from the mean. A summation of the squares of the differences from the mean. Considers both factors and error
What is the one way ANOVA SS equation?
SS total = SS between + SS within
What does SS total mean?
SS of squares of all scores from the grand mean
What does SS between mean?
SS of group means from grand mean
Reflects variance due to IV
What does SS within mean?
SS of individual scores about their group mean
Reflects variance due to error
What can be considered accountable for variability in one way ANOVA?
Differences among subjects (within group) - random variance
Effects of conditions (between groups) - variance due to condition
How do we calculate the F statistic?
F= MS between/MS within
If variance associated with IV is greater than random variance, F will exceed 1.0
How to write up a one way ANOVA?
Refer to statistical significance
Stats F(df,df) = x, p = .001
Means, SD and CI for each condition
Summarise results and suggestions
What is the issue with performing multiple t-tests?
Family-wise error rate
Increases the risk of type 1 error
Are procedures to control
Why shouldn’t you do ANOVA for 3 or more means?
It’s too ambiguous
What are conservative tests?
Multiple comparison tests that maximally control type 1 error (false positives) - only occurs 5% of the time
However increases the risk of type 2 errors
What are liberal tests?
Multiple comparison test
They reduce the risk of type 1 errors but not as much as conservative tests to
They have a greater statistical power to detect true effect
What is a bonferroni test?
Most conservative of all multiple comparison tests
Is simple and effective
Adjusts p value required for statistical significance by dividing desired alpha level by the number of tests performed
Only p values that are less than the adjusted p are considered significant
Adjustment is severe when many comparisons are required so best used when number of comparisons is small
What is Tukey’s honestly significant difference (HSD) test?
It is moderately conservative
Very popular
Required p value calculated using the studentised range stat
The test is performed by determining difference between means required for significance
Good when lots of comparisons to be made!
What is Fishers protected least significant difference test
Most liberal test
No adjustment to the p value
Controls type 1 error rate by requiring statistically significant ANOVA before interpreting- others do not require this.
Series of t tests but SE is calculated using all available groups
Use when ANOVA is significant and there are only 3 means
What is a repeated measures ANOVA?
Used when IV is a within-subjects factor (a repeated measure)
It’s an extension of paired samples t test for 3 or more conditions
