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
What are the assumptions for a repeated measures ANOVA
Independence: scores for different participants must be independent
Normality: data within groups should be normally distributed
Sphericity: variance of scores within groups should be equal for all groups. Tested through levene’s test and/of F max <4.0
Absence of outliers
What is SSwithin-groups divided into in repeated measures ANOVA?
SS within subjects
SS between subjects
What is sphericity?
Sphericity is assumed in repeated measures ANOVA not homogeneity of variance
Requires equal variance for sets of difference scores
What are some critiques of repeated measures ANOVA?
Practice effects and sequence effects
What study design calls for a one way ANOVA?
DV is interval or ratio
IV is categorical with 3 or more levels
Hypotheses regard difference among means
What claims can be made with a statistically significant ANOVA?
There is a difference somewhere among the means. You don’t know which pairs differ significantly
How do we determine which pairs of means differ significantly in a one way ANOVA?
Multiple comparison tests can be performed
Do we make explicit statements about the null hypothesis when reporting ANOVA?
Not usually. Instead, frame statements and discussion of the results in terms of the alternative hypothesis that we are altering to support
What effect sizes are used for ANOVA?
ETA squared
Cohen’s d
What is eta square?
Eta squared is the proportion of variance associated with one or more main effects, errors or interactions in ANOVA.
How is cohens d calculated for ANOVA and what does it suggest?
It quantifies how large the difference is between a pair of means. Therefore important for comparisons among means.
Calculated using the effect size excel worksheet
What do we report in a one-way ANOVA if the homogeneity of variance assumption is violated?
Select Welch’s test and report this F-test instead of the standard f test
Does Jamovi provide confidence intervals for one-way ANOVA?
No it does not. Need to use the effect size worksheet
How do we calculate degrees of freedom for a between groups one way ANOVA?
Number of groups - 1
How do we calculate the degrees of freedom for a within groups one way ANOVA?
If group has 10 participants, 9 df (N-1)
If 5 groups, 45 df (9x5)
What does a larger F value mean for a one way ANOVA?
Greater probability that differences between the groups will be significant
How should we report the p value in a one way ANOVA?
A one-way between groups ANOVA revealed a significant effect of group…
What are the strengths of eta squared?
Weak/small: 0.01
Moderate: 0.06
Strong/large: 0.14
