One-way & Factorial ANOVAs Flashcards
What are the two types of error?
- *Type I**
- We reject the null hypothesis when the null hypothesis is actually correct (false positive)
- i.e. conclude from our sample that there is a significant difference when for our population there would be no difference
Type II
- We fail to reject the null hypothesis when the null hypothesis is incorrect (false negative)
- i.e. conclude from our sample that the difference is not significant when for our population there actually is a difference
What is the uses and assumptions of a between-group ANOVA?
Establish the difference between two or more independent samples drawn from a population
Assumptions:
Population from which the samples are drawn is normally distributed (Shapiro-Wilk)
Homogeneity of variances
- All groups should have data that are equally spread out around mean (Levene’s Test)
Scores in all the groups are independent
- e.g. Groups are mutually exclusive
Data are either interval or ratio
- ANOVA is a parametric test so data must have both magnitude and scale
What is the test statistic and null hypothesis of an ANOVA?
F-statistic, Null Hypothesis= 1=2=3=4….
Therefore, reject difference between at least one pair of means is big enough
What is the degrees of freedom in an ANOVA?
Between-group is Level of the group (K) -1
Within-group is total sample (N) - k
If you know that your ANOVA is significant what do you do next to test significance?
Post-hoc test, Tukey’s honestly significant difference (HSD)
What are the 4 steps in interpreting a anova?
- Statement of what type of test was conducted, what the independent and
dependent variables were (typically done in methods section of a paper)
- Describe whether the ANOVA itself was significant or not significant, provide relevant statistical information (F, dfB, dfE, p)
- If ANOVA was significant, report post-hoc test results (include p-value in brackets)
- Interpret the statistical results relating back to the question of interest (e.g. if significant, go back and look at means to provide specific direction of difference)
What is Eta-squared and what is it used to calculate?
Ratio of treatment variance (effect of independent variable) and total variance (effect of independent variable and confounding variables)
n2= SSb/SSt
n2 can vary between 0.00 and 1.00
i.e. if n2 = 0.6, then 60% of variance attributed to independent variable
What is the n2 implied strength?
N2
0 – 0.1 0.1 to 0.3 0.3 – 0.5 >0.5
Implied Strength
Weak effect Modest effect Moderate Strong
What is a repeated-measures ANOVA used for and its 3 assumptions?
Establish the difference between two or more levels of an independent variable when each level is assessed in the same group of individuals
Assumptions:
Population from which the samples are drawn is normally distributed
Data are either interval or ratio
ANOVA is a parametric test so data must have both magnitude and scale
Sphericity (Mauchly test)
Variance of difference scores is equivalent across all time point
What is the advantage of repeated measures vs between groups?
A repeated measures test, means we can remove the duplicated unexplained variance
How does removing the duplicated unexplained variance in a repeated measures ANOVA change the likelihood of getting a significant result?
It would increase the likelihood of significance
How to calculate degrees of freedom for Repeated ANOVA?
dfB = k-1
dfe = (k-1)(N-1)
How do you lower the probability of making Type I error in repeated measures ANOVA?
We counteract the probability of making a Type I error by reducing the df
What is the Bonferroni and what is it used for?
adjust p-value based upon number of planned comparisons
Bonferroni p = alpha/ # of planned comparisons
Modified Bonferroni p = # of level x a/ # of planned comparisons
What is the effect on the probability of making a Type I error if you run a repeated measures ANOVA when the groups are mutually exclusive (i.e. should have run a between groups ANOVA)?
You would increase the probability because you are removing variance
4 way mixed measures ANOVA
