Introduction to ANOVA Flashcards
What problems arise when multiple pairwise t-tests are used?
- computationally inefficient
- increases probability of type 1 error, known as ‘familywise error’
What is ANOVA?
ANalysis Of VAriance
- Statistical test designed for factors with more than two levels
What is one-way ANOVA?
One independent variable with more than two conditions
What is factorial ANOVA?
more than one independent variable
How is the F statistic calculated?
between groups variance (deviation of group means from grand/overall means)/ within-groups variance (deviation within each group from group mean)
Ideally, what should the between groups variance and within groups variance consist of?
between groups - treatment or condition effect plus measurement error
within groups - only measurement error
What are the 2 degrees of freedom in the F statistic?
- df of number of conditions
- df of number of participants in each condition
What are the assumptions of one-way ANOVA?
- interval/ratio scale
- normal distribution
- homogeneity of variance
How is between-subjects ANOVA used and how do you calculate the df?
- Compare different groups
- df(tot) = total number of measurements (N) - 1
- df (bet) = number of grups (nc) - 1
How is between subjects ANOVA reported?
F(dfbet, dftot) = F-value, p = (p-value)
When is within-subjects ANOVA used? What additional assumption must be made?
To compare observations from the same group
Sphericity, or the variances of the differences between conditions should be equal
How do you calculate the degrees of freedom for within-subjects ANOVA?
df (tot) = total measurements (N) -1
df (bet sub) = number of participants (np) -1
df (treat) = number of treatment conditions (nc) - 1
How is the F statistic for within subjects ANOVA calculated?
= between groups variance (treatment + error)/ within groups variance (error)
How is df (error) calculated?
= df(tot) - df(between sub) - df (treat)
How would you conduct t-tests without a specific hypothesis if the F value is significant?
- accepted post hoc tests such as Tukey’s HSD
- controls for familywise error
when do we use one-way ANOVA?
when there is one independent variable with more than two level
how to calculate the critical F value in excel?
=F.INV( )
The significant value changes from FALSE to TRUE depending on whether our computed F value exceeds the critical value.
what is F critical value?
it represents how much the variability among the means exceeds that expected due to chance. An F-statistic greater than the critical value is equivalent to a p-value less than alpha and both mean that you reject the null hypothesis
what does it mean to have the Levene’s test non-significant (i.e. with a p value greater than 0.05)?
the data variance is equal across groups.
how to report f value?
F(treatment or between-group df, within-groups (or error) df) = F-value (2 decimal place), p= p-value (3 decimal place)
why do we say the Bonferroni test is more conservative than the Turkey test?
The bonderroni test systematically produces larger p-values
can we chose one-tailed or two-tailed test in ANOVA?
No. ANOVA is always one-tailed. (i.e. the results are never directional). they merely tell us that there is a difference between one of our conditions and the other
what does the mauchy’s test of sphericity of covariance in SPSS output do?
this is testing the null hypothesis that our data possess sphericity of covariance. we want the p-value (under Sig.) to be non-significant (greater than 0.05) to proceed with ANOVA
what is a Kruskal-Wallis test?
it’s a between-subject ANOVA alternative that compare the sums of the groups’ ranks. If one group’s summed ranks value is much higher than the other groups’, the test returns a significant result.
how to report the results of Kruskal-Wallis test?
A K-W test found a/no significant difference between the groups, X^2(chi-squared)=… (2 decimal), p=… (3 decimal)
what is a Friedman test?
a within-subjects ANOVA alternative that compares the sums of treatment conditions’ ranks.
If one treatment condition’s summed ranks value is much higher than the other treatment conditions’, the test returns a significant result.
