1st ANOVA lecture: 1-way ANOVA and post-hoc testing Flashcards
When to use ANOVA
When you want to compare the mean of a continuous DV between more than 2 groups on a single categorical IV
When you want to compare the mean of a continuous DV between 2 or more groups on 2 or more categorical IVs.
F-ratio
Statistic that tells you how much variability in results is accounted for by ANOVA and how much by RV (random variability). Tells you if the main effect is statistically significant.
F-ratio = Mean squares (model)/mean squares (residual error)
If F-ratio is significant then further exploration of that IV is appropriate.
Levene’s test
For homogeneity of variance. Used in Independent groups ANOVAs.
Mauchly’s test of sphericity
Used in repeated measures ANOVAs to check the variance of each IV level is similar (and covariance between pairs of levels is also similar). Equivalent of homogeneity of variance for independent groups.
DV must be on an:
a) categorical scale
b) interval scale
c) continuous scale
d) b and c
d) DV must be on a continuous and interval scale meaning there is an equal distance between variables.
What is meant by independent sampling?
Each participant can’t have had prior knowledge or have been influenced by another participant in the group (each participant’s performance is independent from each others). This is one of the assumptions of an ANOVA.
What are the 3 assumptions common to both independent groups ANOVAs and repeated measures ANOVAs?
- Independent sampling
- DV on an interval scale
- Normally distributed data within levels
What is a Kolmogorov-Smirnov test?
A nonparemetric test for the equality of continuous, one-dimensional distributions that can be used to compare a sample with a reference probability distribution (ie: tests whether distribution normal). Don’t want this to be significant.
Kurtosis
The sharpness of the peak of a frequency-distribution curve.
Skewness
A measure of the assymetry of a probability distribution about the mean.
If the right tail is longer the skew is…
Positive. The distribution is concentrated on the left side.
What is the difference between the way you would input data for independent groups on SPSS compared with repeated measures?
In independent groups the levels of the IV are nested within the same column. In repeated measures the levels are separated into different columns.
If p>.05 on Levenne’s test what does this mean?
Equal variances can be assumed.
What does SSR refer to?
The variability not explained by the IV.
What are the benefits and limitations of p being less than 0.05?
Benefits: tells you that some variability in the sample is systematically explained by the IV and is likely to be replicated in the population.
Limitations: does not tell you size of this effect.
Whether the result is clinically significant depends on:
a) The p value or
b) The effect size
b) the effect size
Which is a better estimate of effect size?
a) Eta squared or
b) Omega squared
Omega squared. It adjusts for random error so provides a more accurate estimate of the likely effect size in the population.
What is partial Eta Squared?
Proportion of variance uniquely explained by the variable. Used for calculating effect size in repeated measures ANOVA. However, omega squared is still recommended over this even though the calculation is not available on SPSS.
What is meant by the family-wise error rate?
An increased number of paired comparisons mean the 1/20 risk each time adds up to increase the risk of a type 1 error being made.
What is a type 1 error?
Falsely rejecting the null hypothesis when it is true.
What is the Bonferonni correction?
Work out how many pairwise comparisons you are going to do and divide the significance value by these. to reduce the risk of making errors.
The best post-hoc test(/s) when all assumptions are met:
REGWQ or Tukey. Tukey useful when making lots of comparisons.
When taking a conservative approach and making few comparisons this is the best post-hoc test to use:
Bonferonni
When taking a conservative approach and making many comparisons this is the best post-hoc test to use:
Tukey
Post hoc tests to use when conditions have unequal sample sizes:
Gabriel’s or Hochberg’s GT2
Post hoc test to use when conditions have unequal variances and sample sizes:
Games-Howell
Planned contrasts is used when…
we are only interested in making 1 or 2 comparisons that are hypothesis driven. This has the ideal balance between reducing risk of type 1 and 2 error (as corrections have a risk of type 2 error).
