ANOVA – Midterm Review
21. Levene’s Test is simply a one-way ANOVA comparing the absolute deviations from the sample means.
*The null hypothesis of Levene’s test is that the deviations of scores from their group mean are equal for the populations represented in the associated samples.
*A high Levene statistic (and low Sig) indicates that the population deviations are not homogeneous.
22. Power analysis involves four interdependent concepts that give us the mnemonic BEAN:
B = beta error, where power = (1 – Beta error)
E = effect size
A = alpha error rate
N = sample size
23. Computation of effect size:
*A common error is to set the effect size at a value that is expected in the population rather than the minimum value that is considered meaningful.
*Failure to attain statistical significance does not necessarily mean that the study was underpowered.
*The sample size may have been large enough to have an acceptable probability of detecting a meaningful effect if it existed.
24. Blob Tests – when there are 3+ groups.
*The overall F-test doesn’t tell you ‘where’ the an observed significant difference is, only that there is one.
*It is generally better practice to focus on comparisons with df=1 in the numerator.
*Contrasts, including comparisons of two groups at a time, are generally better, because they will identify effects more clearly.
25. Dealing with Outliers
*Transform the data
*Determine whether it is a missing data point or coding error
*If legitimate, pull out of analysis and treat separately
*Winsorizing – some number (g) of scores in each tail are set equal to the next most extreme score (the g+1st score from the end)
*Trimming – discard some proportion of each tail
26. Compelling arguments against using equality of variance testing when deciding whether or not to use ANOVA
*ANOVA is little affected by small to moderate departures from homogeneity, especially if the sample sizes are equal or nearly equal
*The tests of homogeneity are more powerful for larger samples than smaller ones, but ANOVA is less affected by heterogeneity when samples are larger – so you end up being best positioned to find heterogeneity when it least matters
*Several of the most common tests are inaccurate for non-normal distributions
*Box: Testing for homogeneity before using ANOVA is like sending a rowboat out into the ocean to see if it’s calm enough for an ocean liner
27. “Triple Whammy” – when unequal within-group variances present a problem for ANOVA
*The variances are quite unequal (2:1 +)
*Sample sizes are quite unequal (2:1 +)
*At least one sample is small ( < 10 )
28. Skew
If n is large:
Skew = g1 =
Standard Error = se1 =
*For a normal distribution, g1 = 0
*Test Ho: skew = 0 by calculating z = g1 / se1
*Z > 1.96 => p < 0.05
*Skew < -1 or > 1 => may have outliers or is otherwise non-normal
29. Kurtosis
If n is large:
Kurtosis = g2 =
Standard Error = se2 =
*For a normal distribution, g2 = 0
*Test Ho: kurtosis = 0 by calculating z = g2 / se2
*Z > 1.96 => p < 0.05
*Kurtosis > 1 (leptokurtic) => may have outliers or is otherwise non-normal
*Kurtosis < -1 (platykurtic) => generally less of a concern
30. Skew and Kurtosis
*With large samples it is easy to find even trivially small levels
*Less problematic with large samples for common applications
*Skew = kurtosis = 0 does not mean that distribution is normal