Week 3: One-way ANOVA

• When we have one IV with three or more levels and different participants undergo different treatments, we employ a one-way independent ANOVA
• One-way ANOVA means there is only one IV
• A one-way ANOVA can be used:

  • To compare the means of two or more groups
  • When the DV is numerical and the IV is categorical
• The related one-way ANOVA allows us to explore the effects of a single IV on a DV across a number of experimental conditions where the same participants undergo the different experimental conditions.
• Homogeneity of Variance is the assumption that data is equally spread within each group (only for between-groups design)
• If the IV groups are roughly of equal size, ANOVA is regarded as being robust in regard to violations of normality and homogeneity of variance.
• If we have met the assumption of normality, but not the assumption of homogeneity of variance, we report the Welch statistic
• If we have violated both the assumptions of normality and homogeneity of variance, we report the Brown-Forsythe statistics.
• To meet the assumption of normality, you would need normally distributed data
• To meet the assumption of homogeneity of variance, the p value for the Levene test has to be greater than .05
• The Levene Test tests whether there is significant difference in variances across all groups.
• independent t-test:

  • Both samples come from normally distributed populations
  • IV is categoric, DV is interval
  • Independent random sampling
• Paired t-test

  • Within subjects
  • Matched pairs
  • One value in each sample can be meaningfully paired with value in another sample.
  • DV at least interval level of data
• Related one-way ANOVA allows us to explore the effects of a single IV, on a DV across a number of experimental conditions where the same participants undergo different experimental conditions
• Homogeneity of variance is an assumption of the variance of the independent samples t-test and ANOVA stating that all comparison groups have the same variance. We want the significance here to be above 0.05 to assume homogeneity of variance.
• Once the ANOVA has identified a significant difference between the group means, if there are more than two levels of the IV, post-hoc tests are needed to explore pattern of significant differences.
• ANOVA indicates that there is a significant difference between treatment means, but does not indicate which combination of means significantly differ.
• Post-hoc tests control for the likelihood of making a type I error.
• Bonferroni correction formula = .05 / # of comparisons
• The Bonferroni correction is a method of adjusting p values so that they remain conservative even when multiple comparisons are made. It involves dividing the alpha level by the number of comparisons being made. This reduces the risk of making type 1 errors (false positives).
• Post hoc test is used when we know that there is a significant difference between the mean scores of our treatments, but do not know which specific pair(s) of means differed significantly.
• One-way repeated ANOVA has one added assumption: sphericity
• There should be sphericity, the differences in scores between two conditions are the same as the difference in scores for any other two conditions
• For repeated measures ANOVA, if we have met all of our parametric assumptions, we report the statistics from the sphericity assumed row.
• If we violate the assumption of sphericity, then we need to use a more conservative approach called Greenhouse Geisser epsilon (ε)