When do we use a one way ANOVA?
When comparing 3+ groups on a continuous variable
Between subjects ANOVA
comparing pre-existing groups (i.e. freshman, sophomore, junior, senior)
or with a between-subjects design with 3+ groups
repeated measures ANOVA
comparing changes across 3+ timepoints
or with a within-subjects experiment with 3+ groups
statistical validity of a one way ANOVA
effect size, confidence interval, statistical significance
effect size for a one way ANOVA
magnitude of difference between groups (eta-squared)
small effect = .01
moderate effect = .06
large effect = .14
assumptions of between-subjects one way ANOVA
independence, levels of measurement, normality, homogeneity of variance
assumption of independence
IV has 2+ separate, discrete groups
assumption of levels of measurement
DV must be continuous
assumption of normality
DV must be normally distributed at all levels of IV
assumption of homogeneity of variance
variance of all groups should roughly be equal
assumption of repeated measures one way ANOVA
multiple observations, levels of measurement, normality, sphericity
assumption of multiple observations
each participant must have exactly 2+ data points for the DV
assumption of levels of measurement
DV must be continuous
assumption of normality
DV must be normally distributed (visualized via Q-Q plot)
what is a Q-Q plot?
plots data points for a repeated measures ANOVA. the closer the dots follow a linear pattern, the more normal the data is
assumption of sphericity
variances of differences between all timepoints must be equal
purpose of post-hoc tests in one way ANOVAs
ANOVAs only tell you if there are differences between groups. post-hoc tests allow you to determine which groups are different. allows for multiple observations
it reports a p-value for comparisons between groups. lower p-values indicate that the groups are significantly different
types of post-hoc tests
LSD: least significant difference
Tukey’s HSD: honest significant difference (most used)
Bonferroni Correction
how to report a between subjects one way ANOVA
F(dfbetween, dfwithin) = x.xx, p = .xxx, η2 = .xx.
We found a significant effect of letter type on money donated to charity, F(2, 194) = 5.01, p < .001, η2 = .10. Tukey HSD post-hoc tests indicate that participants who wrote a gratitude letter donated significantly more money compared to those who wrote a business letter (p < .001, d =.80) or ordinary letter to a friend (p = .023, d = .52). The business letter and ordinary letter conditions did not significantly differ from each other (p = .765, d = .05).
how to report a repeated measures one way ANOVA
F(dfbetween, dfwithin) = x.xx, p = .xxx, η2 = .xx
There was a significant effect of group size on taste ratings, F(2, 102) = 2.24, p = .045, η2 = .05. Tukey HSD tests indicated that participants rated the chocolate as tasting best when in a large group compared to a small group (p = .030) or alone (p < .001).
