Source: One-way ANOVA table; Creative Commons: http://commons.wikimedia.org/wiki/File:Pulse_Rate_Error_Bar_By_Exercise_Level.png, Two-way ANOVA table; Creative Commons: http://en.wikipedia.org/wiki/File:Two-way_ANOVA_data.png
This tutorial talks about one-way and two-way ANOVAs. With a one-way ANOVA, we're considering the population means based on one characteristic. So we're comparing three or more sample means for only one characteristic. So we're comparing the sample means for beats per minute based only on how often people exercise.
A two-way ANOVA, we're going to consider the population means based on multiple characteristics. So based on how people exercise and whether or not they are male or female, or how old they are, things like that. So we're looking across two different characteristics instead of just one.
Now this here is an example of a one-way ANOVA. Like I mentioned before, we're comparing the beats per minute, so how fast your pulse is rated, and how much you participate in the sport. So we're only looking across one category, so this is a one-way ANOVA.
Here, this would be a two-way because we're comparing across two categories. We're looking at whether or not the teams were playing home versus away, and whether or not they're in the American League or the National League. And so for each of those parts, we're comparing the variances between the samples and across the samples to start to draw some conclusions about how the National League and the American LEAGUE handle playing home and away. This has been your tutorial on one-way and two-way ANOVAs.
