Two-way ANOVA by hand

In this video third video about two-way ANOVA, we will see how to calculate a two-way ANOVA (between-between) by hand so that we fully understand the ANOVA table. We will calculate the group means, grand mean, sum of squares within, between and for the interaction, degrees of freedom, F-ratios and p-values.

[SK-rjti]

Very nice video, sir! However, I would put the emphasis on the principle, not the procedure. Show your students the "model" of the two-way anova. How one number "grows" from another depending on signal(s) and noise. Global mean -> Factor mean(s) -> Group mean(s) -> Individual numbers. For example, put together an Excel spreadsheet where each datapoint is first represented by the global mean (as a column). Then add a column where each datapoint is represented by the corresponding "group mean". That's actually the last step in "number evolution". But this will be your important reference for "noise". Then add a column where each datapoint is represented by the corresponding "temperature mean" (effect of one factor). That's your signal number 1. Then add a column where each datapoint is represented by the corresponding "watering mean" (effect of the second factor). That's your signal number 2. When you have these equally-sized (!) columns ready, calculate the SS for: (A) raw data vs global mean (total variation), (B) raw data vs group means (noise); (C) temp means vs global mean (signal 1), (D) water means vs global mean (signal 2). As for the interaction, admittedly, the formula is not very intuitive. I would approach this differently by asking: How much SS and DF remains unaccounted for from the "signal" and "noise" comparisons if we consider the two factors separately? Okay, this much and this much... This is called interaction... This is what it means...Etc... This topic is tough, of course, but it can be broken down into simpler, more intuitive blocks. It's not just a cooking recipe. Students need to understand what "salt" and "pepper" are, so to speak. Of course, this is just a suggestion. Everyone is free to teach the way they see fit. Again, thank you for your thought-provoking video, sir!

[RealMcDudu]

Great video! Why do we need the SST? We didn't use it, at least not in this video.

[melissaann]

Hi! Why do we use the a or b value of the opposite group we are evaluating when calculating the sum of squares between groups? For example, there are 3 temperature groups, you used the b value of 2 for high vs. low watering for the SSB for temperature group differences. Thanks for the help! great video!

[StonedApeMonk]

How would we calculate SSerror when we have standard deviation for each group, but not individual points?

[abbasatashdehghan]

Thank you for the video; it was quite useful. How should we have computed the anova if the design was not balanced?

[antygona-iqew]

Impossible to not make a mistake when calculating this by hand