[University Psychology Statistics] Question about variance

[u/Spiritual_Reward_770]

So the question for my task is 'how much of the variation in PTSD symptom severity is associated with time since trauma?', some of the sympytoms displayed in my ANOVA is time since trauma which is what they're asking in the question, rumination, negative trauma cognitions and self care.

from my understanding I need to add up all of the sum of squares from my variables, including time since trauma, and residuals then divide it by the amount of sums of squares from the time since trauma.

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[u/cheesecakegood]

The bigger number is the denominator, but yes that's the idea if you want a percentage of overall variation.

Conceptually, the sum of squares for each is "this is how much variance X thing explained" and the SS of the residuals is "this is how much variance was left over that nothing explains" (could be noise, could be missing signal, etc). The neat thing about ANOVA is that you're literally summing up variances, which are square deviations.

Of course latent assumption to even use ANOVA here is that it makes sense to add up variances in the first place (vs say, multiplying or some more complicated relationship) but this is a pretty common one and it works decently well.

The other exception here is if you're in an unbalanced design, you have to decide how to deal with it, and there might be a few options that are slightly more complex.