Can someone explain ɳ -squared?

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Can someone explain ɳ -squared?

In: Mathematics

Assuming we’re talking about the statistics thing in ANOVA-type analysis, the η^2 figure tells you how much of the variation in one thing is linked to another thing.

So, for example, let’s say we were looking at time of day and outside temperature.

Outside temperature varies quite a lot.

Some of that variation is linked to the time of day (it gets colder at night, warmer during the day).

But some of that variation is independent of time of day – caused by things like the time of year, where you are, the weather.

So the η^2 number for time of day, in relation to temperature, will tell you what proportion (or percentage, depending on how you set it up) of the variation in temperature can be explained by or is linked to the time of day. It gives you an idea of how well you could predict the temperature *just* given the time of day (and not any of those other factors).

Important disclaimer: an η^2 value doesn’t tell you anything about how the two things are linked, or what the causal relationship is. It is purely a statistical tool. It just tells you there is a statistical link, not if there is a causal link, or if there is a link whether it is direct or indirect, or which way it goes.

For example, you would get a non-0 η^2 value for the link between temperature and time of day; temperature helps predict the time of day, but obviously the temperature doesn’t *cause* the time to change.