## How strong would you rate the association between this nominal predictor variable and continuous response variable?

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I've yet to find an easy-to-understand and easy-to-implement way to statistically model the strength of association between nominal data and continuous data. So I'm trying to get a rough idea visually with box plots ordered by mean or median.

For example:

There is a lot of overlap, but to a novice like myself, there is at least an upward trend. However, it's hard for me to rate the strength of the trend.

On the other hand, I've got this plot where where the separation between the boxes is mostly quite distinct, and I'm unafraid to say, "Yes! that's pretty strong association!":

I know the data here is ordinal, but it's just for contrast to the other chart.

Thanks!