I can't stop looking at the data from this retracted university exam ceiling height paper. Unrelated to ceiling height, I found this interesting nonlinear fit for exam score versus coursework score. #dataviz www.sciencedirect.com/science/arti... - ThreadSky

xangregg.bsky.social • 86 days ago

I can't stop looking at the data from this retracted university exam ceiling height paper. Unrelated to ceiling height, I found this interesting nonlinear fit for exam score versus coursework score. #dataviz https://www.sciencedirect.com/science/article/pii/S0272494424001403

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leecreighton.com•86 days ago

I want to look at the density of the points to think about whether the points outside of the main cloud do enough to support the nonlinear fit (vs only a linear fit using scores over 50 or so). Maybe also a Principal Components analysis?

danz68.bsky.social•85 days ago

I can't really see a functional relationship (not really predictable).

However, the visible ellipse rather shows (kind of) a statistical dependency, but only if the range calculated scales dont foul us (if that would be a circle it would be no dependency).

danz68.bsky.social•85 days ago

I would love to see some isodensity or probability contours on this dataset with adjusted scales based on that. I would not filter out anything, I would just rescale the axis based on the ratio of, say, 90% probability ranges.

xangregg.bsky.social•85 days ago

Not sure what you mean about rescaling the axes, but here are density contours on isometric x/y scaling.

danz68.bsky.social•85 days ago

In a scatterplot, the visual shape of the distribution (ellipse or circle) is influenced by the scaling of the axes. Adjusting the scales can transform a 0 or 90deg oriented ellipse into a circle. This means the elongation might be a plotting artifact rather than a true feature of the data.

danz68.bsky.social•85 days ago

It wasn't the case here, because of the orientation, but I didn't know how the isolines shapes look. The ellipsis clearly have an angle. The "rotation" spreads the variance across both axes, so rescaling any axis will not convert the ellipse into a circle.

danz68.bsky.social•85 days ago

What I would conclude: 1. The concentric elliptical isolines might be the representation of a bivariate normal distribution. 2. The nearly constant orientation of the ellipses indicates also a linear relationship where values matter the most, in areas with high density.

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