Goodies from Gordon: ‘distributions’, ‘d picture’, ‘correlation’–all part of ‘esci web’

I’m delighted to say we’re releasing three new goodies from Gordon Moore: distributions, d picture, and correlation. These follow his wonderful dances introduced here.

As I explained, ITNS2 will be accompanied by Bob’s data analysis software, esci, in R, and Gordon’s web-based simulations and tools, all of which are based on, and go beyond, my Excel-based ESCI. Together the web-based goodies comprise esci web, which you can open in your browser here. (Or use the ESCI menu above and choose esci web from the dropdown.) From today, esci web has four components, with perhaps two yet to come.

distributions, d picture, and correlation are visual statistical tools, developed in JavaScript. We’d love to have your feedback.

distributions: Explore normal and t distributions

See the curves, explore z scores, find areas, find critical values.

Normal distribution, z scores below, IQ scores (or whatever you choose) above.
Normal, and t distribution (df = 9). Watch the shape difference as df zooms up or down.

d picture: Explore Cohen’s d values visually

What does d = 0.2 look like? How much overlap of distributions? What about d = 0.5, 1.0, 1.5, …?

Cohen’s d = 0.5, with the area under E above mean of C shaded.

correlation: See scatterplots and eyeball r values

What do you think is the r value in each of these scatterplots?

——— Don’t read on just yet. Have an eyeball of the scatterplots. What is each r?

——— Last chance… look back up…

OK, the correlation is .3 in all cases. True, if possibly strange. (All the data sets come from a bivariate normal distribution, and in all cases the data set correlation is .3.)

Pro tip: Eyeball, or turn on, a cross through the means, as in lower right. Then eyeball the approximate comparative number of dots in (top right + lower left) quadrants and the (top left + lower right) quadrants. Correlation is a tussle between those first two (the matched quadrants) and the second two (the unmatched).

Investigate that and other cool things in correlation.

As I say, access esci web here, and please let us have your comments.



2 Comments on “Goodies from Gordon: ‘distributions’, ‘d picture’, ‘correlation’–all part of ‘esci web’

  1. Apologies if this is the wrong place for a comment. I’m a Newbie to Stats and doing OK, but cannot get the SE info from data put into ‘Normal’ Histogram in Chapter 4. If there is a better place for this issue please advise.
    Best – Joanna Meringoff

    • Joanna,
      Welcome to the fascinating world of stats–fascinating I hope you find it, and I hope our pictures and simulations help make it all make sense!
      ‘Normal’ in ESCI lets you investigate the smooth curve of the normal distribution, which you could think of as the distribution of all the infinite number of values in a population. The standard error (SE) arrives once we start sampling from that population, so play with CIjumping. Collect the dropping means into the mean heap, turn on the smooth curve on the heap, then the SE is the standard deviation of that smooth curve. See Figs 4.6 to 4.8.
      Bob and I are currently working hard on the second ed. of ITNS, which will use esci on the web (by Gordon Moore), as well as esci in jamovi (for data analysis and making cool figures) by Bob. You can start playing with either of these new goodies, at the ESCI menu at our site.
      Enjoy, and I hope you do find stats to be fascinating, as well as highly useful and important!

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