Gordon Does It Again: See the Correlations Dance

Here comes one more goodie from Gordon Mooredance r. This follows his wonderful dances, introduced here, and three other goodies introduced here. Have a play with dance r, the latest component in esci web. Please tell us what you think.

From dance r. Correlation in the population (grey cloud at top) is .80. The scatterplot shows also the latest sample (blue dots), size N = 30, with correlation r = .83. That r is the top value (green dot with 95% CI) in the dance picture below. Earlier sample correlations have danced down the screen and collected into the r heap. CIs that don’t capture population correlation ρ (blue line) are red.

As you may recall, 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, now including dance r, 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 five components, with one more to come.

dance r takes random samples from a bivariate normal distribution with chosen correlation ρ. As in the figure above, see the scatterplot of each sample, and also the r values from successive samples dancing down the screen. That’s the sampling variability of the correlation–and often it’s scarily large!

Playing yourself is *way* better than seeing the pic. A few things to try:

  • Watch the population cloud change for different ρ values
  • Explore the changing length and asymmetry of CIs for different r values
  • Watch the sampling distribution of correlations (the r heap) build
  • See how its skew changes with ρ
  • Investigate the capture percentage of 95% CIs
  • Study what changes, and how fast, as you change N

A key challenge for students–and researchers–is to build good intuitions about the extent of uncertainty, including the extent of sampling variability. dance r is a great arena in which to build those intuitions about correlation.

As I say, we’d love to have your feedback.

Enjoy.

Geoff

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