Conditioned Steps

Conditional frequency distributions of footfall wear on several wooden steps at the Simon Pearce glassworks Mill at Quechee, Vermont. The lowest of these four steps is on the left, showing a distribution of wear ranging across much of the step. The variability of footfall placement along the edge of this narrow step is great. The next step to the right in this image shows a greater concentration of wear near the middle of a slightly wider step, allowing for a more full foot placement. The next step is wider still with a concentration of wear shifting slightly to the right (downward in this image). Finally, arriving on the top step of the landing (rightmost in this image) the footfalls cause a  nearly circular pattern of wear as feet need to turn to the right (where you can see my feet standing to take the picture). This path continues ascending on the next set of stairs to an upper floor.

Left to right we see conditional frequency distributions of wear: conditioned on each step. Imagining a line connecting the means of these distributions would show a line of decreasing slope. This line is that of the conditional mean of footfall placement conditioned on each step. The changing variability of wear on each step, shows the pattern of the conditional variance: greater variance on the lower (leftmost) step and lesser variance on the higher (rightmost) step, a concept termed heteroscedasticity.