Have you ever found yourself using the Smart Tile function within the Tile Tool, but don't completely understand how the tiles are calculated? While the function itself may seem a bit "black box", we actually have a pretty standard formula for calculating the tile values. Some clients have mentioned that it incorporates a z-score, but this is untrue. Our actual formula is (range * std dev) + mean.
As with all of our tools, the Help File is the best start for understanding the functionality of the Smart Tile. In this case, the help states the Smart Tile function as the tiles being based on just the standard deviation and average. The tile value represents the mean of the data range. The tile numbers explain the range directly (and are used as the data points for starting). Take the following table:
| Tile | Range |
| 0 | -0.5 to 0.5 |
| -1 | -1.5 to -0.5 |
| 1 | 0.5 to 1.5 |
The above states the ranges for a given set of data. In the case of the example, the standard deviation of DEN90 for a random sample of geographies is 1083.50499 and the mean is 171.396371 (I'm rounding off those numbers). With this information, we determine the ranges of the field DEN90 as follows (I blew it out to 5 ranges in the attached example):
| Tile Number | Low Range | High Range |
| -1 | (1083.50433 * -1.5) + 171.396371 = -1453.861114 | (1083.50433 * -0.5) + 171.396371 = -370.355794 |
| 0 | (1083.50433 * -0.5) + 171.396371 = -370.355794 | (1083.50433 * 0.5) + 171.396371 = 713.148536 |
| 1 | (1083.50433 * 0.5) + 171.396371 = 713.148536 | (1083.50433 * 1.5) + 171.396371 = 1796.652866 |
Because of the functionality of the smart tile, the tile numbers can increase as well. If you look at the Tile Tool, you can actually select to Output Verbose Name Field, where the output name displays a rounded range the value fits in. This can be especially helpful when viewing your smart tile data.
Finally, I have attached a module that displays the Tile Tool using the Smart Tile function, then a group of other tools replicating the same smart tile function with the same results.
I hope this helps clear up any questions in regards to the Smart Tile. Until next time!
- Chad
Follow me on Twitter! @AlteryxChad
