Monday, January 25, 2010

Poughkeepsie Journal Commits Roundoff Error — Again

This is the second of three blog posts on the Poughkeepsie Journal's January 11 feature story Most cities, towns cut spending, raise taxes to balance the books by reporter John Davis.  That story contained a tax table and sidebar (in the print edition only, unfortunately) with mistakes in each of these three steps:
  1. Get accurate data.
  2. Determine the correct way to analyze the data.
  3. Do the arithmetic correctly.
My first blog post, Poughkeepsie Journal's Incorrect Tax Rate Analysis, discussed a serious error in Item 2 — Determining the correct way to analyze the data.  This post discusses a mistake in Item 3 — Doing the arithmetic correctly.  A third post on Item 1 — Getting accurate data — is in preparation.

Round-Off Error

The last column of the story's tax table lists the percent change in the tax rate of Towns and Cities from 2009 to 2010.  The percent change in the tax rate is the key measure of whether taxpayers' property is being taxed at a higher or lower rate, and by how much.  For example, in the Town of Fishkill, the Poughkeepsie Journal's story lists the tax rate increase as 4.13 percent.  Unfortunately, this figure is inaccurate because the Poughkeepsie Journal calculated the tax rate increase using the rounded tax rates of $1.21 and $1.26 per thousand for 2009 and 2010.  If they'd used the more precise tax rates of $1.213139 and $1.260599 per thousand — the rates used to compute individual tax bills, they would have found the tax rate increase for the Town of Fishkill to be “only” 3.91 percent.  The small difference between 4.13 and 3.91 probably matters to Fishkill government officials, who might prefer to say that the tax increase is “only 3.9 percent”, rather than “over 4 percent”.

Round-off errors like this appear not just for the Town of Fishkill, but appear systematically for every one of the 25 towns and cities in the story's table.  The round-off errors are random in direction, and can just as well understate the tax rate increase as overstate it.

Last Two Significant Figures are Garbage

Another way to characterize the Poughkeepsie Journal's mistake is to say that the table displayed more significant figures for tax rate changes than can be supported by their input data.  The table displayed tax rate changes to one hundredth of a percent, while the accuracy of the tax rates only supports tax rate changes to the nearest percent.  In other words, the last two digits in the table's display of tax rate change are garbage.

This Is Not the First Time

This is not the first time the Poughkeepsie Journal has used rounded tax rates to calculate inaccurate tax rate changes, and not the first time I've written about it.  On December 11 — one month to the day before the towns-and-cities story — the Journal published a story on the Dutchess County tax rate stating that the tax rate increase was 14.6 percent, when it was actually 14.3 percent.  Reporter Jenny Lee-Adrian confirmed that her calculation used rounded tax rates.  My post Poughkeepsie Journal Gets It Almost Right discussed the problem of using rounded tax rates, and described two ways the mistake could be avoided in the future.

Restricted Contact with Poughkeepsie Journal

Every tax rate change listed in the Journal's table is consistent with the interpretation that it was calculated using the rounded tax rates displayed in the table.  However, I haven't been able to confirm with the Journal exactly what they did.  As noted in my previous post, Poughkeepsie Journal management stands by their figures, and has denied my request to speak with whoever prepared the story's tax table.  Without direct confirmation, there is always the risk that my interpretation of the Poughkeepsie Journal's table is incorrect.  I'm frankly surprised and disappointed that the Poughkeepsie Journal would choose such an oppositional response.  I would have much preferred a collaborative dialog in which all parties focus on how best to inform property taxpayers and residents about tax issues.

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