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Jim Plante wrote:Hey, Rhonda!
You need to blow fifty bucks on AI's new book: An Introduction to Statistics for Appraisers by Marvin L. Wolverton, PhD, MAI. (The rest of you could make good use of this book too.) This guy is both an appraiser and a professional educator. Good example: Why be suspicious of Excel's R-square? Well, if your data are linear, and the QQ plot shows that they're linear, using the Pearson's Product-Moment correlation is accurate. But if your data are non-linear, you should be using the Spearman's Rho calculation to determine the correlation. You square the correlation coefficient to get the R-square. (Which correlation is Excel calculating?) Pearson's will always underestimate correlation for non-linear data. After about three chapters of this book, you'll fully understand what I just wrote--and you'll know why it's true, and you'll be able to write down the formulae on a legal pad and calculate these values by hand.
Buy the book, work through it chapter by chapter, answer the quiz questions at the end of each chapter. Re-read until you've got it. Then move on to the next chapter. And note that Excel isn't totally useless. In fact, the author gives good examples of doing these calculations using Excel. When you've finished, you'll be using Excel functions you've never used before: STDEV, STDEVP, VAR, VARP, finding the coefficient of variation (STDEV/AVERAGE), and on and on and on.
Until I started reading this book, I would gather my data, make a new column for $/sqft GLA, and take the MIN, MAX, MED, and STDEV of these. I would then eliminate any sales whose sale price/sqft was more than one standard deviation from the mean in order to show a general trend. As the book shows, this is incorrect. To eliminate the fringes and just examine the central trend, one should use the interquartile range instead of mean-plus-or-minus-1stdev.
The reason is obvious once you've read the book (or applied a couple of brain cells to the problem). Interquartile range is calculated like a median. To find the median, you sort the prices and pick the middle one. Now take each half of the data and find the median of that. Now you've got four "quarters," called "quartiles" in statistics. Use the data points contained within quartiles 2 and 3, and you have a good representation of the central trend of the data; this is called the "interquartile range." It is defined from the first data point in Quartile 2 to the last data point in Quartile 3.
Here's why that works: Assume your sales are mostly of houses less than $100K. There are several that are over $100K and extending to $350K, but most of them are under. If we take the mean (a.k.a. Average) of these sales, it might fall, for example at $140K with a big STDEV. Subtracting and adding the STDEV to/from the mean is going to give you properties which mostly favor the high side of the range, because of where the mean falls. But if you use the interquartile range, you'll be working with the middle 50% of your data, which is usually what you want when you're trying to discern general trends.
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