# Measurement Variations in Home Sales

Last week, the National Association of REALTORS® reported that homes sold at a 5.55 million unit pace in September and that this was 4.7 percent above the August sales pace and 8.8 percent above the September 2014 sales pace. This figure is seasonally adjusted—to account for fewer sales in winter months like January and greater sales in summer months like June—and at an annual pace—meaning we multiply the resulting number by 12 so that it can easily be compared with the total figure for the year. For example, in 2014, there were 4.94 million homes sold in the calendar year, so we know that this September’s pace is better than 2014

Along with the Seasonally Adjusted Annual Rate data, we also produce an estimate of unadjusted sales. In September 2015, we reported that there were 471,000 home sales across the United States, a figure that was 8.0 percent higher than September 2014 and 6.5 percent lower than August 2015. You’ll notice that the measured increase from September 2014 to September 2015 differs depending on whether we use the adjusted or unadjusted data (8.8 percent versus 8.0 percent). This is mainly because the seasonal adjustment process can result in slightly different seasonal factors from year to year.

So is the 471,000 unadjusted home sales we reported the actual number of homes that sold in September? No; the unadjusted home sales we reported are the best estimate of home sales given our data collection methodology and reporting process. This is a very good estimate of the number of homes sold in the US in September 2015, but like all estimates, it is subject to variation and error.

What are sources of variation in the data? First, there is the issue of rounding. When we report 471,000 home sales, this is a rounded estimate from our data collection process and could mean that the raw number was as low as 470,500 or as high as 471,499. The variation from rounding gives a differential of roughly a quarter percentage point and could sway a growth rate by up to 0.5 percent.

Another source of variation in the home sales data is the sample. While we collect data from hundreds of MLSs and local associations across the country, we only use data from roughly 200 of the most regular data reporters in the panel used to construct the monthly estimates. These reporters account for roughly 40 percent of home sales across the country. If our panel markets have sales trends that mirror the markets in non-panel areas, our estimate will be a solid reflection of the entire market. Alternately, if our panel data varies from non-panel data areas in random ways, our data will be too high some months and too low other months, yet it should be roughly consistent with the entire market over time.

Assuming random sampling error in our sample, the best estimate of a 95 percent confidence interval around the monthly existing home sales estimate is plus or minus 4 percent. When we report 471,000 sales in September, the 95 percent confidence interval for the count of home sales in September is in the range of 452,000 to 490,000 (452,160 to 489,840 before rounding. More generally, in repeated random samples of home sales, the confidence interval would contain the true count of home sales 95 percent of the time). This also means that we can be quite certain that sales in September 2015 were higher than sales in September 2014, and the true rate of increase likely fell between 3.7 percent and 12.4 percent.

If you look, you’ll find confidence intervals around all kinds of data. They don’t often garner much attention, but they provide useful information. One reason why analysts sometime focus more on building permits than on housing starts or completions as an indicator of construction is that the building permits survey has a much narrower confidence interval than either of the other two construction indicators.

 Monthly Change in Recent Point Estimate Confidence Interval Source New Home Sales -11.5% +/- 11.3%* https://www.census.gov/construction/nrs/pdf/newressales.pdf Total Nonfarm Employment +142,000 +/- 105,000* http://www.bls.gov/news.release/empsit.tn.htmhttp://www.bls.gov/news.release/empsit.nr0.htm Unemployment Rate +0.0% +/- 0.2%* http://www.bls.gov/news.release/empsit.tn.htmhttp://www.bls.gov/news.release/empsit.nr0.htm Building Permits +5.0% +/- 1.4%* http://www.census.gov/construction/nrc/pdf/newresconst.pdf Housing Starts +6.5% +/- 16.4%* http://www.census.gov/construction/nrc/pdf/newresconst.pdf Housing Completions +7.5% +/- 13.6%* http://www.census.gov/construction/nrc/pdf/newresconst.pdf

*Indicates 90 percent confidence interval

### Danielle Hale, Director of Housing Statistics

As a Research Economist at NAR, Danielle studies tax issues, the wealth impact of home ownership, and different measures of home prices.