Monday, July 15, 2013

Home Advice Lacks Skewness

I recently saw this TV commercial for Home Advisor a website that helps homeowners find home improvement professionals. The homeowners then report their costs for the repairs. The site displays a symmetric bell-shaped curve to show the distribution of these costs, irrespective of the shape of their actual distribution. The image above shows that the average cost for cleaning gutters is $180 and that "most homeowners" spent between $158 and $202. These values appear to mark the locations of  the inflection points for the curve. If we assume the curve describes a normal distribution of costs, these points lie at one standard deviation above and below the mean. Indicating that the standard deviation is $22. For a normal distribution, about 68% ( the website's "most homeowners") spent within $22 of the mean of $180. The minimum cost of $90 is about 4.1 standard deviations below the mean. Its placement on the graph seems appropriate. But the maximum cost of $300 is about 5.5 standard deviations above the mean. Maximum costs for other services sometimes exceed 5 and even 6 standard deviations above the mean, but are placed symmetrically with costs at about 4 standard deviations below the mean. The symmetric graphic hides the right skewness that we should expect in almost any monetary variable that is only bounded below by zero.

It would be better to show the actual  histogram of costs perhaps with a superimposed curve like we have seen previously with GetMarketPrice or TRUEcar.

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