cabarrus county board of commissioners regular meeting november ...

October 17, 2011 (Regular Meeting)Page76 100.0%Then classify all parcels for the area into groups of a like interval usedwith the sale parcels. For example:TABLE OF ACTUAL FREQUENCIESFOR SALE PARCELSAGE (in years) FREQUENCY PERCENT OFINTERVAL IN NUMBER TOTAL1 - 5 128 12.26 -10 234 22.411 -15 355 33.916 -20 139 13.321 -25 87 8.326 -30 104 9.91,047 100.0%The question we really want to ask is are the two distributions the same (inthe sense that the distribution of parcels by age makes them equal forpurposes of judging similarities) or are the distributions different. Toanswer this, we must consider the element of chance. It is possible that thesales are distributed like the total area but show difference in cellfrequencies due to chance alone, for as you may observe, the percentages ofthe total by age are indeed different.We would expect the sales to be distributed in like frequencies as the totalarea was distributed unless the sales do not represent the area under study.The use of a very handy tool, the statistic tistic known as theCHI-SQUARE (X 2 )test, is worth learning. It is useful ul in that itdoes not require that onehave normally distributed data to be valid; hence it is non parametric. Itis used by taking an expected frequency and comparing it to the actual orobserved frequency. In our case, it is the area parameters projected uponthe sales data.We would expect the number of sale parcels per age group to be the same asthe frequencies observed for the total of all parcels in the hypotheticalarea under consideration. on. Therefore, we usethe percentages for the total togenerate the expected number of sales foreach age interval.The CHI-SQUARE statistic expressed as aformula is:x 2 =Σ[(fo-fe)2/fe] fe)2/fe]where fo = frequency observedfe = frequency expectedExample:EXPECTED NUMBERPERCENT OFTOTAL OF SALES INTOTAL PARCEL x SALES = EACH INTERVAL12.2 76 9.322.4 76 17.033.9 76 25.813.3 76 10.18.3 76 6.39.9 76 7.5100.0% 76.The actual number of sales in each interval is set down. One then subtractsthe estimated number from the observed number of sales, interval by interval,squaring the result and dividing by the expected number.Example:GROUP OBSERVED EXPECTED OBSERVED SQUARED DIVIDED BYFREQUENCY FREQUENCY MINUS EXPECTED RESULT EXPECTED1 10 09.3 0.70 00.49 0.0532 22 17.0 5.00 25.00 1.4713 17 25.8 8.80 77.44 3.002A-1Page 149