Amanda Johnson 22S 030 May 3 2004 Proportion Testing of USDF Award Winners INTRODUCTION Dressage is an equestrian sport that had its start 2000 years ago with classical Greek horsemanship and later developed in the Renaissance Today it is an Olympic sport where horse and rider perform a test of a prescribed series of movements of very high difficulty in an arena The test performed at the Olympic Games is the Grand Prix the test with the highest degree of difficulty Dressage is much like ballet on horseback horse and rider appear to be moving as one and dance around the arena The Grand Prix level is so difficult it takes a minimum of five years to train a horse in the Grand Prix movements The United States Dressage Federation USDF was founded in 1973 to promote dressage in the United States Today it has over 45 000 members and provides educational opportunities competitions rider and year end awards for its members The year end and rider awards are based on test percentages earned at a USDF competition This project focuses on the three major rider awards that can be earned through USDF The three major rider awards are bronze medal silver medal and gold medal USDF has various levels of dressage beginning with the basic training level levels 1 through 4 then the FEI Federation Equestrian International levels which include Prix St George Intermediare 1 and 2 and finally the highest level Grand Prix The USDF levels training through fourth are levels only shown in America and the FEI levels are those that are shown in international competitions and they are the same in every country The bronze medal is won through achievements in first level through fourth level the silver medal is won through achievements at fourth level and Prix St George and the gold medal is won through achievements at Intermediare and Grand Prix A list of all award winners can be viewed at http www usdf org Programs awards RiderAwards asp Figure 2 Silver medal caliber Figure 1 Bronze medal caliber DATA COLLECTION Lists of bronze silver and gold medal award winners were retrieved from www usdf org and compiled together into an excel file Table 1 The first column lists the riders name the second column lists the bronze third and fourth the gold Figure 3 Gold medal caliber the silver medal award Under each column a Y or N was placed depending on if that rider won that award There are people that have only won one award and some that have won all three awards Normally people will earn their bronze medal first and then their silver and gold medals as they progress through the levels It would be unusual for a rider to have solely there gold medal as it takes a lot of skill to ride at that level and they would have to be competent at the lower levels in order to be successful enough to earn the gold medal One reason a rider may only have earned their gold medal is they have not sent in their paper work to earn the silver or bronze medal Table 1 Sample of data set Name membership number James Erika T 46703 Jansen Ann 42497 Jaraczewski Kathleen A 50540 Jaskiel Brown Linda D 43 Jeffers Deri 640 Jendrowski Lynn M 14776 Jenkins Breen 50818 Jenkins Valerie L 18655 Jensen Bent 8796 Jensen Bennett Cindy 52562 Jerdeman Sharon 22179 Jerman Carol L 26425 Jewell Roxanne E 17998 Jo Cassandra 40640 Joaquin Tricia Ziebell 30026 Johansen Kay 22004 Johns Kathleen 30104 Johnson Alice A 7287 Johnson Amanda L 42779 Bronze Y Y Y Silver Y N Y Gold N N N Y N Y Y Y N Y Y Y Y Y Y Y Y N Y Y Y Y N Y N Y Y N Y N Y N Y Y Y Y N N N N Y N N N N N N N N N Y METHODOLOGY 1 Find the proportion of bronze silver gold of bronze and silver of bronze and gold and silver and gold using the proc freq feature in SAS from the data set The input from SAS is proc freq data usdfYN tables bronze silver gold chisq run 2 Create a pie chart of bronze silver and gold medal winners The SAS input will be data usdf input type count datalines G 416 S 1667 B 2858 run 3 Carry out a significance test for a proportion Find if more than 80 of the population is a not gold medal winner Ho 80 of the population are not gold medal winners Ha More than 80 of the population are not gold medal winners Ho p 0 8 Ha p 0 8 This is tested by the Z statistic z p po po 1 po n The SAS input will be proc freq data usdfYN tables gold binomial p 0 8 run 4 Find a 99 confidence interval for the proportion of Gold medal winners Find the 99 confidence interval for silver and bronze medal winners for comparison The approximate level C confidence interval for p is p z p 1 p n The SAS input for the variable gold is proc freq data usdfYN tables gold binomial alpha 01 run RESULTS From the data below there are 2858 people who won the bronze medal 1667 people who won the silver medal and 416 people won the gold with a total of 3364 people receiving awards There are 51 people who only received their gold medal 393 people who only received their silver and 1635 people who only received their bronze medal These numbers show that it is more difficult to receive the gold medal than the bronze This is very plausible considering the amount of time it takes to get the horse trained to the Grand Prix level I have earned my bronze silver and gold medal as shown in Table 1 bottom of the list The proportion of people that have won their bronze medal would be 8 68 Table 2 shows the numbers in a more readable format Table 2 Awards Awards Won Bronze Silver Gold Bronze Silver Bronze Gold Silver Gold Bronze Silver Gold Number of People who won award 292 920 11 62 1635 393 51 Proportion 8 68 27 35 0 327 1 84 48 6 11 68 1 52 The FREQ Procedure Table 1 of Silver by Gold Controlling for Bronze N Silver Silver Gold Gold Frequency Percent Row Pct Col Pct N Y Total N 0 51 51 0 00 10 08 10 08 0 00 100 00 0 00 45 13 Y 393 62 455 77 67 12 25 89 92 86 37 13 63 100 00 54 87 Total 393 113 506 77 67 22 33 100 00 Statistics for Table 1 of Silver by Gold Controlling for Bronze N Statistic DF Value Prob Chi Square 1 197 2529 0001 Likelihood Ratio Chi Square 1 175 1595 0001 Continuity Adj Chi Square 1 192 3045 0001 Mantel Haenszel Chi Square 1 196 8631 0001 Phi Coefficient 0 6244 Contingency Coefficient 0 5296 Cramer s V 0 6244 …