Statistics 2 Coursework Essay Example

Statistics 2 Coursework Essay Example Statistics 2 Coursework Essay Statistics 2 Coursework Essay Essay Topic: Orlando In my coursework, I am going to investigate the correlation between the field goals attempted (FGA) and field goals made (FGM) of 50 different basketball players in NBA. It is worth to do because it will prove if the players attempt more field goals, whether he will get more points or not. Furthermore, the accuracy of shooting is dependent on many factors, such as the performance of players, home and away match, the shooting distance, the players position. To consider these factors, the percentage of field goals should be different from each NBA players. Also, it is useful to discuss whether a player will get more points if he makes more shootings in the games. Because it is necessary for the coach to know whether a reliable player will keep his accuracy on shooting even if his field goals attempted is large, and to find out whether it is easier to get points inside rather than outside in the basketball court. This is the important factor to win the match. Data Collecting The data is collected from NBA 2003 league. There are totally 476 players in NBA, and 29 teams, 65 international players from 34 countries. As I only need 50 sampling, so I choose my 50 sampling randomly from different teams. In my sampling, it contains Centre, Power Forward, Small Forward, Shooting Guard, and Point Guard. Field goals attempted (FGA) and field goals made (FGM) is recorded from the previous 60 matches including home and away in NBA 2003 season. And FGA includes 3-points FGA, and 2-points FGA, even when the players dunks or throws the basketball in the basket luckily in the last few second, it is also counted. All the data are collected by NBA staffs. Their special job is to record the data in each game. So I believe that the data are very reliable and of good quality. So, the following data are presented neatly and concisely. NBA PLAYER FGA FGM Shaquille ONeal ( Los Angeles Lakers) 848 477 Carlos Boozer ( Cleveland Cavaliers) 448 237 P.J. Brown ( New Orleans Hornets) 488 256 Radoslav Nesterovic ( Minnesota Timberwolves) 684 358 Pau Gasol ( Memphis Grizzlies) 842 440 Yao Ming ( Houston Rockets) 611 315 Brad Miller ( Indiana Pacers) 583 300 Nene Hilario ( Denver Nuggets) 491 249 Brian Grant ( Miami Heat) 535 270 Elton Brand ( Los Angeles Clippers) 754 379 Matt Harpring ( Utah Jazz) 796 397 Tim Duncan ( San Antonio Spurs) 1,098 547 Kevin Garnett ( Minnesota Timberwolves) 1,205 599 Keith Van Horn ( Philadelphia 76ers) 804 396 Calbert Cheaney ( Utah Jazz) 514 253 Richard Jefferson ( New Jersey Nets) 685 336 Bobby Jackson ( Sacramento Kings) 588 286 John Stockton ( Utah Jazz) 525 253 Kurt Thomas ( New York Knicks) 811 389 Shareef Abdur-Rahim ( Atlanta Hawks) 944 450 Rasheed Wallace ( Portland Trail Blazers) 839 395 Sam Cassell ( Milwaukee Bucks) 926 435 Jermaine ONeal ( Indiana Pacers) 992 464 Dirk Nowitzki ( Dallas Mavericks) 1,133 528 Larry Hughes ( Washington Wizards) 640 298 Michael Redd ( Milwaukee Bucks) 763 355 Chris Webber ( Sacramento Kings) 1,069 496 Antawn Jamison ( Golden State Warriors) 1,110 515 Donyell Marshall ( Chicago Bulls) 788 365 Amare Stoudemire ( Phoenix Suns) 650 301 Karl Malone ( Utah Jazz) 1,026 475 Kenyon Martin ( New Jersey Nets) 859 397 Mike Bibby ( Sacramento Kings) 520 240 Predrag Stojakovic ( Sacramento Kings) 804 371 Steve Nash ( Dallas Mavericks) 859 396 Vlade Divac ( Sacramento Kings) 554 255 Lorenzen Wright ( Memphis Grizzlies) 571 262 Kerry Kittles ( New Jersey Nets) 534 245 Tony Parker ( San Antonio Spurs) 802 367 Tracy McGrady ( Orlando Magic) 1,454 665 Drew Gooden ( Orlando Magic) 712 324 Richard Hamilton ( Detroit Pistons) 990 450 Eric Snow ( Philadelphia 76ers) 634 288 Kobe Bryant ( Los Angeles Lakers) 1,520 689 Corliss Williamson ( Detroit Pistons) 638 289 Scottie Pippen ( Portland Trail Blazers) 582 262 Juwan Howard ( Denver Nuggets) 992 446 Gary Payton ( Milwaukee Bucks) 1,197 537 Desmond Mason ( Milwaukee Bucks) 794 355 Gilbert Arenas ( Golden State Warriors) 895 398 Modelling procedures In the case of the data in my sample, there are two variables, FGA and FGM. This is an example of bivariate data, where each item in the population requires the values of two variables. The best way I can do to present these data is to plot a scatter diagram. However, I have to decide which variable is independent and which is dependent. The independent one is going to be x-axis, and the dependent one is going to be y-axis. Anyway, it is very obvious in my sample that FGA must be independent, because the player has to attempt the field goal for the field goal made in the game. So FGA is my x-axis, and FGM is my y-axis. In the examples both the variables have unpredictable values and so are random. The same is true for my sample about FGM and FGA in NBA. Both variables are random variables, free to assume any of a particular set of discrete values in a given range. The variables are uncontrolled, we cannot assume a set of predetermined values. A scatter diagram is drawn with the axis clearly and correctly labelled. It is shown as below: According to the scatter diagram, we notice that almost all the observation points can be contained within an ellipse. As the elliptical profile is narrow, so the correlation is large. Analysis In the case of the data in my sample, what we will be looking at is the correlation between two variables. This is because in using correlation we are looking at the level of association between the two variables. From the scatter diagram, it can be seen that the sample data when plotted graphically is roughly a line with positive direction. What this shows us is that there is a correlation, and there is linear correlation. As a result, Pearsons product moment correlation coefficient is the appropriate measure of correlation to use, as it is a measure of linear correlation, this technique works out the correlation between the variables. I use the Product Moment Correlation which the formula is showed below: Value Number of team(n) 50 The sum of x: 40101 The mean of x: 40101/50=802 The square of mean of x: 643236 The sum of y: 19050 The mean of y: 19050/50=381 The square of mean of y: 145161 The sum of xà ¯Ã‚ ¿Ã‚ ½: 35138525 The sum of yà ¯Ã‚ ¿Ã‚ ½: 7871876 The sum of xy: 16609313 The mean of x times the mean of y 305570 =0.98 As 0.98 is very close to +1, so we can say that this is a very strong positive correlation. The further of the analysis is to see whether or not this strong positive correlation is likely to exist for its parent population. This is because the value r, we have calculated above is merely a measure of correlation of a sample from the parent population. To see whether the sample is similar to its parent population, we work out through a hypothesis test. Hypothesis Test: I will start a 1- tail hypothesis test with 5% significant level. When the value is in 5%significant level, it means that it is the critical value, it is not acceptable, it cannot represent that there is the same situation in its parent population. Null hypothesis There is no correlation between the variables Alternative hypothesis There is positive correlation between the variables The critical values for pmcc: ( from the table) For: n=50, at 5% significant level =0.2353 The pmcc of the FGA and FGM is: r = 0.98 0.2353 As 0.98 0.2353, the critical value, alternative hypothesis is accepted. The evidence from this 50 sample is sufficient to justify the claim that there is positive correlation between FGA and FGM. Interpretation According to the modelling procedures and analysis, there are a few things that has been discovered. From the scatter diagram, we can see that there is a linear correlation between FGA and FGM. As I process the Product Moment Correlation, r is equal to 0.98, which is very close the +1, so it shows that there is a very strong positive correlation between FGA and FGM. As I have carried out the hypothesis test with 5 % significant level, it indicates that my sample is not critical, there is also a positive correlation between FGA and FGM in its parent population. The conclusion that I can draw now is FGA(field goals attempted) is a key factor of FGM(field goals made). This is also true in its parent population. The parent population is like the other basketball matches in the other countries, for example the National Cup, or Brimingham League in Britain. A player attempts more field goals, he will make more field goals, this is my conclusion from analysis. However, the data were worth collecting because now we know that there is a strong positive correlation between FGA and FGM, it indicates that a player can get more points when he keeps on shooting. It doesnt matter if he misses more shot in each game, because he can make more field goals as well. Also, it is useful for the coach to consider whether a player is still accurate on shooting when he attempts more field goals, this is the key factor to bring the winning in each game. Accuracy and refinements In my investigation I have made effort to make sure that my data is accurate as possible. I have collected my data in the number of ways: 1. collect the data which is up-to-date from a reliable source, nba.com 2. taking the sample in a random order to stop the effects of human error 3. using a large sample size(50 samples) to make sure that the sample is large enough to represent its parent population As a result, my data are in good quality. However, there ae some possible sources of error, which may have affected my data. From the scatter diagram, it shows that there are outliers in my sample, we regard these as outlier because these two sample are far awasy from the group of data. These outlier may make the correlation becomes more positive. The correlation may get closer to +1. And from my data source, they are collected from NBA league. However, I think that I can improve the data, by collecting the sample which is not only from NBA league, but also in the other countries, like Britain or China. Because NBA, the league in Britain or China are at different level, it is clear that NBA players are much better than the players in China. So ensure that FGM(field goals made) is based on FGA(field goals attempted), without considering the ability of players, the best way to do is to collect the data from more different leagues. Also, to take even more sample to ensure that the sample is really large enough to represent its parent population. Finally, the data should be collected from the professional players only, this is also the restriction. Because only the professional players can keep his accuracy from time to time. We should not collect the data from the junior basketball match, like inter-house basketball in the school, but the large league like NBA or uni versities league.