As a piece of Statistics coursework Essay Example

As a piece of Statistics coursework Essay As a piece of Statistics coursework, I have decided to compare two items of data, in order to prove, or disprove my theory: A countrys position in the Commonwealth games varies accordingly to that countrys population size.My theory is that a countrys position in something such as the Olympics or Commonwealth Games is proportional to that countrys population size. I say this because I believe that if a country has a large population, there will be more potential athletes to choose from.I am doing this because I would be genuinely interested in finding out whether or not this theory is true, and I believe that it is a theory that many people reading this essay would be curious in finding out. In addition, I am comparing the results from the Commonwealth Games, instead of something as renowned as the Olympic games because the Commonwealth Games are dominated by countries with very different traditions and cultures. Conversely, countries that dominate the Olympic games are countries such as France, England, or Germany, and are all countries that live a very western way of life similar to ours.In order to do the comparisons that I will need to make properly, I will use three different occasions of the Commonwealth Games, and then make an average for the number of medals awarded for each country. I will use the most recent of games 2002, 1998 and 1994. I will do this, as the data collected from these three games, will contain the data from each of the countries that enter, since in the first games in 1930, only a fraction of the countries that enter now entered. I will also use fifty different countries in order to give me a large enough sample size to make an accurate conclusion. Unfortunately though, all of the data that I will be collecting will be secondary data and not primary data as all of the data that I need is on the Internet.Firstly however, I must do a pilot test with ten samples in order to judge whether the data is suitable enough to be used.To find th is data, I went on the Internet and used an Internet search engine to find the Commonwealth Games official website. Fortunately, several answers came up, with one website having all of the data which I required. However, this data was unusable to me, as I had to sort it. Below is what the data looked like in its original form from the website www.commonwealthgames.com:CountryMedals WonGoldSilverBronzeTotalAustralia826263207Bahamas4048Bangladesh1001Barbados0011Botswana0213Cameroon91212Canada314144116Cayman Islands0011Cyprus2114England545160165Fiji1113Ghana0011Guyana1001India30221769Jamaica46717Kenya48416Lesotho0011Malaysia791834Malta0011Mauritius0011Mozambique1001Namibia1045Nauru25815New Zealand11132145Nigeria531119Northern Ireland2215Pakistan1348Samoa0123Scotland681630Singapore42713South Africa9201746St. Kitts1001St. Lucia0011Tanzania1012Trinidad ; Tobago0101Uganda0202Wales6131231Zambia1113Zimbabwe1102As you can see, all of this data is not sorted in a manner that is usable to me. S o therefore, I will sort it into descending order, using Excel, by the total number of medals awarded. Since I will not need the data for the amount of gold, silver and bronze medals awarded to each country, I will delete those columns and have merely the total number of medals.Below is the sorted data:CountryNo. Medals AwardedAustralia207England165Canada116India69South Africa46New Zealand45Malaysia34Wales31Scotland30Nigeria19Jamaica17Kenya16Nauru15Singapore13Cameroon12Bahamas8Pakistan8Namibia5Northern Ireland5Cyprus4Botswana3Fiji3Samoa3Zambia3Tanzania2Uganda2Zimbabwe2Bangladesh1Barbados1Cayman Islands1Ghana1Guyana1Lesotho1Malta1Mauritius1Mozambique1St. Kitts1St. Lucia1Trinidad ; Tobago1As you can see, all of the data that I collected contains integers, instead of decimals, since you cannot have a fraction of a medal. This is ideal considering that there will be, as a consequence, no rounding error in totalling the average amount of medals awarded to each country in the collecting o f data from three of the games.Unfortunately, I soon realised after glancing at this data, that the data that I collected does not contain the data for all of the countries that enter the Commonwealth Games. Only thirty-nine countries were mentioned although I needed at least fifty different countries in order to give me a large enough sample size, and since I knew that there were more than fifty countries that enter the Commonwealth Games.In order to get the data for all of the countries that enter, I had to go to another section of that website. However, I couldnt get all of the countries in a list, they simply gave me a listing of the countries by locality. In addition, it was impossible to copy and paste the data, so I had to type each one out individually. Below is an example of how the data was originally shown on screen:As you can see, the information was split up into six different localities Asia, Oceania, Europe, Caribbean and Americas. Once I had typed down the name of e ach country, I had all of the data that I needed. Below is a copy of the completed list of countries that I found:AnguillaAntigua BarbudaAustraliaBahamasBangladeshBarbadosBelizeBermudaBotswanaBritish Virgin IslandsBruneiCameroonCanadaCayman IslandsCook IslandsCyprusDominicaEnglandFalkland IslandsFijiGambiaGhanaGibraltarGrenadaGuernseyGuyanaIndiaIsle of ManJamaicaJerseyKenyaKiribatiLesothoMalawiMalaysiaMaldivesMaltaMauritiusMontserratMozambiqueNamibiaNauruNew ZealandNigeriaNiueNorfolk IslandsNorthern IrelandPakistanPapua New GuineaSamoaScotlandSeychellesSierra LeoneSingaporeSolomon IslandsSouth AfricaSri LankaSt HelenaSt KittsSt LuciaSt Vincent The GrenadinesSwazilandTanzaniaTongaTrinidad TobagoTurks CalcosTuvaluUgandaVanuatuWalesZambiaZimbabweInserting the missing data was easy since presumably, all of the countries that they neglected to mention, obtained no medals. In addition, the countries that are there total seventy-two, which is easily the amount of samples that I require . Regardless of the countries getting no medals, they are still valid sample units as zero is still a number.But before any comparison in this exercise can be made I must find each countrys population size. To do this, I will go on the World Factbooks website http://www.odci.gov/cia/publications/factbook/index.html that I obtained from the Internet search engine Ask Jeeves.After viewing the website, I discovered that it told me any data that I wanted for any country in the world. All I had to do was select the country that I wanted the data to be displayed for. Therefore, I searched for each of the countries individually and then recording the population in Excel to be sorted later.Below is the data that I collected from The World Factbooks website after I found the missing countries, sorted in alphabetical order:CountryPopulation (recorded in 2002)Anguilla12,446Antigua ; Barbuda67,448Australia19,546,792Bahamas300,529Bangladesh133,376,684Barbados276,607Belize262,999Bermuda63,960Bot swana1,591,232British Virgin Islands21,272Brunei350,898Cameroon16,184,748Canada31,902,268Cayman Islands36,273Cook Islands20,811Cyprus767,314Dominica70,158England49,138,831Falkland Islands2,967Fiji856,346Gambia1,455,842Ghana20,244,154Gibraltar27,714Grenada89,211Guernsey64,587Guyana698,209Hong Kong7,303,334India1,045,845,226Isle of Man76,535Jamaica2,680,029Jersey89,775Kenya31,138,735Kiribati96,335Lesotho2,207,954Malawi10,701,824Malaysia22,662,365Maldives320,165Malta397,499Mauritius1,200,206Montserrat8,437Mozambique19,607,519Namibia1,820,916Nauru12,329New Zealand3,908,037Nigeria129,934,911Niue2,134Norfolk Islands1,866Northern Ireland1,685,267Pakistan147,663,429Papua New Guinea5,172,033Samoa178,631Scotland5,062,011Seychelles80,098Sierra Leone5,614,743Singapore4,452,732Solomon Islands494,786South Africa43,647,658Sri Lanka19,576,783St Helena7,367St Kitts43054St Lucia150,157St Vincent ; The Grenadines120,519Swaziland1,123,605Tanzania37,187,939Tonga106,137Trinidad ; Tobago1,163,724Turks ; C alcos18,738Tuvalu11,146Uganda24,699,073Vanuatu196,178Wales2,903,085Zambia9,959,037Zimbabwe11,376,676Now that I have both the data for the countries population sizes and the amounts of medals awarded to them, I can test my theory in a pilot test.I will select ten different samples from the finite population that I collected using stratified random sampling. By saying random, I mean that the out coming country cannot be predicted and is chosen without conscious decision.There are many types of sampling that can be done including simple random sampling, stratified sampling, systematic sampling, cluster sampling, quota sampling, convenience sampling and opinion polls.Simple Random Sampling In this type of sampling, every sample unit within the population has an equal chance of being chosen.Stratified Sampling For this type of sampling, the population is divided into strata (categories) and then a random sample is chosen from each of the strata within the population. The size of each s ample is in proportion to the size of each stratum (category) within the population.Systematic Sampling As the name suggests, systematic sampling is where a regular pattern is devised to choose the sample. Every item in the population is listed and a starting point is chosen at random, with every nth item being selected.Cluster Sampling For cluster sampling, the population is divided into groups, or like the name suggested clusters. A random sample of groups or clusters is chosen and every item in the chosen cluster is surveyed.Quota Sampling In quota sampling, instructions are given concerning the amount (quota) of each section of the population to be sampled.Convenience Sampling Convenience sampling is by far the easiest sampling to make as it is, as the name suggests, convenient. The most convenient sample is chosen which for thirty countries, could be the first thirty countries in the list.Opinion Polls Opinion polls, as the name suggests are large-scale opinion polls that often use a combination of cluster and quota sampling.As you can see, stratified sampling is the most suited type of sampling that I can use. Stratification of sampling is necessary when the sampling frame is significantly non-homogeneous (which tends to be true of most human populations and I believe is true of this exercise). Some characteristics will be shared but most will be influenced by cultural, socio-economic, gender, religious and ethnic differences. For example, I believe that countries in the developing world (e.g. Zimbabwe, Malaysia), who do not have the benefit of the intense training that athletes in the developed world (e.g. England, Australia) endure, will not win as many medals.Firstly, I will categorise each the population into stratum. I will do this by using the method in which the Commonwealth Games website used separating each country into that countrys locality (Asia, Oceania, Europe, Caribbean and the Americas).Below are the strata that I have made:LOCALITY COUNTRYPOPULATION (2002)AmericasBelize262,999Bermuda63,960Canada31,902,268Falkland Islands2,967Guyana698,209St Helena7,367AfricaBotswana1,591,232Cameroon16,184,748Gambia1,455,842Ghana20,244,154Kenya31,138,735Lesotho2,207,954Malawi10,701,824Mauritius1,200,206Mozambique19,607,519Namibia1,820,916Nigeria129,934,911Seychelles80,098Sierra Leone5,614,743South Africa43,647,658Swaziland1,123,605Uganda24,699,073Tanzania37,187,939Zambia9,959,037Zimbabwe11,376,676AsiaBangladesh133,376,684Brunei350,898India1,045,845,226Malaysia22,662,365Maldives320,165Pakistan147,663,429Singapore4,452,732Sri Lanka19,576,783CaribbeanAnguilla12,446Antigua and Barbuda67,448Bahamas300,529Barbados276,607British Virgin Islands21,272Cayman Islands36,273Dominica70,158Grenada89,211Jamaica2,680,029Montserrat8,437St Kitts43,054St Lucia150,157St Vincent ; The Grenadines120,519Trinidad ; Tobago1,163,724Turks ; Calcos18,738EuropeEngland49,138,831Cyprus767,314Gibraltar27,714Guernsey64,587Isle of Man76,535Jersey89,775Malta397,4 99Northern Ireland1,685,267Scotland5,062,011Wales2,903,085OceaniaAustralia19,546,792Cook Islands20,811Fiji856,346Kiribati96,335Nauru12,329New Zealand3,908,037Niue2,134Norfolk Islands1,866Papua New Guinea5,172,033Samoa178,631Solomon Islands494,786Tonga106,137Tuvalu11,146Vanuata196,178Now that I have made the strata, I can now take samples from them. Before I can do this, I must determine the number of samples that will be chosen from each stratum -Samples to be taken from the Americas = ? (American Strata) x 50? (Population)= 6 x 5072= 0.083 x 50= 4.16= 4To avoid any confusion, I truncated the answer, which means that I simply cut off the decimal. This will negate any rounding errors that may occur. I will do this for each of the other strata.Now that I have determined the number of samples to be chosen from the Americas, I must use a way to decide which sample will be chosen. In order to do this, I will use the random number generator on my calculator. The random number generator ch ooses, at random, a decimal number. Then I must simply multiply that number by the number of sample units that there are within that stratum. Since if you were to get a small decimal, when you multiplied it by any integer, the answer will be less that 1 so therefore, I will add 1 to the answer. Seeing that the random number generator will only give me a number, I will have to label each of the sample units within the strata. Below are the listings that I have created for the Americas -LOCALITYCOUNTRYPOPULATION (2002)NUMBER LISTINGAmericasBelize262,9991Bermuda63,9602Canada31,902,2683Falkland Islands2,9674Guyana698,2095St Helena7,3676Now that I have created a listing for each sample unit, I will use the random number generator in order to pick a unit at random. Now I must do this four different times.1st sample unit to be chosen = (Random # x 6) + 1= (0.81 x 6) + 1= 4.86 + 1= 5.86= 52nd sample unit to be chosen = (Random # x 6) + 1= (0.112 x 6) + 1= 0.672 + 1= 1.672= 13rd sample unit to be chosen = (Random # x 6) + 1= (0.381 x 6) + 1= 2.286 + 1= 3.286= 34th sample unit to be chosen = (Random # x 6) + 1= (0.785 x 6) + 1= 4.71+ 1= 5.71= 5As you can see, 5 has appeared once already, so I must try again -4th sample unit to be chosen = (Random # x 6) + 1= (0.638 x 6) + 1= 3.828 + 1= 4.428= 4Now that I have chosen the sample units to be chosen, which are 5,1,3,4, I can now translate those numbers to the countries, Guyana, Belize, Canada and Falkland Islands.Since I have chosen the sample units that will be chosen from the Americas, I will now choose the sample units for Africa. But first, I will need to create a listing for Africa, much like I did for the Americas -LOCALITYCOUNTRYPOPULATION (2002)NUMBER LISTINGAfricaBotswana1,591,2321Cameroon16,184,7482Gambia1,455,8423Ghana20,244,1544Kenya31,138,7355Lesotho2,207,9546Malawi10,701,8247Mauritius1,200,2068Mozambique19,607,5199Namibia1,820,91610Nigeria129,934,91111Seychelles80,09812Sierra Leone5,614,74313South Africa43,647 ,65814Swaziland1,123,60515Uganda24,699,07316Tanzania37,187,93917Zambia9,959,03718Zimbabwe11,376,67619Now I will need to find out how many samples will need to be taken from this stratum -Samples to be taken from the Africa = ? (Africa Strata) x 50? (Population)= 19 x 5072= 0.2638 x 50= 13.19= 13Therefore, I will need to choose 13 different samples from the stratum -1st sample unit to be chosen = (Random # x 19) + 1= 13.319 + 1= 14.319= 142nd sample unit to be chosen = (Random # x 19) + 1= 1.387 + 1= 2.387= 23rd sample unit to be chosen = (Random # x 19) + 1= 18.131 + 1= 19.131= 194th sample unit to be chosen = (Random # x 19) + 1= 10.051 + 1= 11.051= 115th sample unit to be chosen = (Random # x 19) + 1= 8.018 + 1= 9.018= 96th sample unit to be chosen = (Random # x 19) + 1= 15.884 + 1= 16.884= 167th sample unit to be chosen = (Random # x 19) + 1= 16.562 + 1= 17.562= 178th sample unit to be chosen = (Random # x 19) + 1= 0.114 + 1= 1.114= 19th sample unit to be chosen = (Random # x 19) + 1= 2.66 + 1= 3.66= 310th sample unit to be chosen = (Random # x 19) + 1= 4.218 + 1= 5.218= 511th sample unit to be chosen = (Random # x 19) + 1= 11.628 + 1= 12.628= 1212th sample unit to be chosen = (Random # x 19) + 1= 17.043 + 1= 18.043= 1813th sample unit to be chosen = (Random # x 19) + 1= 12.065 + 1= 13.065= 13As you can see, I have chosen the four different sample units to be chosen, which translates to the countries, South Africa, Cameroon, Tanzania, Nigeria, Mozambique, Uganda, Zimbabwe, Botswana, Gambia, Kenya, Seychelles, Zambia and Sierra Leone.Now, like Africa and the Americas, I will label the different countries for Asia -LOCALITYCOUNTRYPOPULATION (2002)NUMBER LISTINGAsiaBangladesh133,376,6841Brunei350,8982India1,045,845,2263Malaysia22,662,3654Maldives320,1655Pakistan147,663,4296Singapore4,452,7327Sri Lanka19,576,7838Samples to be taken from the Asia = ? (Asia Strata) x 50? (Population)= 8 x 5072= 0.111 x 50= 5.555= 51st sample unit to be chosen = (Random # x 8) + 1 = 1.464 + 1= 2.464= 22nd sample unit to be chosen = (Random # x 8) + 1= 2.416 + 1= 3.416= 33rd sample unit to be chosen = (Random # x 8) + 1= 7.704 + 1= 8.704= 84th sample unit to be chosen = (Random # x 8) + 1= 4.632 + 1= 5.632= 55th sample unit to be chosen = (Random # x 8) + 1= 0.704 + 1= 1.704= 1These numbers translate to the countries, Brunei, India, Sri Lanka, the Maldives and Bangladesh.Now I must repeat the procedure for the Caribbean -LOCALITYCOUNTRYPOPULATION (2002)NUMBER LISTINGCaribbeanAnguilla12,4461Antigua and Barbuda67,4482Bahamas300,5293Barbados276,6074British Virgin Islands21,2725Cayman Islands36,2736Dominica70,1587Grenada89,2118Jamaica2,680,0299Montserrat8,43710St Kitts43,05411St Lucia150,15712St Vincent ; The Grenadines120,51913Trinidad ; Tobago1,163,72414Turks ; Calcos18,73815Samples to be taken from the Caribbean = ? (Caribbean Strata) x 50? (Population)= 15 x 5072= 0.208 x 50= 10.416= 101st sample unit to be chosen = (Random # x 15) + 1= 5.025 + 1= 6.025= 62nd sample unit to be chosen = (Random # x 15) + 1= 10.845 + 1= 11.845= 113rd sample unit to be chosen = (Random # x 15) + 1= 8.94 + 1= 9.94= 94th sample unit to be chosen = (Random # x 15) + 1= 11.715 + 1= 12.715= 125th sample unit to be chosen = (Random # x 15) + 1= 0.39 + 1= 4.39= 46th sample unit to be chosen = (Random # x 15) + 1= 9.135 + 1= 10.135= 107th sample unit to be chosen = (Random # x 15) + 1= 0.315 + 1= 1.315= 18th sample unit to be chosen = (Random # x 15) + 1= 7.485 + 1= 8.485= 89th sample unit to be chosen = (Random # x 15) + 1= 14.685 + 1= 15.685= 1510th sample unit to be chosen = (Random # x 15) + 1= 13.425 + 1= 14.425= 14These numbers translate to the countries, Cayman Islands, St Kitts, Montserrat, St Lucia, Barbados, Jamaica, Anguilla, Grenada, Turks ; Calcos and Trinidad ; TobagoNow I will do the same for Europe -LOCALITYCOUNTRYPOPULATION (2002)NUMBER LISTINGEuropeEngland49,138,8311Cyprus767,3142Gibraltar27,7143Guernsey64,5874Isle of Man76,5355Jersey89,7756Malta3 97,4997Northern Ireland1,685,2678Scotland5,062,0119Wales2,903,08510Samples to be taken from Europe = ? (Europe Strata) x 50? (Population)= 10 x 5072= 0.138 x 50= 6.944= 61st sample unit to be chosen = (Random # x 10) + 1= 9.83 + 1= 10.83= 102nd sample unit to be chosen = (Random # x 10) + 1= 6.26 + 1= 7.26= 73rd sample unit to be chosen = (Random # x 10) + 1= 4.18 + 1= 5.18= 54th sample unit to be chosen = (Random # x 10) + 1= 2.2 + 1= 3.2= 35th sample unit to be chosen = (Random # x 10) + 1= 5.83 + 1= 6.83= 66th sample unit to be chosen = (Random # x 10) + 1= 7.21 + 1= 8.21= 8These numbers translate to the countries, Wales, Malta, the Isle of Man and Gibraltar, Jersey and Northern Ireland.I must now repeat the procedure once more for the region of Oceania -LOCALITYCOUNTRYPOPULATION (2002)NUMBER LISTINGOceaniaAustralia19,546,7921Cook Islands20,8112Fiji856,3463Kiribati96,3354Nauru12,3295New Zealand3,908,0376Niue2,1347Norfolk Islands1,8668Papua New Guinea5,172,0339Samoa178,63110Solomo n Islands494,78611Tonga106,13712Tuvalu11,14613Vanuata196,17814Samples to be taken from Oceania = ? (Oceania Strata) x 50? (Population)= 14 x 5072= 0.194 x 50= 9.722= 91st sample unit to be chosen = (Random # x 14) + 1= 1.064 + 1= 2.064= 22nd sample unit to be chosen = (Random # x 14) + 1= 7.938 + 1= 8.938= 83rd sample unit to be chosen = (Random # x 14) + 1= 6.384 + 1= 7.384= 74th sample unit to be chosen = (Random # x 14) + 1= 13.636 + 1= 14.636= 145th sample unit to be chosen = (Random # x 14) + 1= 5.936 + 1= 6.936= 66th sample unit to be chosen = (Random # x 14) + 1= 10.64 + 1= 11.64= 117th sample unit to be chosen = (Random # x 14) + 1= 4.86 + 1= 5.86= 58th sample unit to be chosen = (Random # x 14) + 1= 12.838 + 1= 13.838= 139th sample unit to be chosen = (Random # x 14) + 1= 2.428 + 1= 3.428= 3These numbers translate to the countries, the Cook Islands, Norfolk Islands, Niue, Vanuata, New Zealand, the Solomon Islands, Nauru, Tuvalu and Fiji.I have now collected all of the sampl es that I will be using. Below is the complete listing of the countries that I have chosen through the random number generator and through stratified sampling -REGIONCOUNTRYAmericasGuyanaBelizeCanadaFalkland IslandsAfricaSouth AfricaCameroonZimbabweNigeriaMozambiqueUgandaTanzaniaBotswanaGambiaKenyaSeychellesZambiaSierra LeoneAsiaBruneiIndiaSri LankaMaldivesBangladeshCaribbeanCayman IslandsSt KittsMontserratSt LuciaBarbadosJamaicaAnguillaGrenadaTurks ; CalcosTrinidad ; TobagoEuropeWalesMaltaIsle of ManGibraltaJerseyNorthern IrelandOceanaCook IslandsNorfolk IslandsNiueVanuataNew ZealandSolomon IslandsNauruTuvaluFijiNOTE: There are 47 countries here instead of the originally intended 50. This is because of errors in truncating the number of samples to be taken.Now I shall compare each countrys population with their amount of total number of medals awarded -CountryAverage No. of Medals AwardedPopulation SizeGuyana0698,209Belize0262,999Canada10931,902,268Falkland Islands02,967South Afric a3843,647,658Cameroon816,184,748Zimbabwe411,376,676Nigeria13129,934,911Mozambique119,607,519Uganda224,699,073Tanzania237,187,939Botswana11,591,232Gambia01,455,842Kenya1631,138,735Seychelles180,098Zambia29,959,037Sierra Leone05,614,743Brunei0350,898India461,045,845,226Sri Lanka119,576,783Maldives0320,165Bangladesh0133,376,684Cayman Islands036,273St Kitts043,054Montserrat08,437St Lucia0150,157Barbados1276,607Jamaica112,680,029Anguilla012,446Grenada089,211Turks Calcos018,738Trinidad Tobago21,163,724Wales212,903,085Malta0397,499Isle of Man076,535Gibraltar027,714Jersey089,775Northern Ireland61,685,267Cook Islands020,811Norfolk Islands01,866Niue02,134Vanuata0196,178New Zealand403,908,037Solomon Islands0494,786Nauru812,329Tuvalu011,146Fiji2856,346Now I must compare this data. In order to this, I will do a scatter graph.